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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 2, Iss. 7 — Jul. 1, 2011
  • pp: 2022–2034
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Microfluidic characterization of cilia-driven fluid flow using optical coherence tomography-based particle tracking velocimetry

Stephan Jonas, Dipankan Bhattacharya, Mustafa K. Khokha, and Michael A. Choma  »View Author Affiliations


Biomedical Optics Express, Vol. 2, Issue 7, pp. 2022-2034 (2011)
http://dx.doi.org/10.1364/BOE.2.002022


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Abstract

Motile cilia are cellular organelles that generate directional fluid flow across various epithelial surfaces including the embryonic node and respiratory mucosa. The proper functioning of cilia is necessary for normal embryo development and, for the respiratory system, the clearance of mucus and potentially harmful particulate matter. Here we show that optical coherence tomography (OCT) is well-suited for quantitatively characterizing the microfluidic-scale flow generated by motile cilia. Our imaging focuses on the ciliated epithelium of Xenopus tropicalis embryos, a genetically manipulable and experimentally tractable animal model of human disease. We show qualitative flow profile characterization using OCT-based particle pathline imaging. We show quantitative, two-dimensional, two-component flow velocity field characterization using OCT-based particle tracking velocimetry. Quantitative imaging and phenotyping of cilia-driven fluid flow using OCT will enable more detailed research in ciliary biology and in respiratory medicine.

© 2011 OSA

1. Background

Motile cilia are organelles that protrude from cells and generate directional, low Reynolds number fluid flow [1

1. H. C. Berg, Random Walks in Biology, revised ed. (Princeton University Press, 1993).

] at speeds of ~1-1000 μm/s [2

2. Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]

5

5. B. Guirao, A. Meunier, S. Mortaud, A. Aguilar, J. M. Corsi, L. Strehl, Y. Hirota, A. Desoeuvre, C. Boutin, Y. G. Han, Z. Mirzadeh, H. Cremer, M. Montcouquiol, K. Sawamoto, and N. Spassky, “Coupling between hydrodynamic forces and planar cell polarity orients mammalian motile cilia,” Nat. Cell Biol. 12(4), 341–350 (2010). [CrossRef] [PubMed]

]. During embryo development, cilia-driven fluid flow is essential to normal left-right axis development [2

2. Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]

]. In addition, there is evidence that cilia-driven fluid flow is important for the development of the inner ear [6

6. J. R. Colantonio, J. Vermot, D. Wu, A. D. Langenbacher, S. Fraser, J. N. Chen, and K. L. Hill, “The dynein regulatory complex is required for ciliary motility and otolith biogenesis in the inner ear,” Nature 457(7226), 205–209 (2009). [CrossRef] [PubMed]

] and central nervous system [7

7. A. G. Kramer-Zucker, F. Olale, C. J. Haycraft, B. K. Yoder, A. F. Schier, and I. A. Drummond, “Cilia-driven fluid flow in the zebrafish pronephros, brain and Kupffer’s vesicle is required for normal organogenesis,” Development 132(8), 1907–1921 (2005). [CrossRef] [PubMed]

]. Several different epithelial cell types have motile cilia, including respiratory, ependymal, and fallopian tube (oviduct) epithelium [8

8. K. Baker and P. L. Beales, “Making sense of cilia in disease: the human ciliopathies,” Am. J. Med. Genet. C. Semin. Med. Genet. 151C(4), 281–295 (2009). [CrossRef] [PubMed]

]. Respiratory cilia drive the directional flow of mucus, and defects in these cilia can lead to recurrent sinopulmonary infections [8

8. K. Baker and P. L. Beales, “Making sense of cilia in disease: the human ciliopathies,” Am. J. Med. Genet. C. Semin. Med. Genet. 151C(4), 281–295 (2009). [CrossRef] [PubMed]

]. Ependymal cilia drive cerebrospinal fluid flow, a flow that carries new neurons in the adult brain [9

9. K. Sawamoto, H. Wichterle, O. Gonzalez-Perez, J. A. Cholfin, M. Yamada, N. Spassky, N. S. Murcia, J. M. Garcia-Verdugo, O. Marin, J. L. R. Rubenstein, M. Tessier-Lavigne, H. Okano, and A. Alvarez-Buylla, “New neurons follow the flow of cerebrospinal fluid in the adult brain,” Science 311(5761), 629–632 (2006). [CrossRef] [PubMed]

]. Fallopian tube cilia that line the luminal epithelium are important in tubal transport of ova [10

10. R. A. Lyons, E. Saridogan, and O. Djahanbakhch, “The reproductive significance of human Fallopian tube cilia,” Hum. Reprod. Update 12(4), 363–372 (2006). [CrossRef] [PubMed]

]. Therefore, understanding ciliary physiology and cilia-driven fluid flow has broad relevance in medicine.

Like electro-osmotic driven flow in microfabricated microfluidic systems [11

11. H. A. Stone, A. D. Stroock, and A. Ajdari, “Engineering flows in small devices: microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid Mech. 36(1), 381–411 (2004). [CrossRef]

,12

12. A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, “Patterning electro-osmotic flow with patterned surface charge,” Phys. Rev. Lett. 84(15), 3314–3317 (2000). [CrossRef] [PubMed]

], cilia-driven fluid flow is a surface-driven flow generated by the application of a body force at a distance above a surface [13

13. B. Guirao and J. F. Joanny, “Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia,” Biophys. J. 92(6), 1900–1917 (2007). [CrossRef] [PubMed]

