Abstract

Particle tracking velocimetry (PTV) gives quantitative estimates of fluid flow velocities from images. But particle tracking is a complicated problem, and it often produces results that need substantial post-processing. We propose a novel Gaussian process regression-based post-processing step for PTV: The method smooths (“denoises”) and densely interpolates velocity estimates while rejecting track irregularities. The method works under a large range of particle densities and fluid velocities. In addition, the method calculates standard deviances (error bars) for the velocity estimates, opening the possibility of propagating the standard deviances through subsequent processing and analysis. The accuracy of the method is experimentally evaluated using Optical Coherence Tomography images of particles in laminar flow in a pipe phantom. Following this, the method is used to quantify cilia-driven fluid flow and vorticity patterns in a developing Xenopus embryo.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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2017 (1)

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

2016 (2)

K. C. Zhou, B. K. Huang, U. A. Gamm, V. Bhandari, M. K. Khokha, and M. A. Choma, “Particle streak velocimetry-optical coherence tomography: a novel method for multidimensional imaging of microscale fluid flows,” Biomed. Opt. Express 7, 1590–1603 (2016).
[Crossref] [PubMed]

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

2015 (5)

A. Vlasenko, E. C. C. Steele, and W. A. M. Nimmo-Smith, “A physics-enabled flow restoration algorithm for sparse piv and ptv measurements,” Meas. Sci. Technol. 26, 065301 (2015).
[Crossref]

K. C. Zhou, B. K. Huang, H. Tagare, and M. A. Choma, “Improved velocimetry in optical coherence tomography using bayesian analysis,” Biomed. Opt. Express 6, 4796–4811 (2015).
[Crossref] [PubMed]

B. K. Huang, U. A. Gamm, S. Jonas, M. K. Khokha, and M. A. Choma, “Quantitative optical coherence tomography imaging of intermediate flow defect phenotypes in ciliary physiology and pathophysiology,” J. Biomed. Opt. 20, 030502 (2015).
[Crossref] [PubMed]

B. K. Huang, U. A. Gamm, V. Bhandari, M. K. Khokha, and M. A. Choma, “Three-dimensional, three-vector-component velocimetry of cilia-driven fluid flow using correlation-based approaches in optical coherence tomography,” Biomed. Opt. Express 6, 3515–3538 (2015).
[Crossref] [PubMed]

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

2014 (3)

H. J. Zar and T. W. Ferkol, “The global burden of respiratory disease - impact on child health,” Pediatr. Pulmonol. 49, 430–434 (2014).
[Crossref] [PubMed]

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

W. Thielicke and E. Stamhuis, “Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab,” J. Open Res. Softw. 2, e30 (2014).
[Crossref]

2012 (4)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

J. Lee, W. Wu, J. Y. Jiang, B. Zhu, and D. A. Boas, “Dynamic light scattering optical coherence tomography,” Opt. Express 20, 22262–22277 (2012).
[Crossref] [PubMed]

M. K. Khokha, “Xenopus white papers and resources: folding functional genomics and genetics into the frog,” Genesis 50, 133–142 (2012).
[Crossref] [PubMed]

M. Werner and B. Mitchell, “Understanding ciliated epithelia: the power of xenopus,” Genesis 50, 176–185 (2012).
[Crossref]

2011 (1)

2006 (1)

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

2005 (1)

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref] [PubMed]

1987 (2)

J. C. Agui and J. Jimenez, “On the performance of particle tracking,” J. Fluid Mech. 185, 447–468 (1987).
[Crossref]

H. Stuer and S. Blaser, “Interpolation of scattered 3d ptv data to a rectangular grid,” J. Fluid Mech. 185, 447–468 (1987).

Agui, J. C.

J. C. Agui and J. Jimenez, “On the performance of particle tracking,” J. Fluid Mech. 185, 447–468 (1987).
[Crossref]

Arganda-Carreras, I.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Bednarek, S. Y.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Bhandari, V.

Bhattacharya, D.

Bishop, C. M.

C. M. Bishop, Pattern Recognition and Machine Learning (Springer Science+Business Media, LLC, 2006), 1st ed.

Blaser, S.

H. Stuer and S. Blaser, “Interpolation of scattered 3d ptv data to a rectangular grid,” J. Fluid Mech. 185, 447–468 (1987).

Boas, D. A.

Cardona, A.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Cengel, Y. A.

J. M. Cimbala and Y. A. Cengel, Essentials of Fluid Mechanics, Fundamentals and Applcations (McGraw-Hill, 2008).

Chamorro, L. P.

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

Choma, M. A.

Cimbala, J. M.

J. M. Cimbala and Y. A. Cengel, Essentials of Fluid Mechanics, Fundamentals and Applcations (McGraw-Hill, 2008).

Drexler, W.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Eliceiri, K.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Eliceiri, K. W.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

Ferkol, T. W.

