## Correcting photoacoustic signals for fluence variations using acousto-optic modulation |

Optics Express, Vol. 20, Issue 13, pp. 14117-14129 (2012)

http://dx.doi.org/10.1364/OE.20.014117

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### Abstract

We present a theoretical concept which may lead to quantitative photoacoustic mapping of chromophore concentrations. The approach supposes a technique capable of tagging light in a well-defined tagging volume at a specific location deep in the medium. We derive a formula that expresses the local absorption coefficient inside a medium in terms of noninvasively measured quantities and experimental parameters and we validate the theory using Monte Carlo simulations. Furthermore, we performed an experiment to basically validate the concept as a strategy to correct for fluence variations in photoacoustics. In the experiment we exploit the possibility of acousto-optic modulation, using focused ultrasound, to tag photons. Results show that the variation in photoacoustic signals of absorbing insertions embedded at different depths in a phantom, caused by fluence variations of more than one order of magnitude, can be corrected for to an accuracy of 5%.

© 2012 OSA

## 1. Introduction

2. J. R. Rajian, P. L. Carson, and X. D. Wang, “Quantitative photoacoustic measurement of tissue optical absorption spectrum aided by an optical contrast agent,” Opt. Express **17**(6), 4879–4889 (2009). [CrossRef] [PubMed]

3. A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging **28**(12), 1997–2006 (2009). [CrossRef] [PubMed]

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

*a priori*knowledge of bulk optical properties. The most common approach is a combination of photoacoustics with the application of a model of light transport [5

5. 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]

10. Z. Yuan, Q. Wang, and H. B. Jiang, “Reconstruction of optical absorption coefficient maps of heterogeneous media by photoacoustic tomography coupled with diffusion equation based regularized Newton Method,” Opt. Express **15**(26), 18076–18081 (2007). [CrossRef] [PubMed]

11. A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. **16**(9), 096016 (2011). [CrossRef] [PubMed]

12. X. Q. Li, L. Xi, R. X. Jiang, L. Yao, and H. B. Jiang, “Integrated diffuse optical tomography and photoacoustic tomography: phantom validations,” Biomed. Opt. Express **2**(8), 2348–2353 (2011). [CrossRef] [PubMed]

13. L. H. Wang, S. L. Jacques, and X. M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. **20**(6), 629–631 (1995). [CrossRef] [PubMed]

14. L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. **87**(4), 043903 (2001). [CrossRef] [PubMed]

## 2. Theory

*i*and

*j*inside or on the surface of a turbid medium, as depicted in Fig. 1 . On injection in point

*i*of light at power

*P*, through an aperture placed in point

_{i}*j*with area

*A*and solid opening angle

_{j}*Ω*an optical power is detected ofHere

_{j}*Pr(i,j)*is the probability per unit aperture area and per unit solid angle that a photon starting in

*i*will cross an aperture at point

*j*, following any possible photon trajectory. The fluence rate

*j*can be writtenthe expressions for

*P*and

_{ij}*j*. In an analogous manner, a pulse with pulse energy

*E*applied at surface point

_{p,i}*i*will generate fluenceProbability

*Pr(i,j)*is affected by the unknown optical properties of that part of the medium that is interrogated by the light travelling from

*i*to

*j*. A key aspect of our method is that we exploit the principle that all photon trajectories contributing to

*Pr(i,j)*can be followed in both directions with equal probability, hence

*Pr(i,j) = Pr(j,i)*. Photon reversibility has been recently used in an extreme form by Xu et al. [15

15. X. A. Xu, H. L. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics **5**(3), 154–157 (2011). [CrossRef] [PubMed]

*µ*. The absorbed energy density at point 2 iswith

_{a,2}*i = 1,3*for injection of light at points 1 and 3, respectively. Here we used Eq. (3) relating the internal fluence to the injected pulse energy. Under the condition of stress confinement, this leads to local stressesfor

*i*= 1,3, which are the result of photoacoustic tomography experiments with excitation at points 1 and 3. Around point 2 a volume

*V*is defined in which a known fraction of photons that address this volume are ‘tagged’. Here a unit tagging efficiency is assumed. Assuming an incoming fluence rate

_{2}*A*the average frontal area of volume 2, with averaging over all possible orientations. Here we used Eq. (2) relating the internal fluence rate to the power injected at the medium surface. The internally injected stream of ‘tagged’ photons at power

_{2}*P*gives rise to detection of ‘tagged’ photons within an area

_{L,i2}*A*and solid opening angle

_{j}*Ω*at point

_{j}*j*, at a power that with the use of Eq. (1) can be writtenwith

*(i,j) = (1,3)*or

*(i,j) = (3,1).*

*i = 1,3,*and Eq. (8), we can obtain an expression for the absorption coefficient,

*Pr(i,j)*associated with the unknown absorption and scattering properties of the medium. Hence the unknown potentially inhomogeneous optical properties of the tissue, are removed from the problem.