]. Cilia-driven flow physiology has been investigated using a variety of imaging techniques. However, the quantitative nature of cilia-driven flow is incompletely characterized. One of the main challenges in imaging cilia-driven fluid flow is that the ciliated surface that drives the flow is often orthogonal to the optical axis (Fig. 1
Fig. 1 Left: Idealized cilia-driven flow seeded with tracer particles (black dots). Velocity vectors v(x,y,z) are open-tipped arrows. The ability of OCT to perform depth-resolved imaging along its depth of focus (DOF) enables visualization of flow generated by a ciliated surface that is largely orthogonal to the optical axis. Right: Scanning electron micrograph of a ciliated Xenopus tropicalis epithelial cell. Each multicilated cell is surrounded by several non-ciliated cells. The scale bar is 5 μm.
). As a consequence, depth-resolved imaging is required to characterize two- and three-dimensional features of the flow field. Current methods, including dye imaging [9

9. K. Sawamoto, H. Wichterle, O. Gonzalez-Perez, J. A. Cholfin, M. Yamada, N. Spassky, N. S. Murcia, J. M. Garcia-Verdugo, O. Marin, J. L. R. Rubenstein, M. Tessier-Lavigne, H. Okano, and A. Alvarez-Buylla, “New neurons follow the flow of cerebrospinal fluid in the adult brain,” Science 311(5761), 629–632 (2006). [CrossRef] [PubMed]

,14

14. B. Mitchell, J. L. Stubbs, F. Huisman, P. Taborek, C. Yu, and C. Kintner, “The PCP pathway instructs the planar orientation of ciliated cells in the Xenopus larval skin,” Curr. Biol. 19(11), 924–929 (2009). [CrossRef] [PubMed]

], light microscopy-based particle pathline imaging and particle tracking imaging [2

2. Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]

,3

3. B. Mitchell, R. Jacobs, J. Li, S. Chien, and C. Kintner, “A positive feedback mechanism governs the polarity and motion of motile cilia,” Nature 447(7140), 97–101 (2007). [CrossRef] [PubMed]

,15

15. R. J. Francis, B. Chatterjee, N. T. Loges, H. Zentgraf, H. Omran, and C. W. Lo, “Initiation and maturation of cilia-generated flow in newborn and postnatal mouse airway,” Am. J. Physiol. Lung Cell. Mol. Physiol. 296(6), L1067–L1075 (2009). [CrossRef] [PubMed]

,16

16. K. Ikegami, S. Sato, K. Nakamura, L. E. Ostrowski, and M. Setou, “Tubulin polyglutamylation is essential for airway ciliary function through the regulation of beating asymmetry,” Proc. Natl. Acad. Sci. U.S.A. 107(23), 10490–10495 (2010). [CrossRef] [PubMed]

], and real-time digitally subtracted radiography [9

9. K. Sawamoto, H. Wichterle, O. Gonzalez-Perez, J. A. Cholfin, M. Yamada, N. Spassky, N. S. Murcia, J. M. Garcia-Verdugo, O. Marin, J. L. R. Rubenstein, M. Tessier-Lavigne, H. Okano, and A. Alvarez-Buylla, “New neurons follow the flow of cerebrospinal fluid in the adult brain,” Science 311(5761), 629–632 (2006). [CrossRef] [PubMed]

], are not depth-resolved. Scanning a high numerical aperture (NA>1) focus through the nodal pit was used to observe recirculating nodal flow [2

2. Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]

]. However, this method has poor depth sectioning compared to confocal microscopy [17

17. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

] and optical coherence tomography/microscopy [18

18. J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissues,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1017–1028 (1996). [CrossRef]

].

Optical coherence tomography (OCT) is an attractive imaging modality for the in vivo quantitative vectorial imaging of cilia-driven flow. OCT is a non-destructive imaging modality that is capable of cross-sectional imaging at micron-scale resolutions [19

19. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

,20

20. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]

]. OCT has demonstrated utility in the in vivo imaging of microscale motions and flow [21

21. M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. 11(2), 024014 (2006). [CrossRef] [PubMed]

23

23. M. A. Choma, M. J. Suter, B. J. Vakoc, B. E. Bouma, and G. J. Tearney, “Physiological homology between Drosophila melanogaster and vertebrate cardiovascular systems,” Dis Model Mech 4(3), 411–420 (2011). [CrossRef] [PubMed]

]. In addition, OCT has been used to characterize flow in microfabricated microfluidic systems [24

24. C. W. Xi, D. L. Marks, D. S. Parikh, L. Raskin, and S. A. Boppart, “Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography,” Proc. Natl. Acad. Sci. U.S.A. 101(20), 7516–7521 (2004). [CrossRef] [PubMed]

,25

25. Y. C. Ahn, W. G. Jung, and Z. P. Chen, “Optical sectioning for microfluidics: secondary flow and mixing in a meandering microchannel,” Lab Chip 8(1), 125–133 (2008). [CrossRef] [PubMed]

], including flow driven by biomimetic artificial cilia [26

26. M. Baltussen, P. Anderson, F. Bos, and J. den Toonder, “Inertial flow effects in a micro-mixer based on artificial cilia,” Lab Chip 9(16), 2326–2331 (2009). [CrossRef] [PubMed]

]. Although Doppler OCT has, in principle, the phase sensitivity to detect flows in the 1-1000 μm/s range [21

21. M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. 11(2), 024014 (2006). [CrossRef] [PubMed]

], Doppler OCT requires multi-angle illumination optics to extract two-component (i.e. v = vx i + vz k) and three-component (i.e. v = vx i + vy j + vz k) velocity vector information [27

27. C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007). [CrossRef] [PubMed]

,28

28. Y. C. Ahn, W. Jung, and Z. P. Chen, “Quantification of a three-dimensional velocity vector using spectral-domain Doppler optical coherence tomography,” Opt. Lett. 32(11), 1587–1589 (2007). [CrossRef] [PubMed]

]. An alternate approach employed in cardiovascular imaging is to estimate the Doppler angle through structural OCT imaging the vessel lumen [29