H. J. Zar and T. W. Ferkol, “The global burden of respiratory disease - impact on child health,” Pediatr. Pulmonol. 49, 430–434 (2014).
[Crossref] [PubMed]

Frise, E.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Gamm, U. A.

Gharib, M.

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

Graff, E. C.

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

Hartenstein, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Hiner, M. C.

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

Hoopes, G. M.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Huang, B. K.

Jiang, J. Y.

Jimenez, J.

J. C. Agui and J. Jimenez, “On the performance of particle tracking,” J. Fluid Mech. 185, 447–468 (1987).
[Crossref]

Jonas, S.

B. K. Huang, U. A. Gamm, S. Jonas, M. K. Khokha, and M. A. Choma, “Quantitative optical coherence tomography imaging of intermediate flow defect phenotypes in ciliary physiology and pathophysiology,” J. Biomed. Opt. 20, 030502 (2015).
[Crossref] [PubMed]

S. Jonas, D. Bhattacharya, M. K. Khokha, and M. A. Choma, “Microfluidic characterization of cilia-driven fluid flow using optical coherence tomography-based particle tracking velocimetry,” Biomed. Opt. Express 2, 2022–2034 (2011).
[Crossref] [PubMed]

Kamali, T.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Kaynig, V.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Khokha, M. K.

Kim, D.

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

Kim, J.-T.

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

Koumoutsakos, P.

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref] [PubMed]

Krieg, P. A.

A. S. Warkman and P. A. Krieg, “Xenopus as a model system for vertebrate heart development,” in Seminars in cell & developmental biology, vol. 18 (Elsevier, 2007), pp. 46–53.
[Crossref]

Kumar, A.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Laplantine, E.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Lee, J.

Leitgeb, R. A.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Liberzon, A.

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

Liu, M.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Longair, M.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Mitchell, B.

M. Werner and B. Mitchell, “Understanding ciliated epithelia: the power of xenopus,” Genesis 50, 176–185 (2012).
[Crossref]

Nimmo-Smith, W. A. M.

A. Vlasenko, E. C. C. Steele, and W. A. M. Nimmo-Smith, “A physics-enabled flow restoration algorithm for sparse piv and ptv measurements,” Meas. Sci. Technol. 26, 065301 (2015).
[Crossref]

Pereira, F.

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

Perry, N.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Pietzsch, T.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Preibisch, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Rasmussen, C. E.

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (The MIT Press, 2005).
[Crossref]

Reynolds, G. D.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Rueden, C.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Rueden, C. T.

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

Saalfeld, S.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Sbalzarini, I. F.

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref] [PubMed]

Schindelin, J.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Schmid, B.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Shorte, S. L.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Stamhuis, E.

W. Thielicke and E. Stamhuis, “Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab,” J. Open Res. Softw. 2, e30 (2014).
[Crossref]

Stamhuis, E. J.

W. Thielicke and E. J. Stamhuis, “Pivlab - time-resolved digital particle image velocimetry tool for matlab,” (2018).

Steele, E. C. C.

A. Vlasenko, E. C. C. Steele, and W. A. M. Nimmo-Smith, “A physics-enabled flow restoration algorithm for sparse piv and ptv measurements,” Meas. Sci. Technol. 26, 065301 (2015).
[Crossref]

Stuer, H.

H. Stuer and S. Blaser, “Interpolation of scattered 3d ptv data to a rectangular grid,” J. Fluid Mech. 185, 447–468 (1987).

Stüer, H.

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

Tagare, H.

Thielicke, W.

W. Thielicke and E. Stamhuis, “Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab,” J. Open Res. Softw. 2, e30 (2014).
[Crossref]

W. Thielicke, “The flapping flight of birds: Analysis and application,” Ph.D. thesis, University of Groningen (2014).

W. Thielicke and E. J. Stamhuis, “Pivlab - time-resolved digital particle image velocimetry tool for matlab,” (2018).

Tinevez, J.-Y.

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Tomancak, P.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Unterhuber, A.

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

Vlasenko, A.

A. Vlasenko, E. C. C. Steele, and W. A. M. Nimmo-Smith, “A physics-enabled flow restoration algorithm for sparse piv and ptv measurements,” Meas. Sci. Technol. 26, 065301 (2015).
[Crossref]

Warkman, A. S.

A. S. Warkman and P. A. Krieg, “Xenopus as a model system for vertebrate heart development,” in Seminars in cell & developmental biology, vol. 18 (Elsevier, 2007), pp. 46–53.
[Crossref]

Werner, M.

M. Werner and B. Mitchell, “Understanding ciliated epithelia: the power of xenopus,” Genesis 50, 176–185 (2012).
[Crossref]

White, D. J.

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Williams, C. K. I.

