Abstract

Thermal Diffusion Flowmetry (TDF) (also called Heat Clearance Method or Thermal Clearance Method) is a longstanding technique for measuring blood flow or blood perfusion in living tissues. Typically, temperature transients and/or gradients are induced in a volume of interest and the temporal and/or spatial temperature variations which follow are measured and used for calculation of the flow. In this work a new method for implementing TDF is studied theoretically and experimentally. The heat deposition which is required for TDF is implemented photothermally (PT) and the measurement of the induced temperature variations is done by photoacoustic (PA) thermometry. Both excitation light beams (the PT and the PA) are produced by directly modulated 830 nm laser diodes and are conveniently delivered to the volume under test by the same optical fiber. The method was tested experimentally using a blood-filled phantom vessel and the results were compared with a theoretical prediction based on the heat and the photoacoustic equations. The fitting of a simplified lumped thermal model to the experimental data yielded estimated values of the blood velocity at different flow rates. By combining additional optical sources at different wavelengths it will be possible to utilize the method for non-invasive simultaneous measurement of blood flow and oxygen saturation using a single fiber probe.

© 2012 OSA

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References

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  1. F. A. Gibbs, “A thermoelectric blood flow recorder in the form of a needle,” Proc. Soc. Exp. Biol. Med.31, 141–146 (1933).
  2. M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
    [CrossRef] [PubMed]
  3. M. Nitzan and Y. Mahler, “Theoretical analysis of the transient thermal clearance method for regional blood flow measurement,” Med. Biol. Eng. Comput.24(6), 597–601 (1986).
    [CrossRef] [PubMed]
  4. A. Shitzer and R. C. Eberhart, Heat Transfer in Medicine and Biology (Plenum, 1985), Chap. 9.
  5. S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010).
    [CrossRef] [PubMed]
  6. L. V. Wang, Photoacoustic Imaging and Spectroscopy (CRC Press, 2009).
  7. R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
    [CrossRef] [PubMed]
  8. I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
    [CrossRef]
  9. M. Pramanik and L. V. Wang, “Thermoacoustic and photoacoustic sensing of temperature,” J. Biomed. Opt.14(5), 054024 (2009).
    [CrossRef] [PubMed]
  10. A. Sheinfeld and A. Eyal, “Flow-dependant photothermal modulation of the photoacoustic response,” Proc. SPIE8223, 82231D (2012).
    [CrossRef]
  11. P. Newfield and J. E. Cottrell, Handbook of Neuroanesthesia (Lippincott Williams&Wilkins, 2006), Chap. I(3).
  12. L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
    [CrossRef] [PubMed]
  13. E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
    [PubMed]
  14. J. Yao, K. I. Maslov, Y. Shi, L. A. Taber, and L. V. Wang, “In vivo photoacoustic imaging of transverse blood flow by using Doppler broadening of bandwidth,” Opt. Lett.35(9), 1419–1421 (2010).
    [CrossRef] [PubMed]
  15. J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
    [CrossRef] [PubMed]
  16. A. Sheinfeld, S. Gilead, and A. Eyal, “Photoacoustic Doppler measurement of flow using tone burst excitation,” Opt. Express18(5), 4212–4221 (2010).
    [CrossRef] [PubMed]
  17. A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
    [CrossRef] [PubMed]
  18. J. Brunker and P. Beard, ““Pulsed photoacoustic Doppler flowmetry using a cross correlation method,” proc,” Proc. SPIE7564, 756426, 756426-8 (2010).
    [CrossRef]
  19. P. Beard, “Biomedical photoacoustic imaging,” Interface Focus1(4), 602–631 (2011).
    [CrossRef]
  20. A. K. Datta, Biological and Bioenvironmental Heat and Mass Transfer (Marcek Dekker, NY, 2002).
  21. J. P. Holman, Heat Transfer (McGraw Hill, 2002), pp. 133–134.
  22. B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
    [CrossRef] [PubMed]
  23. J. A. D. Matthew, CRC Handbook of Chemistry and Physics—Weast, (CRC Press, Boca Raton, 1988), Vol. 331.
  24. M. H. Niemz, Laser-Tissue Interactions—Fundamentals and Applications, 3rd ed. (Springer, 2007), p. 77.
  25. Hemedex, Inc., http://www.hemedex.com .

