Multi-image particle tracking velocimetry of the microcirculation using fluorescent nanoparticles

Microvascular Research 72 (2006) 27 – 33 www.elsevier.com/locate/ymvre

Multi-image particle tracking velocimetry of the microcirculation using fluorescent nanoparticles Dino J. Ravnic a , Yu-Zhong Zhang b , Akira Tsuda c , Juan P. Pratt a , Harold T. Huss a , Steven J. Mentzer a,⁎ a

Laboratory of Immunophysiology, Brigham and Women’s Hospital, Harvard Medical School, Room 259, 75 Francis Street, Boston, MA 02115, USA b Molecular Probes (Invitrogen), Eugene, OR 97402-0469, USA c Department of Physiology, Harvard School of Public Health, Boston, MA 02115, USA Received 20 March 2006; revised 21 April 2006; accepted 23 April 2006 Available online 27 June 2006

Abstract Particle tracking velocimetry provides a Lagrangian description of flow properties in the microcirculation. To determine the utility of fluorescent nanoparticles to provide Lagrangian coordinates, we tracked these particles both in vitro and in vivo. The particles had a neutral charge and fluorescence intensity greater than 1000 times the PKH26-labeled red blood cells. At image acquisition rates of 60 frames per second, particles were tracked at velocities up to 4000 μm/s. Morphometric changes reflecting streaking artifact were significant at velocities of 4000 μm/ s (P b 0.05), but not at lower velocities (P N 0.05). Intravital microscopy monitoring after intravenous injection of the particles demonstrated a circulation half-life that was inversely related to particle size: 500 nm nanoparticles demonstrated a smaller change in plasma concentration than larger particles. Regardless of the size of the particles, more than 50% of the recovered fluorescence was located in the liver. These results suggest that fluorescent nanoparticles provide a convenient and practical Lagrangian description of flow velocity in the microcirculation. © 2006 Elsevier B.V. All rights reserved. Keywords: Microcirculation; Nanoparticles; Fluorescence microscopy; Velocimetry

Introduction Studies of blood flow regulation have focused on the accurate description of the velocity field because other flow property calculations follow directly from these measurements. To obtain a detailed description of the velocity field in the microcirculation, conventional velocimetry techniques consider the field to be composed of a very large number of particles (Raffel et al., 2000; Westerweel, 1997). The spatial displacement of these particles in two separate images provides a measurement of the instantaneous in-plane velocity vector field (Adrian, 1984, 1991). These instantaneous measurements provide a “snapshot” description of the velocity field. Commonly referred to as Eulerian methods, Abbreviations: CCD, charge coupled device; RBC, red blood cells. ⁎ Corresponding author. E-mail address: [email protected] (S.J. Mentzer). 0026-2862/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mvr.2006.04.006

these descriptions provide a highly resolved and computationally manageable velocity profile at a given point in space and moment in time. In contrast to Eulerian methods, Lagrangian methods track the movement of individual particles. Particle tracking as a function of time provides a limited description of the velocity field at a particular point in space but more information regarding the fate of individual particles. Thus, Lagrangian descriptions may be especially useful in studies of leukocyte behavior in the microcirculation (Secomb et al., 2003; Su et al., 2003; West et al., 2001). Leukocyte trajectories that involve margination, mural interactions and prolonged residence times are best characterized using the computation of Lagrangian coordinates. In this report, we investigated the use of submicron fluorescent spheres, here termed nanoparticles, for microcirculatory particle tracking. The motion of the nanoparticles was investigated both in vitro and in vivo. Our findings suggest that

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intravital videomicroscopy and nanoparticles can provide accurate Lagrangian flow description of the microcirculation observed in vivo. Methods Particles and red blood cells The particles were developed by Molecular Probes (Invitrogen, Eugene, OR) for intravascular particle tracking. These particles were of similar composition to those reported previously (Bernard et al., 1996) but manufactured with superior fluorescent characteristics and smaller size. Although many different fluorescent colors were developed, the green (e.g., 490 nm; em 520 nm) and orange (e.g., 545 nm; em 570 nm) fluorescent nanoparticles were used for most experiments. Sheep red blood cells were obtained in a heparinized syringe and separated from white cells by density gradient centrifugation. The red cells were fluorescently labeled using the procedure included in the commercially available PKH26 Red Fluorescent Cell Linker kit (e.g., 551 nm; em 567 nm) (Sigma, St. Louis, MO). Based on empirical preliminary findings, the number of injected nanoparticles was normalized to the volume of red blood in 1 ml; namely, 452 μm3. The number of injected nanoparticles was based on an equivalent total spherical volume: 6.912 × 109 500 nm particles, 1.08 × 108 2 μm particles and 1.3 × 107 4 μm particles.