## 3. Monte Carlo modeling

16. L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Mcml - monte-carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Biol. **47**(2), 131–146 (1995). [CrossRef]

^{8}photons were injected through a circular window of 2mm diameter. The ‘tagged’ photons were detected in a circular window of 2mm diameter and full opening angle of 50 degrees. In the Monte Carlo simulation the estimation of the absorption coefficient of the sphere is performed with an equivalent of Eq. (9) that readswith

*V*the volume of the absorbing and tagging sphere around point 2,

_{2}*E*is now the number of photons absorbed in the volume, and * denotes normalization with the number of injected photons.

_{a,i2}## 4. Experimental validation

13. L. H. Wang, S. L. Jacques, and X. M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. **20**(6), 629–631 (1995). [CrossRef] [PubMed]

_{2}of the tagging volume Eq. (9), are constant. The optical excitation of the phantom during the measurements can also be merged into a constant factor and as a result Eq. (9) can be written as,where

*p*and

_{21}*p*are the measured photoacoustic pressures generated by a local absorber in internal point 2 by illuminating at position 1 and 3 respectively and

_{23}*P*

_{L,}_{13}is the power of ultrasonically modulated light (being modulated at position 2) detected at position 3 when the medium is illuminated at position 1. Hence we assume that these externally measured pressures are linked in a linear manner to the photoelastic stresses σ

*and σ*

_{21}*inside the absorbers, which has to be assured by a correct experimental design. The purpose of this experiment is to demonstrate that for multiple identical insertions, regardless of their depth inside the turbid phantom, it is possible to get the same relative absorption coefficient value from all the insertions, by assuming that C in Eq. (11) has the same value for each insertion (which will be true for identical insertions). The experimentally measured value using Eq. (11) is proportional to the absorption coefficient.*

_{23}^{2}per pulse at 760 nm wavelength, with a duration of 6 ns and a beam diameter of 5 mm. The sample can be illuminated at point 1 by mirror M in the path of the beam and at point 3 by flipping mirror M out of the beam path. PA signals were detected with a single element 5MHz focused ultrasound transducer (Panametrics V309) oriented at 45° to the line along the absorbers, and attached to a linear xy translation stage (MTS50-Z8) which allowed precise scanning of the US focus along a line through the absorbers. The oblique angle was chosen instead of 90° to prevent partly overlap of the signals of the three absorbers. The linear transducer scan parallel to the absorbing objects ensures that the distance from each absorber to the transducer, when in focus, is identical. Hence

*1/r*decay and frequency dependent attenuation are constant, and hence we can expect the pressure amplitude

*p*to be proportional to the photoelastic stress

*σ*inside each absorber. Both sample and UST were immersed in water for acoustic coupling, the PA signal from UST was amplified using Panametric NDT(5077PR) amplifier and sent to an oscilloscope (Textronix TDS 220) which was triggered by the laser and a computer was used to read and store the data from oscilloscope.

17. M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. **28**(24), 2482–2484 (2003). [CrossRef] [PubMed]

18. A. Bratchenia, R. Molenaar, T. G. van Leeuwen, and R. P. H. Kooyman, “Acousto-optic-assisted diffuse optical tomography,” Opt. Lett. **36**(9), 1539–1541 (2011). [CrossRef] [PubMed]

_{tagged}) versus the depth of the US focus along the optical axis (where insertions are embedded), for one of the four independent measurements performed on this phantom in transmission mode. During the AO measurement the sample was illuminated at point 1 and the ultrasonically modulated light was detected at point 3, where the light was modulated by scanning the US focus in steps of 0.5 mm along the line through the embedded insertions. This AO signal is averaged over 8 ultrasound pulses, where each pulse consists of 5 ultrasound cycles. The dips in the AO signal curve are due to the presence of insertions which match with expected locations of insertions. Figure 6(d) shows the estimated relative absorption coefficient normalized by the unknown constant (which is the same for all identical absorbers) for different insertions using Eq. (11). To obtain this relative absorption coefficient for all insertions using Eq. (11), we used the peak-to-peak values of PA signals (

*p*and

_{21}*p*) for each insertion from Fig. 6(a) and Fig. 6(b) and the AO signal (

_{23}*P*

_{L,}_{13}α

*I*

_{tagged}) coming from the location of corresponding absorbing insertions indicated with arrows in Fig. 6(c). The AO values used in Eq. (11) to calculate the relative absorption coefficient are the lowest values in the dips of AO curve caused by the presence of insertions, and are pointed by arrows in Fig. 6(c). The error bars shown in Fig. 7(d) are based on estimation of error propagation due to noise present in multiple independent AO and PA measurements. The estimation of noise (uncertainty) is done by taking the standard deviation of multiple AO and PA measurements.

