Abstract

Microscale quantification of cilia-driven fluid flow is an emerging area in medical physiology, including pulmonary and central nervous system physiology. Cilia-driven fluid flow is most completely described by a three-dimensional, three-component (3D3C) vector field. Here, we generate 3D3C velocimetry measurements by synthesizing higher dimensional data from lower dimensional measurements obtained using two separate optical coherence tomography (OCT)-based approaches: digital particle image velocimetry (DPIV) and dynamic light scattering (DLS)-OCT. Building on previous work, we first demonstrate directional DLS-OCT for 1D2C velocimetry measurements in the sub-1 mm/s regime (sub-2.5 inch/minute regime) of cilia-driven fluid flow in Xenopus epithelium, an important animal model of the ciliated respiratory tract. We then extend our analysis toward 3D3C measurements in Xenopus using both DLS-OCT and DPIV. We demonstrate the use of DPIV-based approaches towards flow imaging of Xenopus cerebrospinal fluid and mouse trachea, two other important ciliary systems. Both of these flows typically fall in the sub-100 μm/s regime (sub-0.25 inch/minute regime). Lastly, we develop a framework for optimizing the signal-to-noise ratio of 3D3C flow velocity measurements synthesized from 2D2C measures in non-orthogonal planes. In all, 3D3C OCT-based velocimetry has the potential to comprehensively characterize the flow performance of biological ciliated surfaces.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]

2015 (3)

B. K. Huang and M. A. Choma, “Microscale imaging of cilia-driven fluid flow,” Cell Mol. Life Sci. 72, 1095–1113 (2015).
[Crossref]

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, 30502 (2015).
[Crossref] [PubMed]

N. Weiss, T. G. van Leeuwen, and J. Kalkman, “Simultaneous and localized measurement of diffusion and flow using optical coherence tomography,” Opt. Express 23, 3448–3459 (2015).
[Crossref] [PubMed]

2014 (4)

L. Liu, S. Shastry, S. Byan-Parker, G. Houser, K. Chu, S. E. Birket, C. M. Fernandez, J. A. Gardecki, W. Grizzle, E. J. Wilsterman, E. J. Sorscher, S. M. Rowe, and G. J. Tearney, “An autoregulatory mechanism governing mucociliary transport is sensitive to mucus load,” Am. J. Respir. Cell. Mol. Biol. 51, 485–493 (2014).
[Crossref] [PubMed]

M. J. Hoegger, A. J. Fischer, J. D. McMenimen, L. S. Ostedgaard, A. J. Tucker, M. A. Awadalla, T. O. Moninger, A. S. Michalski, E. A. Hoffman, J. Zabner, D. A. Stoltz, and M. J. Welsh, “Cystic fibrosis. impaired mucus detachment disrupts mucociliary transport in a piglet model of cystic fibrosis,” Science 345, 818–822 (2014).
[Crossref] [PubMed]

B. K. Huang and M. A. Choma, “Resolving directional ambiguity in dynamic light scattering-based transverse motion velocimetry in optical coherence tomography,” Opt. Lett. 39, 521–524 (2014).
[Crossref] [PubMed]

S. Broillet, A. Sato, S. Geissbuehler, C. Pache, A. Bouwens, T. Lasser, and M. Leutenegger, “Optical coherence correlation spectroscopy (OCCS),” Opt. Express 22, 782–802 (2014).
[Crossref] [PubMed]

2013 (6)

W. Trasischker, R. M. Werkmeister, S. Zotter, B. Baumann, T. Torzicky, M. Pircher, and C. K. Hitzenberger, “In vitro and in vivo three-dimensional velocity vector measurement by three-beam spectral-domain Doppler optical coherence tomography,” J. Biomed. Opt. 18, 116010 (2013).
[Crossref] [PubMed]

L. Liu, K. K. Chu, G. H. Houser, B. J. Diephuis, Y. Li, E. J. Wilsterman, S. Shastry, G. Dierksen, S. E. Birket, M. Mazur, S. Byan-Parker, W. E. Grizzle, E. J. Sorscher, S. M. Rowe, and G. J. Tearney, “Method for quantitative study of airway functional microanatomy using micro-optical coherence tomography,” PLoS One 8, e54473 (2013).
[Crossref] [PubMed]

C.-Y. Chen, P. G. Menon, W. Kowalski, and K. Pekkan, “Time-resolved OCT-μ PIV: a new microscopic PIV technique for noninvasive depth-resolved pulsatile flow profile acquisition,” Experiments in Fluids 54, 1–9 (2013).