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (The MIT Press, 2005).
[Crossref]

Wu, W.

Zar, H. J.

H. J. Zar and T. W. Ferkol, “The global burden of respiratory disease - impact on child health,” Pediatr. Pulmonol. 49, 430–434 (2014).
[Crossref] [PubMed]

Zhou, K. C.

Zhu, B.

Biomed. Opt. Express (4)

Genesis (2)

M. K. Khokha, “Xenopus white papers and resources: folding functional genomics and genetics into the frog,” Genesis 50, 133–142 (2012).
[Crossref] [PubMed]

M. Werner and B. Mitchell, “Understanding ciliated epithelia: the power of xenopus,” Genesis 50, 176–185 (2012).
[Crossref]

J. Biomed. Opt. (2)

B. K. Huang, U. A. Gamm, S. Jonas, M. K. Khokha, and M. A. Choma, “Quantitative optical coherence tomography imaging of intermediate flow defect phenotypes in ciliary physiology and pathophysiology,” J. Biomed. Opt. 20, 030502 (2015).
[Crossref] [PubMed]

W. Drexler, M. Liu, A. Kumar, T. Kamali, A. Unterhuber, and R. A. Leitgeb, “Optical coherence tomography today: speed, contrast, and multimodality,” J. Biomed. Opt. 19, 071412 (2014).
[Crossref] [PubMed]

J. Fluid Mech. (2)

J. C. Agui and J. Jimenez, “On the performance of particle tracking,” J. Fluid Mech. 185, 447–468 (1987).
[Crossref]

H. Stuer and S. Blaser, “Interpolation of scattered 3d ptv data to a rectangular grid,” J. Fluid Mech. 185, 447–468 (1987).

J. Open Res. Softw. (1)

W. Thielicke and E. Stamhuis, “Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab,” J. Open Res. Softw. 2, e30 (2014).
[Crossref]

J. Struct. Biol. (1)

I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol. 151, 182–195 (2005).
[Crossref] [PubMed]

J. Vis. Exp. (1)

J.-T. Kim, D. Kim, A. Liberzon, and L. P. Chamorro, “Three-dimensional particle tracking velocimetry for turbulence applications: Case of a jet flow,” J. Vis. Exp. 108, e53745 (2016).

Meas. Sci. Technol. (2)

A. Vlasenko, E. C. C. Steele, and W. A. M. Nimmo-Smith, “A physics-enabled flow restoration algorithm for sparse piv and ptv measurements,” Meas. Sci. Technol. 26, 065301 (2015).
[Crossref]

F. Pereira, H. Stüer, E. C. Graff, and M. Gharib, “Two-frame 3d particle tracking,” Meas. Sci. Technol. 17, 1680 (2006).
[Crossref]

Methods (1)

J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri, “Trackmate: An open and extensible platform for single-particle tracking,” Methods 115, 80–90 (2017).
[Crossref]

Mol. Rep. Dev. (1)

J. Schindelin, C. T. Rueden, M. C. Hiner, and K. W. Eliceiri, “The imagej ecosystem: an open platform for biomedical image analysis,” Mol. Rep. Dev. 82, 518–529 (2015).
[Crossref]

Nat. Methods (1)

J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, “Fiji: an open-source platform for biological-image analysis,” Nat. Methods 9, 676 (2012).
[Crossref] [PubMed]

Opt. Express (1)

Pediatr. Pulmonol. (1)

H. J. Zar and T. W. Ferkol, “The global burden of respiratory disease - impact on child health,” Pediatr. Pulmonol. 49, 430–434 (2014).
[Crossref] [PubMed]

Other (7)

A. S. Warkman and P. A. Krieg, “Xenopus as a model system for vertebrate heart development,” in Seminars in cell & developmental biology, vol. 18 (Elsevier, 2007), pp. 46–53.
[Crossref]

W. Thielicke, “The flapping flight of birds: Analysis and application,” Ph.D. thesis, University of Groningen (2014).

W. Thielicke and E. J. Stamhuis, “Pivlab - time-resolved digital particle image velocimetry tool for matlab,” (2018).

C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (The MIT Press, 2005).
[Crossref]

C. M. Bishop, Pattern Recognition and Machine Learning (Springer Science+Business Media, LLC, 2006), 1st ed.

MATLAB, version 9.4.0 (R2018a) (The MathWorks Inc., Natick, Massachusetts, 2018).