^{3}, made with 2% agar gel containing a dilution of 3% intralipid (20%IL). This sample contains two nylon tubes with 0.94 mm and 0.75 mm outer and inner diameter respectively, inserted at 10 mm and 22 mm depth from the illuminated surface 1. We prepared two absorbing solutions, solution 1 was made with 30 µl India ink dissolved in 10 ml water whereas solution 2 was made with 10 µl India ink dissolved in 10 ml water. Measurements with a spectrophotometer showed that solution 1 and solution 2 have absorption coefficients of 1.5/mm and 0.45/mm respectively at 532 nm wavelength. Tube 1 positioned at depth of 10 mm inside phantom was filled with absorbing solution 1, whereas tube 2 positioned at depth of 22 mm inside the phantom was filled with absorbing solution 2.

*P*

_{L,}_{13}α

*I*

_{tagged}) when the sample is illuminated at 1 and ultrasonically modulated light is detected at 3. Figure 7(d) shows the estimated relative absorption coefficient normalized by unknown constant C (µ

_{a}/C) of solutions contained in both nylon tubes. The values of the relative absorption coefficient are obtained using Eq. (11) in the same way as before. The error bars shown in Fig. 7(d) are based on estimation of error propagation due to noise present in multiple independent AO and PA measurements.

## 5. Discussion and conclusion

*I*

_{12}(

*s**)*and

*I*

_{32}(

*s**)*in point 2 are each other’s point mirrored version, which will generally be the case for multiply scattered light which creates almost isotropic radiances. Close to light sources, tissue boundaries or strong inhomogeneities and by shadowing of a neighboring absorbing volume, this condition might break down.

19. A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. **32**(3), 381–394 (1985). [CrossRef]

17. M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. **28**(24), 2482–2484 (2003). [CrossRef] [PubMed]

21. Y. Z. Li, P. Hemmer, C. H. Kim, H. L. Zhang, and L. V. Wang, “Detection of ultrasound-modulated diffuse photons using spectral-hole burning,” Opt. Express **16**(19), 14862–14874 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | L. V. Wang, |

2. | J. R. Rajian, P. L. Carson, and X. D. Wang, “Quantitative photoacoustic measurement of tissue optical absorption spectrum aided by an optical contrast agent,” Opt. Express |

3. | A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging |

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

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

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. | J. Laufer, B. Cox, E. Zhang, and P. Beard, “Quantitative determination of chromophore concentrations from 2D photoacoustic images using a nonlinear model-based inversion scheme,” Appl. Opt. |

8. | L. Yao, Y. Sun, and H. B. Jiang, “Transport-based quantitative photoacoustic tomography: simulations and experiments,” Phys. Med. Biol. |

9. | L. Yin, Q. Wang, Q. Z. Zhang, and H. B. Jiang, “Tomographic imaging of absolute optical absorption coefficient in turbid media using combined photoacoustic and diffusing light measurements,” Opt. Lett. |

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

11. | A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt. |

12. | X. Q. Li, L. Xi, R. X. Jiang, L. Yao, and H. B. Jiang, “Integrated diffuse optical tomography and photoacoustic tomography: phantom validations,” Biomed. Opt. Express |

13. | L. H. Wang, S. L. Jacques, and X. M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett. |

14. | L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett. |

15. | X. A. Xu, H. L. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics |

16. | L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Mcml - monte-carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Biol. |

17. | M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett. |

18. | A. Bratchenia, R. Molenaar, T. G. van Leeuwen, and R. P. H. Kooyman, “Acousto-optic-assisted diffuse optical tomography,” Opt. Lett. |

19. | A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason. |

20. | M. Lesaffre, F. Jean, A. Bordes, F. Ramaz, E. Bossy, A. C. Boccara, M. Gross, P. Delaye, and G. Roosen, “Sub-millisecond in situ measurement of the photorefractive response in a self adaptive wavefront holography setup developped for acousto-optic imaging,” Proc. SPIE |

21. | Y. Z. Li, P. Hemmer, C. H. Kim, H. L. Zhang, and L. V. Wang, “Detection of ultrasound-modulated diffuse photons using spectral-hole burning,” Opt. Express |