2012

A. Sheinfeld and A. Eyal, “Flow-dependant photothermal modulation of the photoacoustic response,” Proc. SPIE8223, 82231D (2012).
[CrossRef]

2011

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus1(4), 602–631 (2011).
[CrossRef]

2010

J. Yao, K. I. Maslov, Y. Shi, L. A. Taber, and L. V. Wang, “In vivo photoacoustic imaging of transverse blood flow by using Doppler broadening of bandwidth,” Opt. Lett.35(9), 1419–1421 (2010).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Photoacoustic Doppler measurement of flow using tone burst excitation,” Opt. Express18(5), 4212–4221 (2010).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
[CrossRef] [PubMed]

J. Brunker and P. Beard, ““Pulsed photoacoustic Doppler flowmetry using a cross correlation method,” proc,” Proc. SPIE7564, 756426, 756426-8 (2010).
[CrossRef]

S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010).
[CrossRef] [PubMed]

2009

M. Pramanik and L. V. Wang, “Thermoacoustic and photoacoustic sensing of temperature,” J. Biomed. Opt.14(5), 054024 (2009).
[CrossRef] [PubMed]

2008

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

2007

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

2005

I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
[CrossRef]

1995

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

1986

M. Nitzan and Y. Mahler, “Theoretical analysis of the transient thermal clearance method for regional blood flow measurement,” Med. Biol. Eng. Comput.24(6), 597–601 (1986).
[CrossRef] [PubMed]

1985

M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
[CrossRef] [PubMed]

1933

F. A. Gibbs, “A thermoelectric blood flow recorder in the form of a needle,” Proc. Soc. Exp. Biol. Med.31, 141–146 (1933).

Antesby, S. O.

M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
[CrossRef] [PubMed]

Arridge, S. R.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

Atiles, L.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

Baxter, C.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

Beard, P.

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus1(4), 602–631 (2011).
[CrossRef]

J. Brunker and P. Beard, ““Pulsed photoacoustic Doppler flowmetry using a cross correlation method,” proc,” Proc. SPIE7564, 756426, 756426-8 (2010).
[CrossRef]

Beard, P. C.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

Bleyl, J.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Bowman, F.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Brands, P. J.

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

Brunker, J.

J. Brunker and P. Beard, ““Pulsed photoacoustic Doppler flowmetry using a cross correlation method,” proc,” Proc. SPIE7564, 756426, 756426-8 (2010).
[CrossRef]

Cox, B. T.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

Esenaliev, R. O.

I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
[CrossRef]

Eyal, A.

A. Sheinfeld and A. Eyal, “Flow-dependant photothermal modulation of the photoacoustic response,” Proc. SPIE8223, 82231D (2012).
[CrossRef]

A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Photoacoustic Doppler measurement of flow using tone burst excitation,” Opt. Express18(5), 4212–4221 (2010).
[CrossRef] [PubMed]

Gibbs, F. A.

F. A. Gibbs, “A thermoelectric blood flow recorder in the form of a needle,” Proc. Soc. Exp. Biol. Med.31, 141–146 (1933).

Gilead, S.

A. Sheinfeld, S. Gilead, and A. Eyal, “Photoacoustic Doppler measurement of flow using tone burst excitation,” Opt. Express18(5), 4212–4221 (2010).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
[CrossRef] [PubMed]

Herfarth, C.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Hu, S.

S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010).
[CrossRef] [PubMed]

Hunt, J.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

Kara, S.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

Klar, E.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Kolkman, R. G. M.

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

Kraus, T.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Larin, K. V.

I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
[CrossRef]

Larina, I. V.

I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
[CrossRef]

Mahler, Y.