Electron multiplier CCD (EMCCD) camera The flow chamber and intravital videomicroscopy 14-bit fluorescent images were digitally recorded with a EMCCD camera (C9100-02, Hamamatsu, Japan). The C9100-02 has a hermetic vacuum-sealed air-cooled head and on-chip electron gain multiplication (2000×). Images with 1000 × 1000 pixel resolution were routinely obtained at 30 fps; frame rates exceeding 60 fps were routinely obtained with 2 × 2 binning or subarray acquisition. The images were recorded in image stacks comprising 30 s to 10 min video sequences.

Calculation of diffraction-limited resolution Using matching apertures of the objective and condenser, the radius of the first order Airy diffraction ring was calculated using the formula r ¼ 1:22k=2NA; where k is the wavelength and NA is the numerical aperture of the objective. The minimum resolved distance between Airy patterns (Rayleigh criterion) was calculated as r ¼ 0:61k=NA and was used to determine maximum concentration of the particles in flow chamber experiments. The concentration of red cells and particles was, at maximum, 10-fold less than the concentration defined by the Rayleigh criterion.

Electronic particle and cell volume Quantitative morphometry Electronic particle volume analysis was performed using a Coulter Z2 Particle Analyzer (Beckman Coulter, Miami, FL). The Coulter Z2, based on the Coulter principle (Ben-Sasson et al., 1974; Brecher et al., 1956), measured changes in electrical resistance produced by the nonconductive particles and cells suspended in a standard electrolyte solution (Isoton II; Beckman Coulter). A 50-μm aperture was used with constant voltage settings. Particle minimum and maximum diameter settings were modified for the analysis. The particle size and number distributions were recorded over 256 channels and exported to Microsoft Excel (Redmond, WA) for statistical analysis.

Flow cytometry The nanoparticles and PKH26-labeled red blood cells were analyzed on an Epics XL (Beckman Coulter, Miami, FL) using gain settings calibrated to 4 peak Rainbow calibration particles (Spherotech, Libertyville, IL). The data were processed using WinList 5.0 (Verity, Topsham, ME).

In vitro flow chamber The design of the flow chamber has been previously described (Li et al., 1996, 2001). Briefly, the chamber was machined from high-grade acrylic to minimize optical aberration and facilitate microscopy. Design features included 0.5-mm holes in both inlet and outlet manifolds to rapidly stabilize laminar flow and permit the use of standard microscope slides. At each end of the flow deck, rounded fluid capacitors dampened eddy currents at the higher flows. The flow chamber was perfused with an NE-1000 withdrawal syringe pump (New Era, Farmingdale, NY). In most experiments, the perfusate was normal saline containing either particles or red blood cells.

Optical system The optical systems were Nikon Eclipse TE2000 inverted epifluorescence microscopes using Nikon CFI Plan Fluor ELWD 10×, 20× and 40× objectives. The intravital microscopy system used a Nikon Fluor WD 20× objective. An XCite (Exfo, Vanier, Canada) 120-W metal halide light source and a liquid light guide was used to illuminate the tissue samples. Excitation and emission filters (Chroma, Rockingham, VT) in separate LEP motorized filter wheels were controlled by a MAC5000 controller (Ludl, Hawthorne, NY) and MetaMorph software 6.26 (Molecular Devices, Brandywine, PA).

Out-of-focus blurring and camera-dependent streaking was assessed using quantitative image analysis (MetaMorph; Molecular Devices, Downingtown, PA). The out-of-focus effects were assessed by optical dispersion. The optical dispersion was a measure of the total fluorescence intensity around the centroid of the particle. The camera-dependent streaking was assessed by the elliptical form factor. The elliptical form factor was calculated as the ratio of a particle's breadth to its length.