29. S. Makita, T. Fabritius, and Y. Yasuno, “Quantitative retinal-blood flow measurement with three-dimensional vessel geometry determination using ultrahigh-resolution Doppler optical coherence angiography,” Opt. Lett. 33(8), 836–838 (2008). [CrossRef] [PubMed]

32

32. A. S. G. Singh, C. Kolbitsch, T. Schmoll, and R. A. Leitgeb, “Stable absolute flow estimation with Doppler OCT based on virtual circumpapillary scans,” Biomed. Opt. Express 1(4), 1047–1058 (2010). [CrossRef] [PubMed]

]. While this approach is well-suited to parabolic microvascular and embryonic blood flow since the flow is confined to well-defined geometries, the approach is not well-suited to cilia-driven flow, which occurs in open geometries with less well-characterized flow profiles. An alternate approach to Doppler flow imaging is to track individual seed particles over time (i.e. particle tracking velocimetry (PTV) [33

33. R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23(1), 261–304 (1991). [CrossRef]

35

35. S. J. Lee and S. Kim, “Advanced particle-based velocimetry techniques for microscale flows,” Microfluidics Nanofluidics 6(5), 577–588 (2009). [CrossRef]

]). PTV is particularly useful when the flow can be sparsely seeded with tracer microparticles. PTV also is useful when simplifying geometric assumptions regarding flow patterns may not be appropriate. OCT is well-suited to PTV in that a B-scan is geometrically similar to sheet illumination typically employed by light microscopy-based PTV setups. In traditional PTV, sheet illumination ensures that seed particles from a specific plane are imaged [36

36. M. Raffel, C. E. Willert, S. T. Wereley, and J. Kompenhans, “Introduction,” in Particle Image Velocimetry, 2nd ed. (Springer, New York, 2007).

]. In OCT, linear scanning the low numerical aperture sample beam also ensures that seed particles from a specific plane are imaged.

2. Methods

2.1. Xenopus tropicalis culture and preparation

X. tropicalis embryos were generated according to established protocols [38

38. M. K. Khokha, C. Chung, E. L. Bustamante, L. W. Gaw, K. A. Trott, J. Yeh, N. Lim, J. C. Lin, N. Taverner, E. Amaya, N. Papalopulu, J. C. Smith, A. M. Zorn, R. M. Harland, and T. C. Grammer, “Techniques and probes for the study of Xenopus tropicalis development,” Dev. Dyn. 225(4), 499–510 (2002). [CrossRef] [PubMed]

]. All animal work was done in accordance with Yale IACUC approval.

2.2. OCT imaging, OCT pathline imaging, and color-encoding of time image processing

OCT imaging was performed using a commercially available OCT system (Thorlabs, Inc., Newton, NJ, USA) with an A-scan rate of 16 kHz and a center wavelength of 1325 nm, a transverse resolution of 25 μm, and an axial resolution of 9 μm in water. For OCT imaging, the embryos were placed in a custom-made well of a rubber O-ring glued to a frosted cover glass (Fig. 2
Fig. 2 Photomicrograph of stage 36 X. tropicalis embryo in a well for OCT imaging.
). Cilia-driven fluid flow was seeded with 5 μm diameter polystyrene microspheres (Bangs Laboratories, Fishers, IN, USA). For a discretely indexed image stack Iij(mΔt), two-dimensional particle pathlines can be estimated by taking the maximum projection image across time. For log-transformed images, the minimum projection image across time provides an estimate of the stationary background image Bij. Background-free pathline images were generated by taking the maximum projection across time of Iij(mΔt)-Bij.

Pathline imaging can be enhanced to color-encode time [4

4. F. Miskevich, “Imaging fluid flow and cilia beating pattern in Xenopus brain ventricles,” J. Neurosci. Methods 189(1), 1–4 (2010). [CrossRef] [PubMed]

,6

6. J. R. Colantonio, J. Vermot, D. Wu, A. D. Langenbacher, S. Fraser, J. N. Chen, and K. L. Hill, “The dynein regulatory complex is required for ciliary motility and otolith biogenesis in the inner ear,” Nature 457(7226), 205–209 (2009). [CrossRef] [PubMed]

]. Time is encoded by assigning each image a color according to its timestamp and projecting all images over time. Adding time to the visualization reveals information about the direction of flow. Further, changes in colors also give a qualitative sense of flow rates. Our color-encoding algorithm used six colors: red, green, blue, yellow, cyan, and magenta. For M images (M mod 6 = 0), the MATLAB pseudocode that generates the red, green, and blue color channels (Ir, Ig, Ib) of the color-encoded pathline image is the following:

    Ir = zeros(); Ig = zeros(); Ib = zeros();
    %initialize three empty channels
    for k = 1 to M/6,    %walk through all images
    Ir = Ir     %accumulate red intensities
     + I(0M/6 + k)    %add red for red/first time stamp
     + I(3M/6 + k)    %add red for yellow/fourth time stamp
     + I(5M/6 + k);    %add red for magenta/sixth time stamp
    Ig = Ig     %accumulate green intensities
     + I(1M/6 + k)    %add green for green/second time stamp
     + I(3M/6 + k)    %add green for yellow/fourth time stamp
     + I(4M/6 + k);    %add green for cyan/fifth time stamp
    Ib = Ib     %accumulate blue intensities
     + I(2M/6 + k)    %add blue for blue/third time stamp
     + I(4M/6 + k)    %add blue for cyan/fifth time stamp
     + I(5M/6 + k);    %add blue for magenta/sixth time stamp
    end
    Ir = Ir./Imean; Ig = Ig./Imean; Ib = Ib./Imean;
    %scale channels with mean intensity

