## Reconstruction of sectional images in frequency-domain based photoacoustic imaging |

Optics Express, Vol. 19, Issue 23, pp. 23286-23297 (2011)

http://dx.doi.org/10.1364/OE.19.023286

Acrobat PDF (2768 KB)

### Abstract

Photoacoustic (PA) imaging is based upon the generation of an ultrasound pulse arising from subsurface tissue absorption due to pulsed laser excitation, and measurement of its surface time-of-arrival. Expensive and bulky pulsed lasers with high peak fluence powers may provide shortcomings for applications of PA imaging in medicine and biology. These limitations may be overcome with the frequency-domain PA measurements, which employ modulated rather than pulsed light to generate the acoustic wave. In this contribution, we model the single modulation frequency based PA pressures on the measurement plane through the diffraction approximation and then employ a convolution approach to reconstruct the sectional image slices. The results demonstrate that the proposed method with appropriate data post-processing is capable of recovering sectional images while suppressing the defocused noise resulting from the other sections.

© 2011 OSA

## 1. Introduction

1. X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Non-invasive laser-induced photoacoustic tomography for structural and functional imaging of the brain in vivo,” Nat. Biotechnol. **21**(7), 803–806 (2003). [CrossRef] [PubMed]

7. B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A **26**(2), 443–455 (2009). [CrossRef] [PubMed]

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

9. B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. **15**(2), 021314 (2010). [CrossRef] [PubMed]

10. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am. **123**(5), 2577–2590 (2008). [CrossRef] [PubMed]

11. A. Petschke and P. J. La Rivière, “Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications,” Biomed. Opt. Express **1**(4), 1188–1195 (2010). [CrossRef] [PubMed]

12. K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser,” J. Biomed. Opt. **13**(2), 024006 (2008). [CrossRef] [PubMed]

12. K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser,” J. Biomed. Opt. **13**(2), 024006 (2008). [CrossRef] [PubMed]

13. U. Schnars and W. P. O. Jutner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. **13**(9), R85–R101 (2002). [CrossRef]

15. E. Y. Lam, X. Zhang, H. Vo, T. C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. **48**(34), H113–H119 (2009). [CrossRef] [PubMed]

## 2. Methods

### 2.1 Photoacoustic wave equation

### 2.2 Light propagation in scattering media

18. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. **28**(12), 2331–2336 (1989). [CrossRef] [PubMed]

19. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. **195**(2), 330–351 (1991). [CrossRef] [PubMed]

20. F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. **187**(2), 597–619 (2003). [CrossRef]

### 2.3 Reconstruction of sectional images by the convolution approach

13. U. Schnars and W. P. O. Jutner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. **13**(9), R85–R101 (2002). [CrossRef]

12. K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser,” J. Biomed. Opt. **13**(2), 024006 (2008). [CrossRef] [PubMed]

### 2.4 Data post-processing

_{,}as shown in Fig. 1 . A reconstruction of this sectional image requires recovering

## 3. Numerical simulations

^{3}domain. The slab tissue was modeled as homogeneous with the following values: absorption coefficient

^{−1}; reduced scattering coefficient

^{−1}; reflection coefficient of 0.433 on the top surface and 0 on all other surfaces. While more complicated and informative sources such as patterned modulated incident light could be used, a homogeneously distributed area source modulated at 50MHz was simulated to illuminate the top surface of the chosen domain. Figure 3 shows the calculated complex photon fluence at the excitation wavelength of 785 nm as a function of depth, computed using finite element method. We can see from Fig. 3 that the amplitude of the complex photon fluence decreases exponentially and its phase increases slowly with respect to the depth. When compared to the acoustic wave phase delay shown below, the initial phase value of the induced PA wave can be assumed to be zero. For the pressure wave measurements, the slab tissue and the acoustic transducer are immersed in water and the distance between the top surface of the slab tissue and the measurement plane is 4.0 cm, as shown in Fig. 1.

^{−1}). For these numerical simulations, the coefficient

*en face*images (a gray-scale plot of adding all the reconstructed sectional images) are shown in Fig. 8 , from which we can see that optical absorption coefficients of blood vessels have been reconstructed properly.