Mice Male Balb/c mice (Jackson Laboratory, Bar Harbor, ME), 25–33 g, were used in all experiments. The care of the animals was consistent with guidelines of the American Association for Accreditation of Laboratory Animal Care (Bethesda, MD).

Multi-frame particle tracking Particle tracking was performed on digitally recorded and distance calibrated multi-image “stacks.” The image stacks produced a sequential time history of velocity and direction as the acquired images were time stamped based on the 100 mHz system bus clock of the Xeon processor (Intel, Santa Clara, CA). The movement of individual particles was tracked using the MetaMorph (Molecular Devices) object tracking applications. The intensity centroids of the particles were identified and their displacements tracked through planes in the source image stack. For displacement reference, the algorithm used the location of the particle at its first position in the track. Each particle was imaged as a high contrast fluorescent disk and its position was determined with subpixel accuracy. The image of the particle was tracked using a cross-correlation centroid-finding algorithm to determine the best match of the cell position in successive images. The resulting measures included the x and y coordinates, velocity, mean displacement, mean vector length, mean angle (the angle of the mean vector of the object) and the angular deviation.

Ear microscopy The ear intravital microscopy was performed by using a custom-machined titanium stage (Miniature Tool and Die, Charlton, MA). The tissue contact area consisted of a 2-mm vacuum gallery that provided tissue apposition to the stage surface without compression of the tissue and with minimal circulatory disturbances.

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Organ distribution The relative organ distribution of the fluorescent particles was determined using modified procedures developed previously (Luchtel et al., 1998; Powers et al., 1999; Van Oosterhout et al., 1995). Briefly, tissue samples were harvested from the animals and digested in 8 ml of 4N KOH for 96 h. The fluorescence was separated by individually filtrating the digested samples through a 0.4-μm-pore polycarbonate filter (Whatman Inc. Florham Park, NJ) with negative pressure. The filters containing the fluorescence were rinsed with potassium phosphate buffer (pH 7.0) and followed with deionized water. Each filter was air-dried and then soaked in 4 ml of 2-ethoxyethyl acetate (Cellosolve® acetate, Aldrich Chemical, Milwaukee, WI) for 4 days. Two microliters of supernatant was then transferred into a cuvette and read in a fluorescence spectrophotometer (Hitachi F-4500) at the dye-specific excitation and emission wavelengths.

Results Particle fluorescence intensity The particles used in this study were spheres of 3 diameters: 500 nm, 2 μm and 4 μm. The volumes of the 4μm diameter particles were comparable to the volume of sheep red blood cells when assessed by electrical impedance (Fig. 1A). To compare the fluorescence intensity of the particles to a standard blood tracer, we compared particles of 0.5 μm, 2 μm and 4 μm to PKH26-labeled red blood cells (RBC) by flow cytometry (Fig. 1B). The particles demonstrated a 500- to 10,000-fold increase in fluorescence intensity over the red blood cells labeled with the lipophilic dye PKH26. When normalized for volume, the particles demonstrated a 20,000- to 28,000-fold greater fluorescence intensity per unit volume when compared to the fluorescently labeled red cells.

Fig. 2. Measured flow velocities of the particles (500 nm, 2 μm and 4 μm) and PKH26-labeled red blood cells in the flow chamber. Particle tracking was performed on 1000 frame image stacks obtained at 60–70 fps. A minimum of 100 particles/red cells were tracked at each flow rate. Error bars reflect one standard deviation.

Tracking particles in vitro To assess the resolution of the tracer particles at velocities comparable to those observed in vivo (Johnson and Wayland, 1967), we tracked the 500 nm, 2.0 μm and 4.0 μm particles as well as PKH26-labeled RBCs in a flow chamber at velocities from 125 to 4000 μm/s. As expected, the measured particle velocities demonstrated increasing variance at increased flow velocities (Fig. 2). The information content of particle tracking was dependent on flow velocity, the size of the optical field and the acquisition rate of the CCD camera (Fig. 3). As particle density

Fig. 1. Physical and fluorescence properties of particles and PKH26-labeled red blood cells. (A) The red cell volume, determined by electronic impedance, is shown with the particle volumes (.5 = 500 nm, 2 = 2 μm, 4 = 4 μm particles; R = RBCs). (B) Relative fluorescence intensity histograms obtained by flow cytometry. The histograms were combined on a 5 decade logarithmic scale to represent the relative fluorescence values.