N. Weiss, T. G. van Leeuwen, and J. Kalkman., “Localized measurement of longitudinal and transverse flow velocities in colloidal suspensions using optical coherence tomography,” Phys. Rev. E 88, 0423122013.
[Crossref]

S. Jonas, E. Zhou, E. Deniz, B. Huang, K. Chandrasekera, D. Bhattacharya, Y. Wu, R. Fan, T. M. Deserno, M. K. Khokha, and M. A. Choma, “A novel approach to quantifying ciliary physiology: microfluidic mixing driven by a ciliated biological surface,” Lab on a Chip 13, 4160–4163 (2013).
[Crossref] [PubMed]

C. Hagenlocher, P. Walentek, Christina Muller, T. Thumberger, and K. Feistel, “Ciliogenesis and cerebrospinal fluid flow in the developing Xenopus brain are regulated by foxj1,” Cilia 2, 12 (2013).
[Crossref] [PubMed]

2012 (4)

K. Mogi, T. Adachi, S. Izumi, and R. Toyoizumi, “Visualisation of cerebrospinal fluid flow patterns in albino Xenopus larvae in vivo,” Fluids Barriers CNS 9, 9 (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]

A. L. Oldenburg, R. K. Chhetri, D. B. Hill, and B. Button, “Monitoring airway mucus flow and ciliary activity with optical coherence tomography,” Biomed. Opt. Express 3, 1978–1992 (2012).
[Crossref] [PubMed]

S. A. Klein, J. L. Moran, D. H. Frakes, and J. D. Posner, “Three-dimensional three-component particle velocimetry for microscale flows using volumetric scanning,” Meas. Sci. Technol. 23, 085304 (2012).
[Crossref]

2011 (1)

2010 (3)

V. J. Srinivasan, S. Sakadzic, I. Gorczynska, S. Ruvinskaya, W. Wu, J. G. Fujimoto, and D. A. Boas, “Quantitative cerebral blood flow with optical coherence tomography,” Opt Express 18, 2477–2494 (2010).
[Crossref] [PubMed]

F. Miskevich, “Imaging fluid flow and cilia beating pattern in xenopus brain ventricles,” J. Neurosci. Meth. 189, 1–4 (2010).
[Crossref]

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, 341–350 (2010).
[Crossref] [PubMed]

2009 (1)

C. Wodarczyk, I. Rowe, M. Chiaravalli, M. Pema, F. Qian, and A. Boletta, “A novel mouse model reveals that polycystin-1 deficiency in ependyma and choroid plexus results in dysfunctional cilia and hydrocephalus,” Plos One 4, 7137 (2009).
[Crossref]

2008 (2)

D. J. Smith, E. A. Gaffney, and J. R. Blake, “Modelling mucociliary clearance,” Respiratory Physiol. Neurobiol. 163, 178–188 (2008).
[Crossref]

W. Supatto, S. E. Fraser, and J. Vermot, “An all-optical approach for probing microscopic flows in living embryos,” Biophys. J. 95, L29–L31 (2008).
[Crossref] [PubMed]

2005 (2)

A. M. Marzesco, P. Janich, M. Wilsch-Brauninger, V. Dubreuil, K. Langenfeld, D. Corbeil, and W. B. Huttner, “Release of extracellular membrane particles carrying the stem cell marker prominin-1 (CD133) from neural progenitors and other epithelial cells,” J. Cell Sci. 118, 2849–2858 (2005).
[Crossref] [PubMed]

B. Hebert, S. Costantino, and P. W. Wiseman, “Spatiotemporal image correlation spectroscopy (STICS) theory, verification, and application to protein velocity mapping in living CHO cells,” Biophys. J. 88, 3601–3614 (2005).
[Crossref] [PubMed]

2002 (1)

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, 499–510 (2002).
[Crossref] [PubMed]

1998 (1)