Particle tracking velocimetry analysis was performed using custom Python code. Our process for OCT-based particle tracking velocimetry is outlined in Fig. 3
Fig. 3 Top: Particle and embryo coordinate system. Bottom: Overview of image processing for OCT-based particle tracking velocimetry. tan−1 is the four-quadrant arctangent function.
. The four major steps are image segmentation, particle identification, particle localization, and particle pairing. The first three steps are performed on individual images, while the last step (particle pairing) is performed on each pair of consecutive images. The goal of image segmentation is to distinguish flow tracer particles from the rest of the image. We employed an intensity-based threshold algorithm that uses a threshold intensity Pt to classify a pixel as particle or non-particle. Thus, for a discretely indexed image Iij, a binary segmentation mask Pij is defined as Pij = 1 if Iij>Pt and Pij = 0 otherwise (see, for example, Ref. [39

39. A. Patwardhan, “Subpixel position measurement using 1D, 2D and 3D centroid algorithms with emphasis on applications in confocal microscopy,” J. Microsc. (Oxford) 186(3), 246–257 (1997). [CrossRef]

].). The binary segmentation mask Pij can exclude stationary object by applying the threshold criteria to a background-free image (Iij-Bij) where Bij = min(Iij,T). Here, min() returns the minimum value of each pixel in Iij over a given time interval T.

I(x,z,mΔt)=n=1NPSF(x,z)δ(xxn(mΔt),zzn(mΔt)).
(1)

Here, I(x,z,mΔt) is the image volume formed by n particles located at (xn(mΔt), zn(mΔt)), PSF(x,z) is the two-dimensional OCT point spread function, δ(x,z) is Dirac’s delta function, and ⊗ is the convolution operator. In mathematical terms, the goal of localization is to estimate (xn(mΔt), zn(mΔt)). We will use the center-of-mass location of the particle (xc,n(mΔt), zc,n(mΔt)) as an estimate of the particle location. The center-of-mass coordinates of the nth particle can be calculated using [39

39. A. Patwardhan, “Subpixel position measurement using 1D, 2D and 3D centroid algorithms with emphasis on applications in confocal microscopy,” J. Microsc. (Oxford) 186(3), 246–257 (1997). [CrossRef]

]

xc,n=ijROIniPijIijijROInPijIij;zc,n=ijROInjPijIijijROInPijIij.
(2)

Here, ROIn is a volumetric region of interest defined by the boundaries of the nth particle.

Image segmentation, particle identification, particle localization, and particle pairing provides the information needed for OCT-based particle tracking velocimetry. OCT-based particle tracking velocimetry calculates the displacement of the nth particle along each Cartesian axis from time mΔt to time (m + 1)Δt. Thus, the velocity v x,n along the x-axis is given by [33

33. R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Annu. Rev. Fluid Mech. 23(1), 261–304 (1991). [CrossRef]

35

35. S. J. Lee and S. Kim, “Advanced particle-based velocimetry techniques for microscale flows,” Microfluidics Nanofluidics 6(5), 577–588 (2009). [CrossRef]

]:

Δxn(mΔt)=xn((m+1)Δt)xn(mΔt);vx,n(mΔt)=Δxn(mΔt)Δt.
(3)

Each velocity measurement is located at the calculated center-of-mass of the nth particle during the mth volume acquisition. Δzn and v z,n are defined in a likewise manner. The velocity of the nth particle also can be expressed in polar coordinates (|vn(mΔt)|,θn(mΔt)) (Fig. 3):

|vn(mΔt)|=Δxn2+Δyn2+Δzn2Δt;θn(mΔt)=tan1(ΔznΔxn).
(4)

Here, tan−1() is the four-quadrant artangent function.

2.3. Suitability of tracer particle for flow estimation

The 5 μm diameter polystyrene microspheres are expected to be good flow tracers because they have small expected values for slip velocity and for Brownian motion between consecutive images. Slip velocity (vslip) is the difference between particle velocity and the surrounding fluid flow velocity. A small slip velocity is therefore desirable. vslip is given by [43

43. B. J. McKeon, G. v. Comte-Bellot, J. F. Foss, J. Westerweel, F. Scarano, C. Tropea, J. F. Meyers, J. W. Lee, A. A. Cavone, R. Schodl, M. M. Koochesfahani, D. G. Nocera, Y. Andreopoulos, W. J. A. Dahm, J. A. Mullin, J. M. Wallace, P. V. Vukoslavcevic, S. C. Morris, E. R. Pardyjak, and A. Cuerva, “Velocity, vorticity, and Mach number,” in Springer Handbook of Experimental Fluid Mechanics, C. Tropea, A. L. Yarin, and J. F. Foss, eds. (Springer-Verlag, Berlin, 2007), p. 288.

]:

vslip=29r2(ρpρw)ηap,
(5)

where r is the particle radius, ρp is particle mass density (1.06 g/cm3), ρw is water mass density (1 g/cm3), η is the dynamic viscosity of water (10−3 kg/(m s), and ap is the particle acceleration. Acceleration secondary to gravity generates a very small slip velocity (~0.8 μm/s). Acceleration secondary to time-variation in fluid flow is expected to be even yet smaller. A flow acceleration of ~10 m/s2, the equivalent of accelerating fluid from 0 to 10 mm/s in 1 ms, would be required to generate slip of ~1 μm/s. Cilia-driven fluid flow varies much more slowly than this. In terms of Brownian motion between images, root mean square displacement srms in two dimensions is given by [1

1. H. C. Berg, Random Walks in Biology, revised ed. (Princeton University Press, 1993).

]:

srms=(4DΔt)1/2,
(6)

where D is the particle diffusivity (D~r −1) and Δt is the time interval of interest. Using diffusivity as defined in [44

44. D. A. Boas, K. K. Bizheva, and A. M. Siegel, “Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media,” Opt. Lett. 23(5), 319–321 (1998). [CrossRef] [PubMed]

] and using Δt = 24 ms (the inter-frame interval for the particle tracking experiments), srms~0.1 μm.

