## Iterative algorithm for multiple illumination photoacoustic tomography (MIPAT) using ultrasound channel data |

Biomedical Optics Express, Vol. 3, Issue 12, pp. 3240-3249 (2012)

http://dx.doi.org/10.1364/BOE.3.003240

Acrobat PDF (1255 KB)

### 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

## 1. Introduction

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

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]

4. 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]

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

6. 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]

9. B. Banerjee, S. Bagchi, R. M. Vasu, and D. Roy, “Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map,” J. Opt. Soc. Am. A **25**(9), 2347–2356 (2008). [CrossRef] [PubMed]

10. 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]

11. 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]

12. 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]

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

*a priori*information on the form of the coefficients stably.

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]

## 2. Theory

### 2.1. Light propagation model

*q*is the photon density source strength and

*c*is light speed in the medium.

*D*is the diffusion coefficient, which is defined as a function of optical properties by

### 2.2. Reconstruction of the optical properties with ultrasound channel data

*M*ultrasound transducers and

*S*illumination patterns. If each detector acquires

*T*time points at a given sampling frequency, a column vector of observed pressure measurements may be constructed aswhere

*i*, due to source

*k*. The composite index

*TMS*× 1. For an

*N*×

*N*2D grid of optical properties,

^{2}× 1. Jacobian matrices have dimensions

*TMS ×*2

*N*

^{2}. These matrices can be quite large. The Hessian

**H**of size 2

*N*

^{2}× 2

*N*

^{2}has quadrant symmetry, reducing memory requirements. With the above notation, the

*N*

^{2}vector given as

*k*,

*N*

^{2}× 2

*N*

^{2}matrix and for a given

^{2}× 1 column vector. The Jacobian needs not to be stored, but calculated row by row to find

### 2.3. Inversion

*i*iteration, we minimize the following cost functionFor any vector

^{th}**W**is a 2-dimensional regularization operator matrix or weighting matrix. Here we use the second order derivatives as a smoothing weighting factor. For each iteration, the least-squares minimum solution is found with

## 3. Numerical simulation

^{−1}everywhere except a scattering perturbation of 1 cm

^{−1}. The background absorption coefficient is taken as

^{−1}, with two regions of 10% perturbation. We use 4 illumination sources and an array of 64 ultrasound point detectors distributed 1 cm away from the object (16 on each side of the object). The optical sources are placed 3 mm away from the object to validate the light transport model in the diffusion regime. Modeling incident light as isotropic point sources is equivalent to the pencil beam interrogation that may be used experimentally, by the similarity principle [16]. Keeping these sources far from the simulation area ensures that the diffusion approximation will hold. We sample pressure signals generated by photoacoustic effects with a temporal sampling frequency of 15MHz. The transducer electromechanical response

*D*and

*μ*distributions are faithfully recovered with the proposed method. Generally

_{a}*μ*is better recovered than scattering features. This supports conclusions by other researchers [17]. We believe this is due to stronger dependence of photoacoustic signals on optical absorption. This is also confirmed with faster convergence of optical absorption, as is shown in Fig. 4 . A single iteration provides a reasonable first estimate of both

_{a}*μ*and

_{a}*D*. Additional iterations improve absorption distribution estimates in particular, however, diffusion coefficient begins diverging and this becomes appreciable after 10 iterations. The inclusion in the images of the diffusion coefficient initially have an erroneously low value then iterations improve this mean value, however, successive iterations are sensitive to noise amplification resulting in an overall diverging trend. By simulation and experimental work, Jetzfellner et al. [11

11. 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]

*a priori*information on the imaged object may be necessary. Our simulation showcased improved convergence in absorption distributions, albeit with simulated data. Future work is needed to stabilize diffusion coefficient reconstructions to mitigate iteration-to-iteration noise amplification. As a comparison, we also show results with the ratiometric method described previously in [15

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]

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]

## 4. Conclusions and discussion

## Acknowledgments

## References and links

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

2. | 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. |

3. | Z. Guo, C. Li, L. Song, and L. V. Wang, “Compressed sensing in photoacoustic tomography in vivo,” J. Biomed. Opt. |

4. | B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. |

5. | G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl. |

6. | 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. |

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

8. | J. Ripoll and V. Ntziachristos, “Quantitative point source photoacoustic inversion formulas for scattering and absorbing media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

9. | B. Banerjee, S. Bagchi, R. M. Vasu, and D. Roy, “Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map,” J. Opt. Soc. Am. A |

10. | 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. |

11. | 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. |

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

13. | G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl. |

14. | R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt. |

15. | P. Shao, B. Cox, and R. J. Zemp, “Estimating optical absorption, scattering, and Grueneisen distributions with multiple-illumination photoacoustic tomography,” Appl. Opt. |

16. | L. V. Wang and H.-I. Wu, |

17. | B. Cox, T. Tarvainen, and S. Arridge, in |

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

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.3010) Image processing : Image reconstruction techniques

**ToC Category:**

Image Reconstruction and Inverse Problems

**History**

Original Manuscript: July 23, 2012

Revised Manuscript: September 25, 2012

Manuscript Accepted: September 25, 2012

Published: November 13, 2012

**Citation**

Peng Shao, Tyler Harrison, and Roger J. Zemp, "Iterative algorithm for multiple illumination photoacoustic tomography (MIPAT) using ultrasound channel data," Biomed. Opt. Express **3**, 3240-3249 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-12-3240

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### References

- 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]
- 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]
- G. Bal and K. Ren, “Multi-source quantitative photoacoustic tomography in a diffusive regime,” Inverse Probl.27(7), 075003 (2011). [CrossRef]
- 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).
- 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]
- B. Banerjee, S. Bagchi, R. M. Vasu, and D. Roy, “Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map,” J. Opt. Soc. Am. A25(9), 2347–2356 (2008). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- G. Bal and K. Ren, “On multi-spectral quantitative photoacoustic tomography in diffusive regime,” Inverse Probl.28(2), 025010 (2012). [CrossRef]
- R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt.49(18), 3566–3572 (2010). [CrossRef] [PubMed]
- 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]
- 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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