H. Matsui, S. H. Randell, S. W. Peretti, C. W. Davis, and R. C. Boucher, “Coordinated clearance of periciliary liquid and mucus from airway surfaces,” J. Clin. Invest. 102, 1125–1131 (1998).
[Crossref] [PubMed]

1997 (1)

1996 (2)

A. Wanner, M. Salathe, and T. G. O’Riordan, “Mucociliary clearance in the airways,” Am. J. Respir. Crit. Care Med. 154, 1868–1902 (1996).
[Crossref] [PubMed]

S. A. Boppart, M. E. Brezinski, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, “Investigation of developing embryonic morphology using optical coherence tomography,” Dev. Biol. 177, 54–63 (1996).
[Crossref] [PubMed]

1995 (1)

C. Brücker, “Digital-particle-image-velocimetry (DPIV) in a scanning light-sheet: 3D starting flow around a short cylinder,” Experiments in Fluids 19, 255–263 (1995).
[Crossref]

1993 (1)

A. K. Prasad and R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Experiments in Fluids 15, 49–60 (1993).
[Crossref]

1992 (1)

R. D. Keane and R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[Crossref]

1991 (2)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Experiments in Fluids 10, 181–193 (1991).
[Crossref]

R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Ann. Rev. Fluid Mechanics 23, 261–304 (1991).
[Crossref]

Adachi, T.

K. Mogi, T. Adachi, S. Izumi, and R. Toyoizumi, “Visualisation of cerebrospinal fluid flow patterns in albino Xenopus larvae in vivo,” Fluids Barriers CNS 9, 9 (2012).
[Crossref] [PubMed]

Adrian, R. J.

A. K. Prasad and R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Experiments in Fluids 15, 49–60 (1993).
[Crossref]

R. D. Keane and R. J. Adrian, “Theory of cross-correlation analysis of PIV images,” Appl. Sci. Res. 49, 191–215 (1992).
[Crossref]

R. J. Adrian, “Particle-imaging techniques for experimental fluid-mechanics,” Ann. Rev. Fluid Mechanics 23, 261–304 (1991).
[Crossref]

Aguilar, A.

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, 341–350 (2010).
[Crossref] [PubMed]

Amaya, E.

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, 499–510 (2002).
[Crossref] [PubMed]

Awadalla, M. A.

M. J. Hoegger, A. J. Fischer, J. D. McMenimen, L. S. Ostedgaard, A. J. Tucker, M. A. Awadalla, T. O. Moninger, A. S. Michalski, E. A. Hoffman, J. Zabner, D. A. Stoltz, and M. J. Welsh, “Cystic fibrosis. impaired mucus detachment disrupts mucociliary transport in a piglet model of cystic fibrosis,” Science 345, 818–822 (2014).
[Crossref] [PubMed]

Barton, J. K.

Baumann, B.

W. Trasischker, R. M. Werkmeister, S. Zotter, B. Baumann, T. Torzicky, M. Pircher, and C. K. Hitzenberger, “In vitro and in vivo three-dimensional velocity vector measurement by three-beam spectral-domain Doppler optical coherence tomography,” J. Biomed. Opt. 18, 116010 (2013).
[Crossref] [PubMed]

Bhandari, V.

U. A. Gamm, B. K. Huang, M. Syed, X. Zhang, V. Bhandari, and M. A. Choma, “Quantifying hyperoxia-mediated damage to mammalian respiratory cilia-driven fluid flow using particle tracking velocimetry-optical coherence tomography,” J. Biomed. Opt. in press (2015).

Bhattacharya, D.

S. Jonas, E. Zhou, E. Deniz, B. Huang, K. Chandrasekera, D. Bhattacharya, Y. Wu, R. Fan, T. M. Deserno, M. K. Khokha, and M. A. Choma, “A novel approach to quantifying ciliary physiology: microfluidic mixing driven by a ciliated biological surface,” Lab on a Chip 13, 4160–4163 (2013).
[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]

Birket, S. E.