21. P. Baluk, J. Fuxe, H. Hashizume, T. Romano, E. Lashnits, S. Butz, D. Vestweber, M. Corada, C. Molendini, E. Dejana, and D. M. McDonald, “Functionally specialized junctions between endothelial cells of lymphatic vessels,” J. Exp. Med. **204**(10), 2349–2362 (2007). [CrossRef] [PubMed]

22. J. C. Rasmussen, I. C. Tan, M. V. Marshall, C. E. Fife, and E. M. Sevick-Muraca, “Lymphatic imaging in humans with near-infrared fluorescence,” Curr. Opin. Biotechnol. **20**(1), 74–82 (2009). [CrossRef] [PubMed]

23. C. Kim, K. H. Song, F. Gao, and L. V. Wang, “Sentinel lymph nodes and lymphatic vessels: noninvasive dual-modality in vivo mapping by using indocyanine green in rats--volumetric spectroscopic photoacoustic imaging and planar fluorescence imaging,” Radiology **255**(2), 442–450 (2010). [CrossRef] [PubMed]

^{−1}located at 4.8 cm and lymphatic vessels with

^{−1}located at 4.9 cm, respectively. Their corresponding profiles through

*en face*images are shown in Fig. 10 , from which we can see that both the blood vessels and lymphatic vessels were reconstructed simultaneously. Similar simulation results can be obtained under other modulation frequencies.

## 4. Discussion

10. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am. **123**(5), 2577–2590 (2008). [CrossRef] [PubMed]

^{2}/s and the speed of light in tissue is on the order of 2 x10

^{8}m/s, the calculated ratios of the photonic to the thermal and acoustic wave numbers are small and it follows that the thermal subsystem has little effects on the measurements [10

10. N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am. **123**(5), 2577–2590 (2008). [CrossRef] [PubMed]

24. A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. **220**(1), 441–470 (2006). [CrossRef]

25. Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. **55**(16), 4625–4645 (2010). [CrossRef] [PubMed]

26. H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. **55**(4), 947–962 (2010). [CrossRef] [PubMed]

*z*direction and thus this technique is suitable for imaging the shape of tissue of object. If the blood vessels overlap along

14. X. Zhang, E. Y. Lam, and T. C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express **16**(22), 17215–17226 (2008). [CrossRef] [PubMed]

15. E. Y. Lam, X. Zhang, H. Vo, T. C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. **48**(34), H113–H119 (2009). [CrossRef] [PubMed]

27. X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A **27**(7), 1630–1637 (2010). [CrossRef] [PubMed]

## References and Links

1. | X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Non-invasive laser-induced photoacoustic tomography for structural and functional imaging of the brain in vivo,” Nat. Biotechnol. |

2. | H. P. Brecht, R. Su, M. Fronheiser, S. A. Ermilov, A. Conjusteau, and A. A. Oraevsky, “Whole-body three-dimensional opto-acoustic tomography system for small animals,” J. Biomed. Opt. |

3. | D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics |

4. | Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol. |

5. | L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys. |

6. | L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics |

7. | B. T. Cox, S. R. Arridge, and P. C. Beard, “Estimating chromophore distributions from multiwavelength photoacoustic images,” J. Opt. Soc. Am. A |

8. | L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron. |

9. | B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt. |

10. | N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am. |

11. | A. Petschke and P. J. La Rivière, “Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications,” Biomed. Opt. Express |

12. | K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser,” J. Biomed. Opt. |

13. | U. Schnars and W. P. O. Jutner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. |

14. | X. Zhang, E. Y. Lam, and T. C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express |

15. | E. Y. Lam, X. Zhang, H. Vo, T. C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. |

16. | Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett. |

17. | Z. Yuan, Q. Wang, and H. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media by photoacoustic tomography coupled with diffusion equation based regularized Newton method,” Opt. Express |

18. | M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. |

19. | E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. |

20. | F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. |

21. | P. Baluk, J. Fuxe, H. Hashizume, T. Romano, E. Lashnits, S. Butz, D. Vestweber, M. Corada, C. Molendini, E. Dejana, and D. M. McDonald, “Functionally specialized junctions between endothelial cells of lymphatic vessels,” J. Exp. Med. |

22. | J. C. Rasmussen, I. C. Tan, M. V. Marshall, C. E. Fife, and E. M. Sevick-Muraca, “Lymphatic imaging in humans with near-infrared fluorescence,” Curr. Opin. Biotechnol. |

23. | C. Kim, K. H. Song, F. Gao, and L. V. Wang, “Sentinel lymph nodes and lymphatic vessels: noninvasive dual-modality in vivo mapping by using indocyanine green in rats--volumetric spectroscopic photoacoustic imaging and planar fluorescence imaging,” Radiology |

24. | A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. |

25. | Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. |

26. | H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol. |

27. | X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A |

**OCIS Codes**

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.5120) Medical optics and biotechnology : Photoacoustic imaging

(170.6960) Medical optics and biotechnology : Tomography

(170.2655) Medical optics and biotechnology : Functional monitoring and imaging

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: September 14, 2011

Revised Manuscript: October 4, 2011

Manuscript Accepted: October 5, 2011

Published: November 1, 2011

**Virtual Issues**

Vol. 7, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Banghe Zhu and Eva M. Sevick-Muraca, "Reconstruction of sectional images in frequency-domain based photoacoustic imaging," Opt. Express **19**, 23286-23297 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-23-23286