M. Nitzan and Y. Mahler, “Theoretical analysis of the transient thermal clearance method for regional blood flow measurement,” Med. Biol. Eng. Comput.24(6), 597–601 (1986).
[CrossRef] [PubMed]

M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
[CrossRef] [PubMed]

Maslov, K. I.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

J. Yao, K. I. Maslov, Y. Shi, L. A. Taber, and L. V. Wang, “In vivo photoacoustic imaging of transverse blood flow by using Doppler broadening of bandwidth,” Opt. Lett.35(9), 1419–1421 (2010).
[CrossRef] [PubMed]

Mileski, W.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

Newman, W.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Nitzan, M.

M. Nitzan and Y. Mahler, “Theoretical analysis of the transient thermal clearance method for regional blood flow measurement,” Med. Biol. Eng. Comput.24(6), 597–601 (1986).
[CrossRef] [PubMed]

M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
[CrossRef] [PubMed]

Otto, G.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Pramanik, M.

M. Pramanik and L. V. Wang, “Thermoacoustic and photoacoustic sensing of temperature,” J. Biomed. Opt.14(5), 054024 (2009).
[CrossRef] [PubMed]

Purdue, G.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

Sheinfeld, A.

A. Sheinfeld and A. Eyal, “Flow-dependant photothermal modulation of the photoacoustic response,” Proc. SPIE8223, 82231D (2012).
[CrossRef]

A. Sheinfeld, S. Gilead, and A. Eyal, “Photoacoustic Doppler measurement of flow using tone burst excitation,” Opt. Express18(5), 4212–4221 (2010).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
[CrossRef] [PubMed]

Shi, Y.

Steenbergen, W.

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

Taber, L. A.

van Leeuwen, T. G.

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

von Kummer, R.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Wang, L. V.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

J. Yao, K. I. Maslov, Y. Shi, L. A. Taber, and L. V. Wang, “In vivo photoacoustic imaging of transverse blood flow by using Doppler broadening of bandwidth,” Opt. Lett.35(9), 1419–1421 (2010).
[CrossRef] [PubMed]

S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010).
[CrossRef] [PubMed]

M. Pramanik and L. V. Wang, “Thermoacoustic and photoacoustic sensing of temperature,” J. Biomed. Opt.14(5), 054024 (2009).
[CrossRef] [PubMed]

Xia, Y.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

Yao, J.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

J. Yao, K. I. Maslov, Y. Shi, L. A. Taber, and L. V. Wang, “In vivo photoacoustic imaging of transverse blood flow by using Doppler broadening of bandwidth,” Opt. Lett.35(9), 1419–1421 (2010).
[CrossRef] [PubMed]

Zhang, Y.

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

Interface Focus

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus1(4), 602–631 (2011).
[CrossRef]

J. Acoust. Soc. Am.

B. T. Cox, S. Kara, S. R. Arridge, and P. C. Beard, “k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics,” J. Acoust. Soc. Am.121(6), 3453–3464 (2007).
[CrossRef] [PubMed]

J. Biomed. Opt.

S. Hu and L. V. Wang, “Photoacoustic imaging and characterization of the microvasculature,” J. Biomed. Opt.15(1), 011101 (2010).
[CrossRef] [PubMed]

R. G. M. Kolkman, P. J. Brands, W. Steenbergen, and T. G. van Leeuwen, “Real-time in vivo photoacoustic and ultrasound imaging,” J. Biomed. Opt.13(5), 050510 (2008).
[CrossRef] [PubMed]

M. Pramanik and L. V. Wang, “Thermoacoustic and photoacoustic sensing of temperature,” J. Biomed. Opt.14(5), 054024 (2009).
[CrossRef] [PubMed]

J. Yao, K. I. Maslov, Y. Zhang, Y. Xia, and L. V. Wang, “Label-free oxygen-metabolic photoacoustic microscopy in vivo,” J. Biomed. Opt.16(7), 076003 (2011).
[CrossRef] [PubMed]

A. Sheinfeld, S. Gilead, and A. Eyal, “Simultaneous spatial and spectral mapping of flow using photoacoustic Doppler measurement,” J. Biomed. Opt.15(6), 066010 (2010).
[CrossRef] [PubMed]

J. Burn Care Rehabil.

L. Atiles, W. Mileski, G. Purdue, J. Hunt, and C. Baxter, “Laser Doppler flowmetry in burn wounds,” J. Burn Care Rehabil.16(4), 388–393 (1995).
[CrossRef] [PubMed]

J. Phys. D Appl. Phys.

I. V. Larina, K. V. Larin, and R. O. Esenaliev, “Real-time optoacoustic monitoring of temperature in tissued,” J. Phys. D Appl. Phys.38(15), 2633–2639 (2005).
[CrossRef]

Med. Biol. Eng. Comput.