L. Liu, S. Shastry, S. Byan-Parker, G. Houser, K. Chu, S. E. Birket, C. M. Fernandez, J. A. Gardecki, W. Grizzle, E. J. Wilsterman, E. J. Sorscher, S. M. Rowe, and G. J. Tearney, “An autoregulatory mechanism governing mucociliary transport is sensitive to mucus load,” Am. J. Respir. Cell. Mol. Biol. 51, 485–493 (2014).
[Crossref] [PubMed]

L. Liu, K. K. Chu, G. H. Houser, B. J. Diephuis, Y. Li, E. J. Wilsterman, S. Shastry, G. Dierksen, S. E. Birket, M. Mazur, S. Byan-Parker, W. E. Grizzle, E. J. Sorscher, S. M. Rowe, and G. J. Tearney, “Method for quantitative study of airway functional microanatomy using micro-optical coherence tomography,” PLoS One 8, e54473 (2013).
[Crossref] [PubMed]

Blake, J. R.

D. J. Smith, E. A. Gaffney, and J. R. Blake, “Modelling mucociliary clearance,” Respiratory Physiol. Neurobiol. 163, 178–188 (2008).
[Crossref]

Boas, D. A.

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B. K. Huang and M. A. Choma, “Microscale imaging of cilia-driven fluid flow,” Cell Mol. Life Sci. 72, 1095–1113 (2015).
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Supplementary Material (8)

NameDescription
» Visualization 1: MP4 (464 KB)      DPIV-based flow field reconstruction of flow phantom
» Visualization 2: MP4 (461 KB)      DLS-based flow field reconstruction of flow phantom
» Visualization 3: MP4 (1341 KB)      DPIV-based flow field reconstruction in Xenopus epithelium
» Visualization 4: MP4 (1009 KB)      DLS-based flow field reconstruction in Xenopus epithelium
» Visualization 5: MP4 (771 KB)      Movie of CSF flow in ventricle
» Visualization 6: MP4 (330 KB)      DPIV-based flow field reconstruction of CSF flow in ventricle
» Visualization 7: MP4 (2401 KB)      Movie of tracheal flow
» Visualization 8: MP4 (1144 KB)      DPIV-based flow field reconstruction of tracheal flow

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Figures (8)

Fig. 1
Fig. 1

In this study, we use two distinct correlation-based approaches to directional OCT velocimetry: DPIV (a,b) and DLS (c,d). (a) In DPIV, two frames of intensity information I(x0, z0), acquired with an interframe time of δt, are compared against each. Each image is segmented into smaller regions of interest (ROI) Iroi(x, y), centered around the point (x0, y0), and cross-correlation is calculated in the spatial domain (δx, δz). The process is then repeated for multiple ROIs. (b) The corresponding correlation function g(x0, z0; δx, δz, τ) for each region exhibits a peak where δx = vxδt and δz = vzδt. Estimation of this peak location yields the velocity estimate for (vx, vz) (c) In DLS-OCT, the temporal signal at a single point (x0, z0) is correlated with itself, except now the complex field signal E(x0, z0, t), instead of the intensity, is used, and the correlation is calculated in the time domain. Additionally, scatterers are seeded significantly more densely such that speckle formation occurs. (d) The correlation function g(x0, y0; τ) exhibits a peak at τ = 0, but the rate of decorrelation (γ), i.e. the inverse of the width of the Gaussian, is proportional to the difference in velocity of the scanner and fluid flow. By modulating the scan speed v x scan , we can minimize the decorrelation rate γ and estimate v x flow as the minimum of that curve. The process is then repeated at multiple spatial locations (x0, z0).

Fig. 2
Fig. 2

Scan setup for DPIV and DLS-OCT. (a) Three-dimensional coordinate system, with optical axis defined along z, and en-face plane defined as xy-plane. A particle with velocity v = (vx, vy, vz) can be decomposed into three components based on this Cartesian system. (b) DPIV scan setup, showing (top left) two non-orthogonal plane measurements. The angle of each scan plane, θ1 and θ2, as well as the angle of flow in the en face plane θf, are all defined with respect to the global x-axis. The velocity as measured by DPIV in each plane is the vector component of the velocity v on the unit vector tangent to the plane, either e1 or e2 (bottom left / right). The vector projections of velocity in these two planes are denoted as v1 and v2. From v1 and v2, vx and vy can be calculated along the line of intersection at these planes. Acquiring multiple scan plans (top right) allows for calculation of v at multiple points (x0, y0), to reconstruct an entire 3D volume. (c) DLS-OCT scan protocol showing series of scan bias acquisitions. Each line measurement along z-axis at location (x0, y0) in the en face plane consists of a set of scans along axes oriented around ±45°. Much like the DPIV measurements, the directional DLS-OCT protocol yields two velocity measurements v1 and v2. vx and vy can then be recovered along a single axial line using Eqs. (3) and (4). These scans are then repeated at various (x0, y0) points.