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Fig. 3. Time position tracking of 500 nm particles at 4 flow velocities: (A) 500 μm/s, (B) 1000 μm/s, (C) 2000 μm/s and (D) 4000 μm/s. The flow paths of 8 randomly selected 500 nm particles are shown at each flow velocity. The position of the nanoparticles at 10-ms intervals is noted with an “x”; the arrows show the direction of flow.

increases, and individual particles overlap, it becomes necessary to transition from tracking individual particles to detecting pattern displacement.

increased streaking at 4000 μm/s (P b 0.05) but no significant difference at lower velocities. Particle detection in vivo

Morphometry of particle images In addition to the diffraction limitations of the optical system (Olsen and Adrian, 2000), the sampling error at higher velocities reflects out-of-focus effects and CCD cameradependent streaking artifact. To assess out-of-focus effects, we measured the optical dispersion of the particles at different velocities (Fig. 4A). These morphometric features demonstrated oversampling of the particle image only at velocities of 4000 μm/s (P b 0.05). To assess the characteristic fluorescence streaking on EMCCD acquired images, we assessed the elliptical form factor of the particle images (Fig. 4B). Elliptical form factor, a ratio of particle breadth to length, demonstrated

To assess sampling of particle velocity within the microcirculation, we injected empirically defined concentrations of particles into the mouse tail vein and we evaluated the ear microcirculation by intravital microscopy. The particles were readily tracked in the mouse ear microcirculation (Fig. 5). Continuous monitoring of the ear microcirculation demonstrated that the circulation half-life (t1/2) was inversely related to particle size (Fig. 6). The videomicroscopy demonstrated a progressive increase in the number of static particles within the microscopy window at all three particle sizes; however, the prevalence of static particles was greatest with the 4-μm particles. Organ harvest at the conclusion of the experiment

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Fig. 4. Quantitative morphometry of 500-nm particles perfused through the flow chamber at velocities from 125 to 4000 μm/s. After the application of standard MetaMorph filters, the images were thresholded using a uniform thresholding algorithm and analyzed for (A) optical dispersion (total fluorescence intensity around the centroid of the particle) and (B) elliptical form factor (ratio of the particle's breadth to its length).

demonstrated that greater than 50% of the particles were retained in the liver irrespective of particle size (Fig. 7). Discussion Experimental descriptions of blood flow are based upon either Eulerian or Lagrangian methods. Using the Eulerian approach, blood flow properties – such as the field of velocity Y Y v f ðx ; tÞ – can be described at a given point in space ðxY Þ as a function of time (t). High-density image velocimetry methods are based on this Eulerian approach. The displacement of a large

number of particles in two sequential image fields acquired over a short time interval (between t and t + Δt) defines the velocity field. The differences between the common modes of highdensity particle image velocimetry are primarily related to the effects created by different concentrations of light scattering/ emitting particles in the image field. The basic result of these Eulerian approaches is the same; namely, the use of a large number of particles provides a detailed description of the velocity field at a particular point in space as a function of time. The Lagrangian approach describes the flow from a different viewpoint. Instead of monitoring instantaneous motions of a

Fig. 5. Intravital micrograph and time position tracking of 500-nm particles passing through the ear microcirculation. (A) A selected image obtained 5 min after the intravenous tail vein injection of 500-nm particles. A single nanoparticle is shown (arrow; scale bar = 120 μm). (B) Representative flow paths of two consecutive 500-nm particles. Nanoparticle positions ( and ○) were recorded at 33 ms/s intervals.

•

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▪

Fig. 6. Intravital microscopy observations of the mouse ear microcirculation after intravenous injection of 500 nm ( ), 2 μm ( ) and 4 μm (▴) particles. The microcirculation was sampled at five locations per time point. The number of stationary and moving particles in each 1000 frame image stack was measured. Error bars reflect one standard deviation.