J. M. Cimbala and Y. A. Cengel, Essentials of Fluid Mechanics, Fundamentals and Applcations (McGraw-Hill, 2008).

Supplementary Material (6)

NameDescription
» Data File 1       Table describing TrackMate parameters used to generate tracks used for analysis in paper.
» Data File 2       Table of hyperparameters (theta_signal, sigma_noise for both components, theta_width for both components) obtained from Stage 3 (GPR) of our algorithm. While these hyperparameters are deterministic, we include these for completeness.
» Visualization 1       OCT video of cilia-driven flow in Xenopus embryo (low-flow)
» Visualization 2       OCT video of cilia-driven flow in Xenopus embryo (mid-flow)
» Visualization 3       OCT video of cilia-driven flow in Xenopus embryo (high-flow)
» Visualization 4       OCT video of pipe phantom

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Figures (10)

Fig. 1
Fig. 1 The processing pipeline. Stage 1 consists of the PTV and the the fluid region segmenter. Stage 2 creates velocity vectors from tracks, projects them on the image, and deletes outliers. Stage 3 smoothes and interpolates the vectors to get a dense flow velocity map.
Fig. 2
Fig. 2 Details of Stage 2 of the algorithm. (a) Image sequence is grouped into consecutive N frames. Each track in one set of set of frames is approximated by straight line, and the velocity vector calculated from this is projected onto the image plane. (b) Overlapping windows are used to reject outlier velocities. (c) Vectors within a window are shifted to a common origin and compared with the median vector to identify and delete outliers (see text for details), and (d) the output is a discrete set of noisy flow vectors in the image. Note that the vectors displayed above in (b),(c), and (d) are only illustrative, and are not the result of applying the algorithm to any data set.
Fig. 3
Fig. 3 A zoomed-in portion of the high-flow sequence, demonstrating the inputs and output of Stage 2. The blue curves are tracks found by TrackMate. The arrows are the velocities found by linear fitting in Stage 2, scaled by 10 for visibility. The red arrow is a velocity detected as an outlier and deleted, while the green arrows are inliers and used as input for Stage 3
Fig. 4
Fig. 4 PTV, Stage 2 and GPR velocity estimates for beads in a laminar flow in a cylindrical Pipe. (a) Streak image from the OCT video in Visualization 1, (b) PTV (black arrows), Stage 2 (blue arrows) and GPR velocity (red arrow) estimates, (c) – (d) the fit of a quadratic model to the x- and y- components of the velocity.
Fig. 5
Fig. 5 Imaging preparation. Petri dish coated with clay in which a well is formed. Xenopus embryo are fixed in a slit in the well.
Fig. 6
Fig. 6 Fluid velocity estimates in the low-flow stage. Visualization 2 contains the OCT video, with a single frame shown in (a).
Fig. 7
Fig. 7 Fluid velocity estimates in the mid-flow stage. Visualization 3 contains the OCT video, with a single frame shown in (a).
Fig. 8
Fig. 8 Fluid velocity estimates in the high-flow stage. Visualization 4 contains the OCT video, with a single frame shown in (a).
Fig. 9
Fig. 9 Histograms of normalized differences of velocity estimates of subvideos
Fig. 10
Fig. 10 GPR output for different levels of deletion in the rectangular region shown in the top row. (a) Left column: 0% deletion. (b) Middle column: 50% deletion. (c) Right column: 100% deletion. Top row: input to GPR. Middle row: GPR interpolated velocity estimates. Bottom row: Standard deviation of the velocity estimates.

Tables (3)

Tables Icon

Table 1 Quadratic fits to x- and y-components of PTV and GPR velocities. The variable d in the best fit polynomial is distance along the section. The R value indicates the goodness-of-fit; R values are between 0 and 1, with 1 being a perfect fit.

Tables Icon

Table 2 Fraction of pixels in the segmented region whose normalized difference is less than 1

Tables Icon

Table 3 Track densities and average velocities of the data sets

Equations (9)

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ν x * = median ( ν 1 , x , , ν k 1 , x ) , and ν y * = median ( ν 1 , y , , ν k 1 , y ) ,
k ( x 1 , x 2 ) = θ s 2 exp ( x 1 x 2 2 / 2 θ w 2 )
μ = ( μ ( x 1 ) μ ( x m ) ) , μ * = ( μ ( x m + 1 ) μ ( x N ) ) ,
ν = μ + ,
E [ μ i * μ j * ] = k ( x m + i , x m + j ) , E [ μ i * ν j ] = E [ μ i * ( μ j + j ) ] = k ( x m + i , x j ) , E [ ν i ν j ] = E [ ( μ i + i ) ( μ j + j ) ] = k ( x i , x j ) + σ n 2 δ i j ,
C = ( C μ * μ * C μ * ν C μ * ν T C ν ν . )
p ( μ * | ν ) = 𝒩 ( C μ * ν C ν ν 1 ν , C μ * μ * C μ * ν C ν ν 1 C μ * ν T ) .
( θ w 2 , σ n 2 ) = arg max θ w 2 , σ n 2 log p ( ν 1 , , ν m | θ w , σ n 2 ) .
μ 1 μ 2 σ x , 1 2 + σ y , 1 2 + σ x , 2 2 + σ y , 2 2 .