Fig. 3
Fig. 3

Flow phantom demonstration of 3D3C velocimetry using DPIV and DLS-OCT. (a) Global orientation of planar flow phantom, which is very wide in the y-dimension as compared with z-dimension, yielding a planar Poiseuille flow in region of interrogation far from the lateral walls. (b,c) Log-scale intensity images representing raw data acquisition in flow phantom channel. (b) DPIV single frame of 5 μm polystyrene microspheres in a flow phantom, in a single plane, where e1 emphasizes that the plane is oblique to the x-axis. (c) DLS-OCT single M-mode image of densely seeded 500 nm polystyrene microspheres in the same flow phantom, at single scan bias. (d,e; Visualization 1, Visualization 2) 3D3C flow phantom reconstruction using (d) DPIV and (e) DLS-OCT, from a side, oblique, and superior view. Both methods show expected Poiseuille-like flow in between two parallel plates. Flow is consistent with the geometric orientation of the flow phantom, and flow speed peaks near the expected 0.9 mm/s.

Fig. 4
Fig. 4

In vivo demonstration of directional DLS-OCT protocol in X. laevis epithelial ciliary flow. (right) B-scan of single embryo showing head to tail flow of a bead solution along the ciliated surface of an embryo, with scanning EM micrograph of ciliary patch on surface of animal (inset). The B-scan plane corresponds to the coronal section in Fig. 5. The red bar indicates location of depth-scan where velocimetry data is acquired, where width of bar represents the lateral spatial extent of scanning. (left) Velocimetry profile of vx, as determined by directional DLS-OCT, and vz, as determined by Doppler, along the depth scan highlighted in red. The colored lines indicate the location of the glass-liquid interface (blue) and the embryo surface (green). Flow is zero at the glass-liquid interface, increases to >500 μm/s near the embryo surface, and diminished back to zero at the body of the embryo itself. Axes labels: L-Left, R-right, Cr-cranial, Ca-caudal

Fig. 5
Fig. 5

Measurement of 3D3C epithelial cilia-driven fluid in X. laevis. (a) Global oriention of embryo, showing rendering of surface (green) and flow directed primarily along the head-tail axis. Red line shows orientation of coronal planes. (b, Visualization 3) Tadpole rendering with 3D quiver plot showing 3D3C velocimetry data, as reconstructed using DPIV from several perspectives. (c, Visualization 4) Similar rendering, now with velocity field estimated using directional DLS-OCT. A portion of the embryo surface on the head is missing due to difficulties in automated segmentation. Note the difference in scale bar between the (b) and (c). Axes labels: L-left, R-right, Cr-cranial, Ca-caudal, D-dorsal, V-ventral

Fig. 6
Fig. 6

Measurement of cilia-driven cerebrospinal fluid flow in X. tropicalis ventricle using DPIV. (a) 3D intensity-based rendering of the head region of X. tropicalis, with (b) ventricular space segmented out, and highlighted in red. (c) Rendering of segmented ventricular space as viewed from above (top) and from the side (bottom), showing location of individual ventricles as well as orientation of sagittal and axial planes. IV-fourth ventricle. M-Midbrain ventricle. CA-cerebral aqueduct. L-lateral ventricles. III-third ventricle. (d, Visualization 6) 3D3C vector flow field in ventricular system. (e, Visualization 5) Example of raw acquisition of single cross-sectional movie showing endogenous cellular material circulating in ventricle (with e1 emphasizing that plane is oblique to rostrocaudal axis by 15°). The resulting DPIV 2D2C quantification shows recirculation. (f,g) Axial and sagittal planar reconstructions of velocity data from 3D3C data. Note the different scale bar in (f,g), referring to the magnitude of only the projected velocity component onto each given plane. Axes labels: L-left, R-right, Ro-rostral, C-caudal, D-dorsal, V-ventral