M. Nitzan and Y. Mahler, “Theoretical analysis of the transient thermal clearance method for regional blood flow measurement,” Med. Biol. Eng. Comput.24(6), 597–601 (1986).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

M. Nitzan, S. O. Antesby, and Y. Mahler, “Transient heat clearance method for regional blood flow measurements,” Phys. Med. Biol.30(6), 557–563 (1985).
[CrossRef] [PubMed]

Proc. Soc. Exp. Biol. Med.

F. A. Gibbs, “A thermoelectric blood flow recorder in the form of a needle,” Proc. Soc. Exp. Biol. Med.31, 141–146 (1933).

Proc. SPIE

J. Brunker and P. Beard, ““Pulsed photoacoustic Doppler flowmetry using a cross correlation method,” proc,” Proc. SPIE7564, 756426, 756426-8 (2010).
[CrossRef]

A. Sheinfeld and A. Eyal, “Flow-dependant photothermal modulation of the photoacoustic response,” Proc. SPIE8223, 82231D (2012).
[CrossRef]

Transplant. Proc.

E. Klar, T. Kraus, J. Bleyl, W. Newman, F. Bowman, R. von Kummer, G. Otto, and C. Herfarth, “Thermodiffusion as a novel method for continuous monitoring of the hepatic microcirculation after liver transplantation,” Transplant. Proc.27(5), 2610–2612 (1995).
[PubMed]

Other

P. Newfield and J. E. Cottrell, Handbook of Neuroanesthesia (Lippincott Williams&Wilkins, 2006), Chap. I(3).

A. Shitzer and R. C. Eberhart, Heat Transfer in Medicine and Biology (Plenum, 1985), Chap. 9.

L. V. Wang, Photoacoustic Imaging and Spectroscopy (CRC Press, 2009).

A. K. Datta, Biological and Bioenvironmental Heat and Mass Transfer (Marcek Dekker, NY, 2002).

J. P. Holman, Heat Transfer (McGraw Hill, 2002), pp. 133–134.

J. A. D. Matthew, CRC Handbook of Chemistry and Physics—Weast, (CRC Press, Boca Raton, 1988), Vol. 331.

M. H. Niemz, Laser-Tissue Interactions—Fundamentals and Applications, 3rd ed. (Springer, 2007), p. 77.

Hemedex, Inc., http://www.hemedex.com .

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Figures (6)

Fig. 1
Fig. 1

RC circuit description of the lumped model.

Fig. 2
Fig. 2

The experimental setup.

Fig. 3
Fig. 3

The spectrum of a PA response with PT modulation at 2Hz.

Fig. 4
Fig. 4

Simultaneous measurements of temperature and PA response at different PT modulation power: (a) PA amplitude of carrier frequency, normalized by amplitude without PT modulation, vs. the average temperature τDC. Experimental data marked by squares, linear fit in dashed black. (b) The amplitude of 0.1 Hz modulation peak, normalized by the carrier amplitude without PT modulation, vs. τAC.

Fig. 5
Fig. 5

Normalized PT-PA modulation frequency responses for stationary (blue) and velocities of 1.06 (pink), 2.1 (green), 4.2 (red), 10.6 (black) and 21.2 (gray) mm/s. Solid lines with markers are experimental data. Dotted lines are Lorentzian fits.