3. Results and discussion

Figures 6 and 7 demonstrate two-dimensional, two-component flow velocimetry using OCT-based PTV. Figure 7 is the same embryo in Fig. 6 except it is sitting in a significantly smaller volume of physiologic solution. The orientation of the embryo is otherwise the same in the two figures. Consistency of orientation was ensured by performing imaging in a large volume (Fig. 6) and then removing fluid using a micropipette (Fig. 7). Figures 6a and 7a show particle pathline images, and Figs. 6b and 7b show the two-dimensional, two-component flow velocity fields. Flow velocities span about two orders of magnitude from ~1 to 100 μm/s. For comparison, retinal microvascular bloodflow has maximum velocities of tens of mm/s [29

29. S. Makita, T. Fabritius, and Y. Yasuno, “Quantitative retinal-blood flow measurement with three-dimensional vessel geometry determination using ultrahigh-resolution Doppler optical coherence angiography,” Opt. Lett. 33(8), 836–838 (2008). [CrossRef] [PubMed]

,32

32. A. S. G. Singh, C. Kolbitsch, T. Schmoll, and R. A. Leitgeb, “Stable absolute flow estimation with Doppler OCT based on virtual circumpapillary scans,” Biomed. Opt. Express 1(4), 1047–1058 (2010). [CrossRef] [PubMed]

,46

46. H. Wehbe, M. Ruggeri, S. Jiao, G. Gregori, C. A. Puliafito, and W. Zhao, “Automatic retinal blood flow calculation using spectral domain optical coherence tomography,” Opt. Express 15(23), 15193–15206 (2007). [CrossRef] [PubMed]

,47

47. R. M. Werkmeister, N. Dragostinoff, M. Pircher, E. Götzinger, C. K. Hitzenberger, R. A. Leitgeb, and L. Schmetterer, “Bidirectional Doppler Fourier-domain optical coherence tomography for measurement of absolute flow velocities in human retinal vessels,” Opt. Lett. 33(24), 2967–2969 (2008). [CrossRef] [PubMed]

], and early embryonic blood flow has maximum velocities of ~1-10 mm/s [23

23. M. A. Choma, M. J. Suter, B. J. Vakoc, B. E. Bouma, and G. J. Tearney, “Physiological homology between Drosophila melanogaster and vertebrate cardiovascular systems,” Dis Model Mech 4(3), 411–420 (2011). [CrossRef] [PubMed]

,31

31. Z. Ma, A. Liu, X. Yin, A. Troyer, K. Thornburg, R. K. Wang, and S. Rugonyi, “Measurement of absolute blood flow velocity in outflow tract of HH18 chicken embryo based on 4D reconstruction using spectral domain optical coherence tomography,” Biomed. Opt. Express 1(3), 798–811 (2010). [CrossRef] [PubMed]

,48

48. J. R. Hove, R. W. Köster, A. S. Forouhar, G. Acevedo-Bolton, S. E. Fraser, and M. Gharib, “Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis,” Nature 421(6919), 172–177 (2003). [CrossRef] [PubMed]

50

50. M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010). [CrossRef] [PubMed]

]. Assuming a cilia length of 20 micrometers and a maximum flow velocity of 300 micrometers per second, the Reynolds number is ~2 × 10−3. Even if the embryo body length is used as characteristic size scale in calculating Reynolds number, Reynolds number is ~0.3, much less than 1. The low Reynolds number reinforces that the recirculatory/vortical cilia-driven fluid flow profiles are not turbulent but rather a manifestation of flow dominated by viscous forces in a complex three-dimensional geometry.

Our particle tracking data additionally allowed us to measure how long a particle resided within the B-scan field of view. The results shown in Fig. 8
Fig. 8 Particle residence time in B-scan field of view. The embryo has the same position and orientation as in Fig. 6. The grayscale intensity of the streaks encodes the duration in the field of view. The red rectangle marks the particle that was used for the upper plots in Fig. 9, blue marks the particle used for the lower plots in Fig. 9.
show particle pathlines grayscale encoded with residence time in the field of view. While this map cannot give us quantitative measurement of the flow velocities along the y-axis, it can give us a qualitative sense of the three-dimensional flow patterns. For example, for vortical flow that is roughly parallel or antiparallel to the z-axis, there seems to be less vigorous out-of-plane motion since the residence time in the field of view seems to be longer. Further, for vortical flow parallel or antiparallel to the x-axis, out-of-plane flow seems to be more vigorous since the residence time for these particles is shorter.

Since cilia-driven fluid flow is slow, the calculated frame-to-frame particle displacements were often less than one pixel. In order to minimize errors in velocity calculations, we employed averaging of repeated measurements. For example, in order to generate Fig. 6, a total of ~50,000 frame-to-frame particle displacement measurements were calculated. The ~400 velocity vectors were generated by spatially binning and averaging these individual calculations. Therefore, each velocity vector is the result of ~125 displacement measurements. To demonstrate that spatial averaging results in a value that converges to the expected mean displacement (and therefore expected mean velocity), Fig. 9
Fig. 9 Plots demonstrating convergence of estimated particle displacement as a function of measurements used in the estimation. The plots on the left side display mean displacement along the x-axis, the right plots mean displacement along the z-axis. The upper two plots are extracted from the pathline in the red rectangle in Fig. 8, the lower two plots are extracted from the pathline in the blue rectangle.
shows the average displacement values as a function of number of measurements for two particles traveling at a relatively steady velocity (see Fig. 8 for the pathlines corresponding to these particles). Both x and z displacements converge towards the mean velocity for that streak as more frames are considered. There is notable decrease in the variability in the average displacement once several tens of measurements are included in the calculation, thereby justifying our use of ~125 displacement measurements per velocity vector.