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### References

- X. Wang, Y. Pang, G. Ku, X. Xie, G. Stoica, and L. V. Wang, “Non-invasive laser-induced photoacoustic tomography for structural and functional imaging of the brain in vivo,” Nat. Biotechnol.21(7), 803–806 (2003). [CrossRef] [PubMed]
- H. P. Brecht, R. Su, M. Fronheiser, S. A. Ermilov, A. Conjusteau, and A. A. Oraevsky, “Whole-body three-dimensional opto-acoustic tomography system for small animals,” J. Biomed. Opt.14(6), 064007 (2009). [CrossRef] [PubMed]
- D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3(7), 412–417 (2009). [CrossRef]
- Y. Sun and H. Jiang, “Quantitative three-dimensional photoacoustic tomography of the finger joints: phantom studies in a spherical scanning geometry,” Phys. Med. Biol.54(18), 5457–5467 (2009). [CrossRef] [PubMed]
- L. V. Wang, “Prospects of photoacoustic tomography,” Med. Phys.35(12), 5758–5767 (2008). [CrossRef] [PubMed]
- L. V. Wang, “Multiscale photoacoustic microscopy and computed tomography,” Nat. Photonics3(9), 503–509 (2009). [CrossRef] [PubMed]
- 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]
- L. V. Wang, “Tutorial on photoacoustic microscopy and computed tomography,” IEEE J. Sel. Top. Quantum Electron.14(1), 171–179 (2008). [CrossRef]
- B. E. Treeby and B. T. Cox, “k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields,” J. Biomed. Opt.15(2), 021314 (2010). [CrossRef] [PubMed]
- N. Baddour, “Theory and analysis of frequency-domain photoacoustic tomography,” J. Acoust. Soc. Am.123(5), 2577–2590 (2008). [CrossRef] [PubMed]
- A. Petschke and P. J. La Rivière, “Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications,” Biomed. Opt. Express1(4), 1188–1195 (2010). [CrossRef] [PubMed]
- K. Maslov and L. V. Wang, “Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser,” J. Biomed. Opt.13(2), 024006 (2008). [CrossRef] [PubMed]
- U. Schnars and W. P. O. Jutner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol.13(9), R85–R101 (2002). [CrossRef]
- X. Zhang, E. Y. Lam, and T. C. Poon, “Reconstruction of sectional images in holography using inverse imaging,” Opt. Express16(22), 17215–17226 (2008). [CrossRef] [PubMed]
- E. Y. Lam, X. Zhang, H. Vo, T. C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt.48(34), H113–H119 (2009). [CrossRef] [PubMed]
- Z. Yuan, C. Wu, H. Zhao, and H. Jiang, “Imaging of small nanoparticle-containing objects by finite-element-based photoacoustic tomography,” Opt. Lett.30(22), 3054–3056 (2005). [CrossRef] [PubMed]
- Z. Yuan, Q. Wang, and H. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media by photoacoustic tomography coupled with diffusion equation based regularized Newton method,” Opt. Express15(26), 18076–18081 (2007). [CrossRef] [PubMed]
- M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt.28(12), 2331–2336 (1989). [CrossRef] [PubMed]
- E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem.195(2), 330–351 (1991). [CrossRef] [PubMed]
- F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys.187(2), 597–619 (2003). [CrossRef]
- P. Baluk, J. Fuxe, H. Hashizume, T. Romano, E. Lashnits, S. Butz, D. Vestweber, M. Corada, C. Molendini, E. Dejana, and D. M. McDonald, “Functionally specialized junctions between endothelial cells of lymphatic vessels,” J. Exp. Med.204(10), 2349–2362 (2007). [CrossRef] [PubMed]
- J. C. Rasmussen, I. C. Tan, M. V. Marshall, C. E. Fife, and E. M. Sevick-Muraca, “Lymphatic imaging in humans with near-infrared fluorescence,” Curr. Opin. Biotechnol.20(1), 74–82 (2009). [CrossRef] [PubMed]
- C. Kim, K. H. Song, F. Gao, and L. V. Wang, “Sentinel lymph nodes and lymphatic vessels: noninvasive dual-modality in vivo mapping by using indocyanine green in rats--volumetric spectroscopic photoacoustic imaging and planar fluorescence imaging,” Radiology255(2), 442–450 (2010). [CrossRef] [PubMed]
- A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006). [CrossRef]
- Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55(16), 4625–4645 (2010). [CrossRef] [PubMed]
- H. Shen and G. Wang, “A tetrahedron-based inhomogeneous Monte Carlo optical simulator,” Phys. Med. Biol.55(4), 947–962 (2010). [CrossRef] [PubMed]
- X. Zhang and E. Y. Lam, “Edge-preserving sectional image reconstruction in optical scanning holography,” J. Opt. Soc. Am. A27(7), 1630–1637 (2010). [CrossRef] [PubMed]

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