Fig. 6
Fig. 6

Estimated velocity ( = l VUT / t convection ) vs. real velocity: estimation based on the complete lumped model (red circles). Estimation based on a lumped model which ignores thermal conduction (green circles). Estimation based on only 2 PT modulation frequencies: 1 Hz and 15 Hz (blue x). Dotted black line indicates the 45° line. Inset: zoom-in on the range of low velocities.

Equations (31)

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τ(r,t) t = [ α(r)τ(r,t) ] conduction u ( r )τ(r,t) convection + H PT (r,t) ρ(r) C p (r) heat  source
τ(r,t) t =[ α(r)τ(r,t) ] u ( r )τ(r,t)
τ(r,0)= H r PT (r) ρ(r) C p (r)
τ ˜ (t)= VUT f ^ ( r )τ(r,t)dV
τ ˜ (t) t ={ VUT f ^ ( r )[ α(r) τ ¯ (r,t) ]dV VUT f ^ ( r ) u ( r ) τ ¯ (r,t)dV } τ ˜ (t)
t conduction = 1 VUT f ^ ( r )[ α(r) τ ¯ (r,t) ]dV t convection = 1 VUT f ^ ( r ) u ( r ) τ ¯ (r,t)dV
2 p(r,t) t 2 c 2 2 p(r,t)=Γ H PA (r,t) t
Γ( T )Γ( T 0 )+b( T T 0 ) Γ 0 +bτ
p ^ (r,t t , t )= 1 4πc t A( t- t ) Γ( r , t ) H r PA ( r ) | r- r | dA
p(r,t)= H t PA ( t ) p ^ (r,t t , t ) d t
H t PA ( t )= 1 t total [ 1+cos( ω PA t ) ]= 1 2 t total [ 2+ e j ω PA t + e j ω PA t ]
p ω PA (r,t)= e j ω PA t 2 t total e j ω PA t p ^ (r, t ,t t ) d t
p ω PA (t)=A[ 1+ b Γ 0 τ ˜ (t)    ] e j ω PA t
τ ˜ ( t ) VUT f ^ (r)τ( t,r )dV
f(r) H r PA ( r ) e j ω PA | r | /c | r | , f ^ (r) f(r) VUT f(r)dV
τ ˜ (t)= ( b Γ 0 ) 1 ( p ω PA (t) e j ω PA t A 1   )
τ ˜ (t)= τ ˜ (0)exp( t t eff )   
τ ˜ (ω)= τ ˜ (0) t eff 1+jω t eff
p( f PA ± f PT ) p( f PA ) ( b/ Γ 0 ) τ AC /2 1+( b/ Γ 0 ) τ DC ( b/ Γ 0 ) τ AC /2
τ AC_min 1 SNR( f PA ) ( 2 b/ Γ 0 )
H t PA ( t )= 1 t total [ 1+cos( ω PA t ) ]= 1 2 t total [ 2+ e j ω PA t + e j ω PA t ]
p ω PA (r,t)= e j ω PA t 2 t total e j ω PA t p ^ (r, t ,t t ) d t
p ω PA (r,t)= e j ω PA t 2 t total e j ω PA t 1 4πc t A( t ) Γ( r ,t t ) H r PA ( r ) | r- r | dA d t       
p ω PA (r,t)= j ω PA e j ω PA t 4πc2 t total e j ω PA t A( t ) Γ( r ,t t ) H r PA ( r ) | r- r | dA d t
p ω PA (r,t)= j ω PA e j ω PA t 4πc2 t total VUT Γ( r ,t) H r PA ( r ) e j ω PA | r- r | /c | r- r | dV
p ω PA (r,t)= j ω PA e j ω PA t 4πc2 t total VUT [ Γ 0 +bτ( r ,t) ] H r PA ( r ) e j ω PA | r- r | /c | r- r | dV
p ω PA (t)=A[ 1+ b Γ 0 τ ˜ (t)    ] e j ω PA t
τ ˜ ( t ) VUT f ^ (r)τ( t,r )dV
   f ^ (r) f(r) VUT f(r)dV
f(r) H r PA ( r ) e j ω PA | r | /c | r |
A j ω PA e j ω PA t Γ 0 4πc2 t total VUT f(r)dV

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