Abstract

We present a statistic method to measure the concentration of particles in flow by the use of optical coherence tomography (OCT). This method is based on the fact that the fluctuating numbers of particles contained within a small OCT detection volume caused by Brownian motion are governed by Poissonian distribution. Particle concentration is evaluated from the statistical analyzes of the OCT intensity signals that are backscattered by the moving particles. The method is experimentally verified with flow phantoms of polymer microspheres. Experimental results are in good agreement with the theoretical ones for low concentrations while relatively large discrepancies emerge for high concentrations.

© 2011 Optical Society of America

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[CrossRef] [PubMed]

M. Calderon-Arnulphi, A. Alaraj, and K. V. Slavin, Neurol. Res. 31, 605 (2009).
[CrossRef] [PubMed]

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O. Krichevsky and G. Bonnet, Rep. Prog. Phys. 65, 251(2002).
[CrossRef]

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[CrossRef]

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Y. Aizu and T. Asakura, J. Biomed. Optics 4, 61 (1999).
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Alaraj, A.

M. Calderon-Arnulphi, A. Alaraj, and K. V. Slavin, Neurol. Res. 31, 605 (2009).
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Asakura, T.

Y. Aizu and T. Asakura, J. Biomed. Optics 4, 61 (1999).
[CrossRef]

Baac, H. W.

Bartlett, L. A.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Bonnet, G.

O. Krichevsky and G. Bonnet, Rep. Prog. Phys. 65, 251(2002).
[CrossRef]

Bouma, B. E.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
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Briers, J. D.

Cable, A.

Calderon-Arnulphi, M.

M. Calderon-Arnulphi, A. Alaraj, and K. V. Slavin, Neurol. Res. 31, 605 (2009).
[CrossRef] [PubMed]

Chen, A.

Chen, S. L.

Chen, Z. P.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Frostig, R. D.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Fukumura, D.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Gordon, M. L.

Guo, L. J.

Hao, J.

He, K.

Huang, S. W.

Hurst, S.

Izatt, J. A.

Jain, R. K.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Jiang, J.

Kask, P.

R. Rigler, Ü. Mets, J. Widengren, and P. Kask, Eur. Biophys. J. 22, 169 (1993).
[CrossRef]

Khurana, M.

Krichevsky, O.

O. Krichevsky and G. Bonnet, Rep. Prog. Phys. 65, 251(2002).
[CrossRef]

Kulkarni, M. D.

Lanning, R. M.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Leung, M. K. K.

Ling, T.

Lo, S.

Mariampillai, A.

Mets, Ü.

R. Rigler, Ü. Mets, J. Widengren, and P. Kask, Eur. Biophys. J. 22, 169 (1993).
[CrossRef]

Mok, A.

Moriyama, E. H.

Munce, N. R.

Munn, L. L.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Nelson, J. S.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Padera, T. P.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Pekar, J.

Prakash, N.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Qi, B.

Rigler, R.

R. Rigler, Ü. Mets, J. Widengren, and P. Kask, Eur. Biophys. J. 22, 169 (1993).
[CrossRef]

Seng-Yue, E.

Slavin, K. V.

M. Calderon-Arnulphi, A. Alaraj, and K. V. Slavin, Neurol. Res. 31, 605 (2009).
[CrossRef] [PubMed]

Srinivas, S. M.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Standish, B. A.

Stylianopoulos, T.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Tearney, G. J.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Tyrrell, J. A.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Vakoc, B. J.

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Vitkin, I. A.

Wang, R. K.

Wang, Y.

Widengren, J.

R. Rigler, Ü. Mets, J. Widengren, and P. Kask, Eur. Biophys. J. 22, 169 (1993).
[CrossRef]

Wilson, B. C.

Yang, V. X. D.

Yazdanfar, S.

Zhao, Y. H.

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

Zhou, Z.

Eur. Biophys. J. (1)

R. Rigler, Ü. Mets, J. Widengren, and P. Kask, Eur. Biophys. J. 22, 169 (1993).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Z. P. Chen, Y. H. Zhao, S. M. Srinivas, J. S. Nelson, N. Prakash, and R. D. Frostig, IEEE J. Sel. Top. Quantum Electron. 5, 1134 (1999).
[CrossRef]

J. Biomed. Optics (1)

Y. Aizu and T. Asakura, J. Biomed. Optics 4, 61 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Med. (1)

B. J. Vakoc, R. M. Lanning, J. A. Tyrrell, T. P. Padera, L. A. Bartlett, T. Stylianopoulos, L. L. Munn, G. J. Tearney, D. Fukumura, R. K. Jain, and B. E. Bouma, Nat. Med. 15, 1219 (2009).
[CrossRef] [PubMed]

Neurol. Res. (1)

M. Calderon-Arnulphi, A. Alaraj, and K. V. Slavin, Neurol. Res. 31, 605 (2009).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (4)

Rep. Prog. Phys. (1)

O. Krichevsky and G. Bonnet, Rep. Prog. Phys. 65, 251(2002).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) The magnitudes of the detected OCT signals from fluid particle flow with an average flow velocity of 14.2 mm / s , nonflowing particle suspension, and pure water. (b) The histograms of the detected OCT signals from the particle flow with different relative concentrations and different flowing velocities.

Fig. 2
Fig. 2

Measured relative concentrations of particle flow with the velocities of 14.2, 7.1, and 3.55 mm / s . From top to bottom, the theoretical relative concentrations are 1, 1 / 2 , 1 / 4 , 1 / 8 , 1 / 16 , 1 / 32 , 1 / 64 , and 1 / 128 , respectively.

Fig. 3
Fig. 3

Measured concentrations at the depth of 1.4 mm , and the dash line shows the theoretical relative concentration, i.e., y = 2 x .

Equations (3)

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I ( z , t ) = I R I S ( z , t ) cos ( 2 k n z φ ( z , t ) ) ,
N ( z , t ) = N ( z , t ) 2 ( N ( z , t ) N ( z , t ) ) 2 ,
N ( z , t ) = I R 2 I 0 2 N ( z , t ) 2 I R 2 I 0 2 ( N ( z , t ) N ( z , t ) ) 2 = I R I S ( z , t ) 2 ( I R I S ( z , t ) I R I S ( z , t ) ) 2 .

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