**OCIS Codes**

(170.1065) Medical optics and biotechnology : Acousto-optics

(110.5125) Imaging systems : Photoacoustics

(170.6935) Medical optics and biotechnology : Tissue characterization

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: April 12, 2012

Revised Manuscript: June 1, 2012

Manuscript Accepted: June 3, 2012

Published: June 11, 2012

**Virtual Issues**

Vol. 7, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

K. Daoudi, A. Hussain, E. Hondebrink, and W. Steenbergen, "Correcting photoacoustic signals for fluence variations using acousto-optic modulation," Opt. Express **20**, 14117-14129 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14117

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### References

- L. V. Wang, Photoacoustic Imaging and Spectroscopy (CRC Press, 2009).
- J. R. Rajian, P. L. Carson, and X. D. Wang, “Quantitative photoacoustic measurement of tissue optical absorption spectrum aided by an optical contrast agent,” Opt. Express17(6), 4879–4889 (2009). [CrossRef] [PubMed]
- A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signal representation,” IEEE Trans. Med. Imaging28(12), 1997–2006 (2009). [CrossRef] [PubMed]
- R. J. Zemp, “Quantitative photoacoustic tomography with multiple optical sources,” Appl. Opt.49(18), 3566–3572 (2010). [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]
- 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]
- J. Laufer, B. Cox, E. Zhang, and P. Beard, “Quantitative determination of chromophore concentrations from 2D photoacoustic images using a nonlinear model-based inversion scheme,” Appl. Opt.49(8), 1219–1233 (2010). [CrossRef] [PubMed]
- L. Yao, Y. Sun, and H. B. Jiang, “Transport-based quantitative photoacoustic tomography: simulations and experiments,” Phys. Med. Biol.55(7), 1917–1934 (2010). [CrossRef] [PubMed]
- L. Yin, Q. Wang, Q. Z. 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, Q. Wang, and H. B. 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]
- A. Q. Bauer, R. E. Nothdurft, T. N. Erpelding, L. V. Wang, and J. P. Culver, “Quantitative photoacoustic imaging: correcting for heterogeneous light fluence distributions using diffuse optical tomography,” J. Biomed. Opt.16(9), 096016 (2011). [CrossRef] [PubMed]
- X. Q. Li, L. Xi, R. X. Jiang, L. Yao, and H. B. Jiang, “Integrated diffuse optical tomography and photoacoustic tomography: phantom validations,” Biomed. Opt. Express2(8), 2348–2353 (2011). [CrossRef] [PubMed]
- L. H. Wang, S. L. Jacques, and X. M. Zhao, “Continuous-wave ultrasonic modulation of scattered laser light to image objects in turbid media,” Opt. Lett.20(6), 629–631 (1995). [CrossRef] [PubMed]
- L. V. Wang, “Mechanisms of ultrasonic modulation of multiply scattered coherent light: an analytic model,” Phys. Rev. Lett.87(4), 043903 (2001). [CrossRef] [PubMed]
- X. A. Xu, H. L. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics5(3), 154–157 (2011). [CrossRef] [PubMed]
- L. H. Wang, S. L. Jacques, and L. Q. Zheng, “Mcml - monte-carlo modeling of light transport in multilayered tissues,” Comput. Meth. Prog. Biol.47(2), 131–146 (1995). [CrossRef]
- M. Gross, P. Goy, and M. Al-Koussa, “Shot-noise detection of ultrasound-tagged photons in ultrasound-modulated optical imaging,” Opt. Lett.28(24), 2482–2484 (2003). [CrossRef] [PubMed]
- A. Bratchenia, R. Molenaar, T. G. van Leeuwen, and R. P. H. Kooyman, “Acousto-optic-assisted diffuse optical tomography,” Opt. Lett.36(9), 1539–1541 (2011). [CrossRef] [PubMed]
- A. R. Selfridge, “Approximate material properties in isotropic materials,” IEEE Trans. Sonics Ultrason.32(3), 381–394 (1985). [CrossRef]
- M. Lesaffre, F. Jean, A. Bordes, F. Ramaz, E. Bossy, A. C. Boccara, M. Gross, P. Delaye, and G. Roosen, “Sub-millisecond in situ measurement of the photorefractive response in a self adaptive wavefront holography setup developped for acousto-optic imaging,” Proc. SPIE6086, 8612 (2006).
- Y. Z. Li, P. Hemmer, C. H. Kim, H. L. Zhang, and L. V. Wang, “Detection of ultrasound-modulated diffuse photons using spectral-hole burning,” Opt. Express16(19), 14862–14874 (2008). [CrossRef] [PubMed]

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