4. Conclusion

The methods and results shown here demonstrate that OCT is uniquely well-suited for the quantitative in vivo imaging of cilia-driven fluid flow. In particular, OCT is able to visualize flow profiles in planes that are orthogonal to a ciliated epithelial surface, a notable shortcoming in previously used imaging approaches. The ability of OCT to perform cross-sectional imaging enables calculation of two-dimensional, two-component flow velocity maps using particle tracking velocimetry methods. OCT-based particle tracking velocimetry can be used to characterize or phenotype flow velocities and flow profiles (i.e. recirculatory/vortical flow versus directional flow). It is worth noting that, in contrast to particle tracking, single-beam Doppler OCT yields only one-component vector flow measurements, and that having two- or three-component Doppler flow vector measurements require multiangle approaches [27

27. C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007). [CrossRef] [PubMed]

,49

49. N. V. Iftimia, D. X. Hammer, R. D. Ferguson, M. Mujat, D. Vu, and A. A. Ferrante, “Dual-beam Fourier domain optical Doppler tomography of zebrafish,” Opt. Express 16(18), 13624–13636 (2008). [CrossRef] [PubMed]

]. On the other hand, particle tracking velocimetry cannot be performed in a continuously scattering flowing media (e.g. blood), while Doppler imaging can be.

The techniques demonstrated here can be extended to three-dimensional, three-component flow velocitmetry. To scale up the current techniques in three dimensions using similar B-scan pixel densities would require line rates in the megahertz regime [51

51. W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010). [CrossRef] [PubMed]

]. An alternate approach would be to divide the entire field of fiew into smaller subvolumes with each subvolume capable of being imaged by a submegahertz OCT system. After three-dimensional, three-component velocimetry is performed, the complete volume can be reconstructed by merging the subvolumes.

Qualitative imaging and phenotyping of cilia-driven fluid flow will enable more detailed research in ciliary biology and in respiratory medicine. Flow velocimetry can be used to characterize cilia performance or the overall performance of a ciliated surface. The ability to obtain quantitative vectorial flow profiles will enable the detailed study microfluidic phenomenon in biological cilia-driven fluid flow, including mixing.

Acknowledgments

We acknowledge the loan of the OCT from Thorlabs, Inc. We also acknowledge conversations about microfluidic flow with Michael Loewenberg (Yale Chemical Engineering).

References and links

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2.

Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]

3.

B. Mitchell, R. Jacobs, J. Li, S. Chien, and C. Kintner, “A positive feedback mechanism governs the polarity and motion of motile cilia,” Nature 447(7140), 97–101 (2007). [CrossRef] [PubMed]

4.

F. Miskevich, “Imaging fluid flow and cilia beating pattern in Xenopus brain ventricles,” J. Neurosci. Methods 189(1), 1–4 (2010). [CrossRef] [PubMed]

5.

B. Guirao, A. Meunier, S. Mortaud, A. Aguilar, J. M. Corsi, L. Strehl, Y. Hirota, A. Desoeuvre, C. Boutin, Y. G. Han, Z. Mirzadeh, H. Cremer, M. Montcouquiol, K. Sawamoto, and N. Spassky, “Coupling between hydrodynamic forces and planar cell polarity orients mammalian motile cilia,” Nat. Cell Biol. 12(4), 341–350 (2010). [CrossRef] [PubMed]

6.

J. R. Colantonio, J. Vermot, D. Wu, A. D. Langenbacher, S. Fraser, J. N. Chen, and K. L. Hill, “The dynein regulatory complex is required for ciliary motility and otolith biogenesis in the inner ear,” Nature 457(7226), 205–209 (2009). [CrossRef] [PubMed]

7.

A. G. Kramer-Zucker, F. Olale, C. J. Haycraft, B. K. Yoder, A. F. Schier, and I. A. Drummond, “Cilia-driven fluid flow in the zebrafish pronephros, brain and Kupffer’s vesicle is required for normal organogenesis,” Development 132(8), 1907–1921 (2005). [CrossRef] [PubMed]

8.

K. Baker and P. L. Beales, “Making sense of cilia in disease: the human ciliopathies,” Am. J. Med. Genet. C. Semin. Med. Genet. 151C(4), 281–295 (2009). [CrossRef] [PubMed]

9.

K. Sawamoto, H. Wichterle, O. Gonzalez-Perez, J. A. Cholfin, M. Yamada, N. Spassky, N. S. Murcia, J. M. Garcia-Verdugo, O. Marin, J. L. R. Rubenstein, M. Tessier-Lavigne, H. Okano, and A. Alvarez-Buylla, “New neurons follow the flow of cerebrospinal fluid in the adult brain,” Science 311(5761), 629–632 (2006). [CrossRef] [PubMed]

10.

R. A. Lyons, E. Saridogan, and O. Djahanbakhch, “The reproductive significance of human Fallopian tube cilia,” Hum. Reprod. Update 12(4), 363–372 (2006). [CrossRef] [PubMed]

11.

H. A. Stone, A. D. Stroock, and A. Ajdari, “Engineering flows in small devices: microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid Mech. 36(1), 381–411 (2004). [CrossRef]

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A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, “Patterning electro-osmotic flow with patterned surface charge,” Phys. Rev. Lett. 84(15), 3314–3317 (2000). [CrossRef] [PubMed]

13.

B. Guirao and J. F. Joanny, “Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia,” Biophys. J. 92(6), 1900–1917 (2007). [CrossRef] [PubMed]

14.