Fig. 7
Fig. 7

Quantification of cilia-driven tracheal fluid flow in adolescent mouse using DPIV. (a) 3D intensity-based rendering of trachea, with sagittal plane orientation shown (b) Segmented region of trachea within blue box of (a) showing spatial location where fluid flow was quantified. (c, Visualization 7) Raw acquisition of 5 μm polystyrene microspheres being driven by ciliary fluid flow, and subsequent 2D2C flow field quantification with DPIV. The acqusition is oblique to the sagittal plane by 15° (d, Visualization 8) 3D3C flow field rendering from top view (consistent with view in (a)), oblique superior view, and side view. Large arrows denoting the location and direction of primary tail-head flow as well as recirculatory head-tail flow. Axes labels: L-left, R-right, Cr-cranial, Ca-caudal, D-dorsal, V-ventral

Fig. 8
Fig. 8

Optimization of signal-to-noise ratio (SNR) in DPIV measurements with respect to measurement angle. (a) Overall flow of SNR predictions. Two components of velocity vx and vy are synthesized from two non-orthogonal measurements v1 and v2. The error of the final measurements δvx and δvy, and thus the SNR, depend on error propagation from v1 and v2, as well as on the initial error δv1 and δv2. δv1 and δv2 in turn depend on multiple factors, including the flow angle θf relative to the angles of measurement, θ1 and θ2. (b) Predicted SNR of v1 (and equivalently v2) as a function of angle of measurement θ1, based on relative height of main correlation peak. θf here set to be 90°, and maximum SNR defined to be unity. (gray) low speed flow, (black) high speed flow. (c) Measured SNR of v1 as a function of measurement angle θ1 where θf set at 90°. (d) Predicted SNR of final measurement vxy, defined as SNR v x y = 1 / ( δ v x 2 + δ v y 2 ) 1 / 2 , as a function of measurement angles θ1 and θ2. (left) low speed, (right) high speed. (e) Predicted optimal relative angle of measurement θ1θ2 (black), and subsequent optimal SNR v xy (gray hatched) as a function of flow speed.

Tables (1)

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Table 1 Comparison of DPIV and Scanning DLS-OCT. A comparison of the benefits and limitations of each technique is shown. Sample values as demonstrated in our experiments are given, although these values do not necessarily reflect the theoretical limits of the techniques. ROI = region of intersest. SNR = signal-to-noise ratio. CSF = cerebrospinal fluid.

Equations (10)

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v 1 = v x cos θ 1 + v y sin θ 1
v 2 = v x cos θ 2 + v y sin θ 2
v x = v 2 sin θ 1 v 1 sin θ 2 sin ( θ 1 θ 2 )
v y = v 1 cos θ 2 v 2 cos θ 1 sin ( θ 1 θ 2 )
g ( x 0 , z 0 ; δ x , δ z , δ t ) = 1 N 1 + 4 D δ t w z 2 ( 1 + 4 D δ t w x y 2 ) diffusion e ( v y δ t ) 2 / w x y 2 1 + 4 D δ t / w x y 2 out-of-plane motion e ( v x δ t δ x ) 2 / w x y 2 1 + 4 D δ t / w x y 2 e ( v z δ t δ z ) 2 / w z 2 1 + 4 D δ t / w z 2 in-plane motion
SNR ( θ i , θ f ) = α exp [ ( v sin ( θ i θ f ) δ t w x y ) 2 ]
δ v x 2 = ( v x v 1 ) 2 δ v 1 2 + ( v x v 2 ) 2 δ v 2 2
δ v y 2 = ( v y v 1 ) 2 δ v 1 2 + ( v y v 2 ) 2 δ v 2 2
δ v x 2 = ( sin θ 2 sin ( θ 1 θ 2 ) ) 2 δ v 1 ( θ 1 , θ f ) 2 + ( sin θ 1 sin ( θ 1 θ 2 ) ) 2 δ v 2 ( θ 2 , θ f ) 2
δ v y 2 = ( cos θ 2 sin ( θ 1 θ 2 ) ) 2 δ v 1 ( θ 1 , θ f ) 2 + ( cos θ 1 sin ( θ 1 θ 2 ) ) 2 δ v 2 ( θ 2 , θ f ) 2

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