Abstract

In this paper a novel technique for flow measurement which is based on the photoacoustic (PA) Doppler effect is described. A significant feature of the proposed approach is that it can be implemented using tone burst optical excitation thus enabling simultaneous measurement of both velocity and position. The technique, which is based on external modulation and heterodyne detection, was experimentally demonstrated by measurement of the flow of a suspension of carbon particles in a silicon tube and successfully determined the particles mean velocity up to values of 130 mm/sec, which is about 10 times higher than previously reported PA Doppler setups. In the theoretical part a rigorous derivation of the PA response of a flowing medium is described and some important simplifying approximations are highlighted.

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References

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  1. L. V. Wang, Photoacoustic imaging and spectroscopy (CRC Press, 2009).
  2. M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
    [CrossRef]
  3. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
    [CrossRef] [PubMed]
  4. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
    [CrossRef]
  5. H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. 34(5), 671–673 (2009).
    [CrossRef] [PubMed]
  6. Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
    [CrossRef] [PubMed]
  7. S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. 71(8), 816–818 (2003).
    [CrossRef]
  8. W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974).
    [CrossRef] [PubMed]
  9. G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
    [CrossRef]
  10. A. Sheinfeld, E. Bergman, S. Gilead, and A. Eyal, “The use of pulse synthesis for optimization of photoacoustic measurements,” Opt. Express 17(9), 7328–7338 (2009).
    [CrossRef] [PubMed]

2009 (2)

2007 (2)

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
[CrossRef]

2006 (1)

M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

2004 (1)

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

2003 (1)

S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. 71(8), 816–818 (2003).
[CrossRef]

2000 (1)

G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
[CrossRef]

1974 (1)

W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974).
[CrossRef] [PubMed]

Bergman, E.

Blinder, S. M.

S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. 71(8), 816–818 (2003).
[CrossRef]

Brody, W. R.

W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974).
[CrossRef] [PubMed]

Chen, Q.

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

Eyal, A.

Falteri, S.

G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
[CrossRef]

Fang, H.

H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. 34(5), 671–673 (2009).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
[CrossRef]

Gilead, S.

Guidi, G.

G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
[CrossRef]

Licciardello, C.

G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
[CrossRef]

Maslov, K.

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
[CrossRef]

Meindl, J. D.

W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974).
[CrossRef] [PubMed]

Sheinfeld, A.

Wang, L. V.

H. Fang and L. V. Wang, “M-mode photoacoustic particle flow imaging,” Opt. Lett. 34(5), 671–673 (2009).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
[CrossRef] [PubMed]

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
[CrossRef]

M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

Wang, Y.

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

Xing, D.

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

Xu, M.

M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

Zeng, Y.

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

Am. J. Phys. (1)

S. M. Blinder, “Delta functions in spherical coordinates and how to avoid losing them: fields of point charges and dipoles,” Am. J. Phys. 71(8), 816–818 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler flow measurement in optically scattering media,” Appl. Phys. Lett. 91(26), 264103 (2007).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

W. R. Brody and J. D. Meindl, “Theoretical analysis of the CW doppler ultrasonic flowmeter,” IEEE Trans. Biomed. Eng. 21(3), 183–192 (1974).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

Y. Wang, D. Xing, Y. Zeng, and Q. Chen, “Photoacoustic imaging with deconvolution algorithm,” Phys. Med. Biol. 49(14), 3117–3124 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic Doppler effect from flowing small light-absorbing particles,” Phys. Rev. Lett. 99(18), 184501 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

M. Xu and L. V. Wang, “Photoacoutsic imaging in biomedicine,” Rev. Sci. Instrum. 77(4), 041101 (2006).
[CrossRef]

Ult. Med. Biol. (1)

G. Guidi, C. Licciardello, and S. Falteri, “Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening,” Ult. Med. Biol. 26(5), 853–862 (2000).
[CrossRef]

Other (1)

L. V. Wang, Photoacoustic imaging and spectroscopy (CRC Press, 2009).

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Figures (6)

Fig. 1
Fig. 1

Illustration of PA flow measurement of inhomogeneous fluid flowing in a cylindrical volume

Fig. 2
Fig. 2

Experimental setup

Fig. 3
Fig. 3

The optical burst excitation (black) and the resulting PA response (pink) in the time domain

Fig. 4
Fig. 4

Example of spectra for infusion (blue) and withdrawal (pink) for rates of 20 ml/min (left plot) and 40 ml/min (right plot)

Fig. 5
Fig. 5

The Doppler frequency shift vs. flow rate: measured (blue) and theoretical prediction for γ ¯ =60° (red dotted). Positive rates were measured for infusion (where the flow was towards the transducer) and negative for withdrawal. Inset includes zoom-in on the low velocities section.

Fig. 6
Fig. 6

Spectral width (FWHM) vs. average particles velocity. Inset includes zoom-in on low velocities section

Equations (16)

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p ( t ) = 1 4 π d r r H ˜ ( r , t ' ) t ' | t ' = t r / c
p ( t ) = 1 4 π d r r [ A ( r , t ' ) I ( t ' ) t ' + I ( t ' ) A ( r , t ' ) t ' ] | t ' = t r / c
p ( t ) = a 4 π d r d θ d φ r δ [ r r p ( t ) ] δ [ θ θ p ( t ) ] δ [ φ φ p ( t ) ] I ( t r / c ) t
p ( t ) = a 4 π r p ( t ) I ( t r / c ) t | r = r p ( t )
p ( t ) = i I 0 a f 0 4 r p ( t ) exp { i 2 π f 0 [ t r p ( t ) / c ] }
f P A D ( t ) = f 0 c d r p ( t ) d t = f 0 v c cos [ γ ( t ) ]
A ( r , t ) = A ( r v t ) = d r 0 A ( r 0 ) δ [ r r 0 v t ]
p ( t ) = i I 0 a f 0 4 d r 0 A ( r 0 ) r p ( t ) exp { i 2 π f 0 [ t r p ( t ) / c ] }
p ( t ) i I 0 a f 0 A ˜ ( f 0 / c ) 4 r 0 exp { i 2 π f 0 ( 1 + v / c ) t }
v ( r ) = 2 F A [ 1 ( r R ) 2 ] = 2 v a v g [ 1 ( r R ) 2 ]
I ( t ) = I 0 2 [ cos ( 2 π f 0 t ) + 1 ]     n r e c t ( t n T c T r )
p I I ( t ) = a 4 π d r r I ( t r / c ) δ [ r r 0 + v ( t r / c ) ] t
p I I ( t ) = v a 4 π d r ' r ' v t + r 0 I [ t ( r ' v t + r 0 c v ) ] d δ ( r ' ) d r '
p I I ( t ) = v a 4 π d d r ' { 1 r ' v t + r 0 I [ t ( r ' v t + r 0 c v ) ] } | r ' = 0
p I I ( t ) = v a I 0 8 π     { 1 ( r 0 v t ) 2 + i 2 π f 0 / ( c v ) r 0 v t } exp [ i 2 π f 0 [ t ( r 0 v t c v ) ] ]
| p I I ( t ) | / | p ( t ) | = | 1 2 π f 0 v r 0 v t + i v c v |

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