B. Mitchell, J. L. Stubbs, F. Huisman, P. Taborek, C. Yu, and C. Kintner, “The PCP pathway instructs the planar orientation of ciliated cells in the Xenopus larval skin,” Curr. Biol. 19(11), 924–929 (2009). [CrossRef] [PubMed]

15.

R. J. Francis, B. Chatterjee, N. T. Loges, H. Zentgraf, H. Omran, and C. W. Lo, “Initiation and maturation of cilia-generated flow in newborn and postnatal mouse airway,” Am. J. Physiol. Lung Cell. Mol. Physiol. 296(6), L1067–L1075 (2009). [CrossRef] [PubMed]

16.

K. Ikegami, S. Sato, K. Nakamura, L. E. Ostrowski, and M. Setou, “Tubulin polyglutamylation is essential for airway ciliary function through the regulation of beating asymmetry,” Proc. Natl. Acad. Sci. U.S.A. 107(23), 10490–10495 (2010). [CrossRef] [PubMed]

17.

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]

18.

J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissues,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1017–1028 (1996). [CrossRef]

19.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

20.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]

21.

M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. 11(2), 024014 (2006). [CrossRef] [PubMed]

22.

A. V. Bykov, A. V. Priezzhev, J. Lauri, and R. Myllylä, “Doppler OCT imaging of cytoplasm shuttle flow in Physarum polycephalum,” J Biophotonics 2(8-9), 540–547 (2009). [CrossRef] [PubMed]

23.

M. A. Choma, M. J. Suter, B. J. Vakoc, B. E. Bouma, and G. J. Tearney, “Physiological homology between Drosophila melanogaster and vertebrate cardiovascular systems,” Dis Model Mech 4(3), 411–420 (2011). [CrossRef] [PubMed]

24.

C. W. Xi, D. L. Marks, D. S. Parikh, L. Raskin, and S. A. Boppart, “Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography,” Proc. Natl. Acad. Sci. U.S.A. 101(20), 7516–7521 (2004). [CrossRef] [PubMed]

25.

Y. C. Ahn, W. G. Jung, and Z. P. Chen, “Optical sectioning for microfluidics: secondary flow and mixing in a meandering microchannel,” Lab Chip 8(1), 125–133 (2008). [CrossRef] [PubMed]

26.

M. Baltussen, P. Anderson, F. Bos, and J. den Toonder, “Inertial flow effects in a micro-mixer based on artificial cilia,” Lab Chip 9(16), 2326–2331 (2009). [CrossRef] [PubMed]

27.

C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007). [CrossRef] [PubMed]

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Y. C. Ahn, W. Jung, and Z. P. Chen, “Quantification of a three-dimensional velocity vector using spectral-domain Doppler optical coherence tomography,” Opt. Lett. 32(11), 1587–1589 (2007). [CrossRef] [PubMed]

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S. Makita, T. Fabritius, and Y. Yasuno, “Quantitative retinal-blood flow measurement with three-dimensional vessel geometry determination using ultrahigh-resolution Doppler optical coherence angiography,” Opt. Lett. 33(8), 836–838 (2008). [CrossRef] [PubMed]

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48.

J. R. Hove, R. W. Köster, A. S. Forouhar, G. Acevedo-Bolton, S. E. Fraser, and M. Gharib, “Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis,” Nature 421(6919), 172–177 (2003). [CrossRef] [PubMed]

49.

N. V. Iftimia, D. X. Hammer, R. D. Ferguson, M. Mujat, D. Vu, and A. A. Ferrante, “Dual-beam Fourier domain optical Doppler tomography of zebrafish,” Opt. Express 16(18), 13624–13636 (2008). [CrossRef] [PubMed]

50.

M. W. Jenkins, L. Peterson, S. Gu, M. Gargesha, D. L. Wilson, M. Watanabe, and A. M. Rollins, “Measuring hemodynamics in the developing heart tube with four-dimensional gated Doppler optical coherence tomography,” J. Biomed. Opt. 15(6), 066022 (2010). [CrossRef] [PubMed]

51.

W. Wieser, B. R. Biedermann, T. Klein, C. M. Eigenwillig, and R. Huber, “Multi-megahertz OCT: high quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second,” Opt. Express 18(14), 14685–14704 (2010). [CrossRef] [PubMed]

OCIS Codes
(110.4500) Imaging systems : Optical coherence tomography
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(280.2490) Remote sensing and sensors : Flow diagnostics
(110.4153) Imaging systems : Motion estimation and optical flow

ToC Category:
Optical Coherence Tomography

History
Original Manuscript: May 17, 2011
Revised Manuscript: June 16, 2011
Manuscript Accepted: June 19, 2011
Published: June 22, 2011

Citation
Stephan Jonas, Dipankan Bhattacharya, Mustafa K. Khokha, and Michael A. Choma, "Microfluidic characterization of cilia-driven fluid flow using optical coherence tomography-based particle tracking velocimetry," Biomed. Opt. Express 2, 2022-2034 (2011)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-7-2022