•

large number of marker particles at a fixed location in space, the Lagrangian method tracks the motion of a specific particle, Y x p ðtÞ, in time and space. Mathematically, this is described as a time integration of the velocity field Y

x p ðtÞ ¼

Z

Y

v f ðxY ; tÞdt

Y

x p ð0Þ ¼ Y x 0;

where Y x p ðtÞ is a space coordinate of a tracer particle ‘p' at time t, and Y x p ðt ¼ 0Þ denotes the initial position of the particle ðxY ¼ Y x 0 Þ. As the equation indicates, the Lagrangian method of description includes information about the time history of the velocity fields through which the particle has traveled to arrive at the present position of Y x p ðtÞ. In practice, Lagrangian descriptions track fewer particles than Eulerian methods to diminish the likelihood of overlapping particles. The result is that a Lagrangian description of flow has a less detailed description of the velocity field at a particular point in space but more information regarding the velocity field over space and time. A Lagrangian mode of particle image velocimetry, in which the particle density is sufficiently low that overlapping particle images is unlikely, is referred to as particle tracking velocimetry. As the name implies, particle tracking velocimetry tracks individual particles; particle tracking does not depend upon pattern displacement. The technical obstacles in previous attempts to use particle tracking in vivo have included particle size and signal isolation. The nanoparticles described here provide a convenient tool for seeding the microcirculation with brightly fluorescent particles that are readily tracked in vivo. After a simple tail vein injection, the nanoparticles can be tracked in the microcirculation for 30 min or more to provide a Lagrangian description of the velocity field. For studies of the microcirculation, particle tracking velocimetry is limited by (1) the optical system, (2) the particle diameter

and (3) the out-of-plane displacement (Δz). The optical system presents a range of tradeoffs between lens magnification (including point response function of the lens), the depth of field and the size of the detector array. Each of these components must be tailored to the specific application to optimize optical resolution and minimize out-of-focus effects (Adrian, 1991; Olsen and Adrian, 2000). The physical diameter of particles in the 500-nm to 2-μm range is less relevant to tracking accuracy because the numerical aperture of the objective and the wavelength of the emitted light determine the minimum size of the detected image (Keane et al., 1995; Olsen and Adrian, 2000). Particle diameter is relevant, however, to the particle behavior in complex flow fields, the absolute intensity of particle fluorescence and the particle halflife in the circulation. Finally, the degree of contamination produced by out-of-plane displacement varies with the system being studied. In this report, the horizontal plexus of the ear microcirculation provided a system that minimized out-of-plane (z axis) displacement. The information content of the Lagrangian description depends upon the time resolution of the imaging system and the number of particles in the velocity field. The time resolution, or sampling (frame) rate, is in turn dependent upon the integral time scale of the system. In the flow chamber, we demonstrated that an identical sampling rate produced markedly different amounts of information when particles were tracked at flow velocities from 125 to 4000 μm/s. Because these velocities reflect the velocity range observed in the microcirculation (Wayland and Johnson, 1967), the sampling rate of currently available EMCCD cameras appears to be capable of providing an adequate Lagrangian description of blood flow in vivo. The particle concentrations used in these studies reflected an empirically derived tradeoff between accurate local velocity measurements and the systemic effects of particle entrapment. Microspheres have been used for many years to measure blood flow to end organs based on “single pass” end organ entrapment

Fig. 7. The relative recovered fluorescence of particles entrapped in the lung, liver and spleen 45 min after injection (n = 6). The blood concentration of circulating particles was determined independently and subtracted from the total fluorescence values. Error bars reflect one standard deviation.