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References

  1. H. C. Berg, Random Walks in Biology, revised ed. (Princeton University Press, 1993).
  2. Y. Okada, S. Takeda, Y. Tanaka, J. C. I. Belmonte, and N. Hirokawa, “Mechanism of nodal flow: a conserved symmetry breaking event in left-right axis determination,” Cell 121(4), 633–644 (2005). [CrossRef] [PubMed]
  3. B. Mitchell, R. Jacobs, J. Li, S. Chien, and C. Kintner, “A positive feedback mechanism governs the polarity and motion of motile cilia,” Nature 447(7140), 97–101 (2007). [CrossRef] [PubMed]
  4. F. Miskevich, “Imaging fluid flow and cilia beating pattern in Xenopus brain ventricles,” J. Neurosci. Methods 189(1), 1–4 (2010). [CrossRef] [PubMed]
  5. B. Guirao, A. Meunier, S. Mortaud, A. Aguilar, J. M. Corsi, L. Strehl, Y. Hirota, A. Desoeuvre, C. Boutin, Y. G. Han, Z. Mirzadeh, H. Cremer, M. Montcouquiol, K. Sawamoto, and N. Spassky, “Coupling between hydrodynamic forces and planar cell polarity orients mammalian motile cilia,” Nat. Cell Biol. 12(4), 341–350 (2010). [CrossRef] [PubMed]
  6. J. R. Colantonio, J. Vermot, D. Wu, A. D. Langenbacher, S. Fraser, J. N. Chen, and K. L. Hill, “The dynein regulatory complex is required for ciliary motility and otolith biogenesis in the inner ear,” Nature 457(7226), 205–209 (2009). [CrossRef] [PubMed]
  7. A. G. Kramer-Zucker, F. Olale, C. J. Haycraft, B. K. Yoder, A. F. Schier, and I. A. Drummond, “Cilia-driven fluid flow in the zebrafish pronephros, brain and Kupffer’s vesicle is required for normal organogenesis,” Development 132(8), 1907–1921 (2005). [CrossRef] [PubMed]
  8. K. Baker and P. L. Beales, “Making sense of cilia in disease: the human ciliopathies,” Am. J. Med. Genet. C. Semin. Med. Genet. 151C(4), 281–295 (2009). [CrossRef] [PubMed]
  9. K. Sawamoto, H. Wichterle, O. Gonzalez-Perez, J. A. Cholfin, M. Yamada, N. Spassky, N. S. Murcia, J. M. Garcia-Verdugo, O. Marin, J. L. R. Rubenstein, M. Tessier-Lavigne, H. Okano, and A. Alvarez-Buylla, “New neurons follow the flow of cerebrospinal fluid in the adult brain,” Science 311(5761), 629–632 (2006). [CrossRef] [PubMed]
  10. R. A. Lyons, E. Saridogan, and O. Djahanbakhch, “The reproductive significance of human Fallopian tube cilia,” Hum. Reprod. Update 12(4), 363–372 (2006). [CrossRef] [PubMed]
  11. H. A. Stone, A. D. Stroock, and A. Ajdari, “Engineering flows in small devices: microfluidics toward a lab-on-a-chip,” Annu. Rev. Fluid Mech. 36(1), 381–411 (2004). [CrossRef]
  12. A. D. Stroock, M. Weck, D. T. Chiu, W. T. S. Huck, P. J. A. Kenis, R. F. Ismagilov, and G. M. Whitesides, “Patterning electro-osmotic flow with patterned surface charge,” Phys. Rev. Lett. 84(15), 3314–3317 (2000). [CrossRef] [PubMed]
  13. B. Guirao and J. F. Joanny, “Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia,” Biophys. J. 92(6), 1900–1917 (2007). [CrossRef] [PubMed]
  14. B. Mitchell, J. L. Stubbs, F. Huisman, P. Taborek, C. Yu, and C. Kintner, “The PCP pathway instructs the planar orientation of ciliated cells in the Xenopus larval skin,” Curr. Biol. 19(11), 924–929 (2009). [CrossRef] [PubMed]
  15. R. J. Francis, B. Chatterjee, N. T. Loges, H. Zentgraf, H. Omran, and C. W. Lo, “Initiation and maturation of cilia-generated flow in newborn and postnatal mouse airway,” Am. J. Physiol. Lung Cell. Mol. Physiol. 296(6), L1067–L1075 (2009). [CrossRef] [PubMed]
  16. K. Ikegami, S. Sato, K. Nakamura, L. E. Ostrowski, and M. Setou, “Tubulin polyglutamylation is essential for airway ciliary function through the regulation of beating asymmetry,” Proc. Natl. Acad. Sci. U.S.A. 107(23), 10490–10495 (2010). [CrossRef] [PubMed]
  17. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59(3), 427–471 (1996). [CrossRef]
  18. J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi, and M. V. Sivak, “Optical coherence tomography and microscopy in gastrointestinal tissues,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1017–1028 (1996). [CrossRef]
  19. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
  20. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]
  21. M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. 11(2), 024014 (2006). [CrossRef] [PubMed]
  22. A. V. Bykov, A. V. Priezzhev, J. Lauri, and R. Myllylä, “Doppler OCT imaging of cytoplasm shuttle flow in Physarum polycephalum,” J Biophotonics 2(8-9), 540–547 (2009). [CrossRef] [PubMed]
  23. M. A. Choma, M. J. Suter, B. J. Vakoc, B. E. Bouma, and G. J. Tearney, “Physiological homology between Drosophila melanogaster and vertebrate cardiovascular systems,” Dis Model Mech 4(3), 411–420 (2011). [CrossRef] [PubMed]
  24. C. W. Xi, D. L. Marks, D. S. Parikh, L. Raskin, and S. A. Boppart, “Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography,” Proc. Natl. Acad. Sci. U.S.A. 101(20), 7516–7521 (2004). [CrossRef] [PubMed]
  25. Y. C. Ahn, W. G. Jung, and Z. P. Chen, “Optical sectioning for microfluidics: secondary flow and mixing in a meandering microchannel,” Lab Chip 8(1), 125–133 (2008). [CrossRef] [PubMed]
  26. M. Baltussen, P. Anderson, F. Bos, and J. den Toonder, “Inertial flow effects in a micro-mixer based on artificial cilia,” Lab Chip 9(16), 2326–2331 (2009). [CrossRef] [PubMed]
  27. C. J. Pedersen, D. Huang, M. A. Shure, and A. M. Rollins, “Measurement of absolute flow velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,” Opt. Lett. 32(5), 506–508 (2007). [CrossRef] [PubMed]
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