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(Heymann et al., 1977; Rudolph and Heymann, 1967). These particulate indicator dyes, however, were generally 10–60 μm in diameter; 20–100 times larger than the 500 nm nanoparticles. The entrapment of most 500-nm particles within the liver is not a reflection of a “first pass” or “graveyard” effect because all the particles from a tail vein injection must pass through the lungs and many through the systemic capillary networks prior to encountering the liver. The mechanism of particle entrapment in the liver and its potential influence on microhemodynamics is an area of ongoing investigation. Acknowledgments Supported in part by NIH Grant HL47078 and HL75426. References Adrian, R.J., 1984. Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry versus particle image velocimetry. Appl. Opt. 23, 1690–1691. Adrian, R.J., 1991. Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261–304. Ben-Sasson, S., Patinkin, D., Grover, N.B., Doljanski, F., 1974. Electrical sizing of particles in suspensions: IV. Lymphocytes. J. Cell. Physiol. 84 (2), 205–214. Bernard, S.L., Glenny, R.W., Polissar, N.L., Luchtel, D.L., Lakshminarayan, S., 1996. Distribution of pulmonary and bronchial blood supply to airways measured by fluorescent microspheres. J. Appl. Physiol. 80 (2), 430–436. Brecher, G., Schneiderman, M., Williams, G.Z., 1956. Evaluation of electronic red blood cell counter. Am. J. Clin. Pathol. 26, 1439–1449. Heymann, M.A., Payne, B.D., Hoffman, J.I., Rudolph, A.M., 1977. Blood flow measurements with radionuclide-labeled particles. Prog. Cardiovasc. Dis. 20 (1), 55–79. Johnson, P.C., Wayland, H., 1967. Regulation of blood flow in single capillaries. Am. J. Physiol. 212, 1405–1415. Keane, R.D., Adrian, R.J., Zhang, Y., 1995. Super-resolution particle imaging velocimetry. Meas. Sci. Technol. 6, 754–768.

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Li, X., Abdi, K., Rawn, J., Mackay, C.R., Mentzer, S.J., 1996. LFA-1 and Lselectin regulation of recirculating lymphocyte tethering and rolling on lung microvascular endothelium. Am. J. Respir. Cell Mol. Biol. 14 (4), 398–406. Li, X., Su, M., West, C.A., He, C., Swanson, S.J., Secomb, T.W., Mentzer, S.J., 2001. Effect of shear stress on efferent lymph-derived lymphocytes in contact with activated endothelial monolayers. In Vitro Cell. Dev. Biol. 37, 599–605. Luchtel, D.L., Boykin, J.C., Bernard, S.L., Glenny, R.W., 1998. Histological methods to determine blood flow distribution with fluorescent microspheres. Biotechnol. Histochem. 73 (6), 291–309. Olsen, M.G., Adrian, R.J., 2000. Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry. Exp. Fluids S166–S174 (Suppl.). Powers, K.M., Schimmel, C., Glenny, R.W., Bernards, C.M., 1999. Cerebral blood flow determinations using fluorescent microspheres: variations on the sedimentation method validated. J. Neurosci. Methods 87 (2), 159–165. Raffel, M., Willer, C.E., Kompenhans, J., 2000. Physical and Technical Background. Particle Image Velocimetry, 3rd ed. Springer, Berlin, pp. 13–60. Rudolph, A.M., Heymann, M.A., 1967. The circulation of the fetus in utero. Methods for studying distribution of blood flow, cardiac output and organ blood flow. Circ. Res. 21 (2), 163–184. Secomb, T.W., Konerding, M.A., West, C.A., Su, M., Young, A.J., Mentzer, S.J., 2003. Microangioectasias: structural regulators of lymphocyte transmigration. Proc. Natl. Acad. Sci. U. S. A. 100, 7231–7234. Su, M., West, C.A., Young, A.J., He, C., Konerding, M.A., Mentzer, S.J., 2003. Dynamic deformation of migratory efferent lymph-derived cells trapped in the inflammatory microcirculation. J. Cell. Physiol. 194 (1), 54–62. Van Oosterhout, M.F., Willigers, H.M., Reneman, R.S., Prinzen, F.W., 1995. Fluorescent microspheres to measure organ perfusion: validation of a simplified sample processing technique. Am. J. Physiol. 269 (2 Pt. 2), H725–H733. Wayland, H., Johnson, P.C., 1967. Erythrocyte velocity measurement in microvessels by a two-slit photometric method. J. Appl. Physiol. 22, 333–337. West, C.A., He, C., Su, M., Secomb, T.W., Konerding, M.A., Young, A.J., Mentzer, S.J., 2001. Focal topographic changes in inflammatory microcirculation associated with lymphocyte slowing and transmigration. Am. J. Physiol, Heart Circ. Physiol. 281 (4), H1742–H1750. Westerweel, J., 1997. Fundamentals of digital particle image velocimetry. Meas. Sci. Technol. 8, 1379–1392.