Particle-Tracking Microrheology Using Micro-Optical Coherence Tomography

Article

Particle-Tracking Microrheology Using Micro-Optical Coherence Tomography Kengyeh K. Chu,1 Diana Mojahed,1,3 Courtney M. Fernandez,5 Yao Li,4 Linbo Liu,1 Eric J. Wilsterman,1 Bradford Diephuis,1 Susan E. Birket,4,5 Hannah Bowers,5 G. Martin Solomon,4,5 Benjamin S. Schuster,6 Justin Hanes,6 Steven M. Rowe,4,5 and Guillermo J. Tearney1,2,* 1 Wellman Center for Photomedicine, Department of Dermatology and 2Department of Pathology, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts; 3Department of Biology, Tufts University, Medford, Massachusetts; 4George Fleming James Cystic Fibrosis Research Center and 5Department of Medicine, University of Alabama at Birmingham, Birmingham, Alabama; and 6Center for Nanomedicine, Johns Hopkins University, Baltimore, Maryland

ABSTRACT Clinical manifestations of cystic fibrosis (CF) result from an increase in the viscosity of the mucus secreted by epithelial cells that line the airways. Particle-tracking microrheology (PTM) is a widely accepted means of determining the viscoelastic properties of CF mucus, providing an improved understanding of this disease as well as an avenue to assess the efficacies of pharmacologic therapies aimed at decreasing mucus viscosity. Among its advantages, PTM allows the measurement of small volumes, which was recently utilized for an in situ study of CF mucus formed by airway cell cultures. Typically, particle tracks are obtained from fluorescence microscopy video images, although this limits one’s ability to distinguish particles by depth in a heterogeneous environment. Here, by performing PTM with high-resolution micro-optical coherence tomography (mOCT), we were able to characterize the viscoelastic properties of mucus, which enables simultaneous measurement of rheology with mucociliary transport parameters that we previously determined using mOCT. We obtained an accurate characterization of dextran solutions and observed a statistically significant difference in the viscosities of mucus secreted by normal and CF human airway cell cultures. We further characterized the effects of noise and imaging parameters on the sensitivity of mOCT-PTM by performing theoretical and numerical analyses, which show that our system can accurately quantify viscosities over the range that is characteristic of CF mucus. As a sensitive rheometry technique that requires very small fluid quantities, mOCT-PTM could also be generally applied to interrogate the viscosity of biological media such as blood or the vitreous humor of the eye in situ.

INTRODUCTION The viscoelastic properties of biological media often play a vital role in functional processes. One prominent example is airway mucus. The viscoelasticity of mucus is thought to be inherently elevated in diseases such as cystic fibrosis (CF) (1) and chronic obstructive pulmonary disease (2), but its role in the pathogenesis of lung disease remains clouded. Research in this area is hindered by the lack of tools that can directly interrogate rheology in a native mucus layer that may be only a few tens of microns thick, rather than relying on expectorated samples that may have a questionable correlation with ongoing processes in the lungs. Recently, rheological techniques have emerged that capitalize on the relationship between the random motion of

Submitted November 6, 2015, and accepted for publication July 15, 2016. *Correspondence: [email protected] Steven M. Rowe and Guillermo J. Tearney contributed equally to this work. Editor: James Grotberg. http://dx.doi.org/10.1016/j.bpj.2016.07.020

particles (Brownian or diffusive motion) and the viscoelastic properties of the surrounding medium (3,4). Thus, any imaging technique that is capable of imaging, localizing, and tracking small particles over time is theoretically able to act as a rheometer. Fluorescence microscopy has emerged as a popular imaging modality for performing particle-tracking microrheology (PTM), and it has a number of advantages. Fluorescently labeled beads are widely available, easily placed onto many media of interest, and can be readily distinguished from the mucus, facilitating automated processing. However, imaging is typically limited to nonscanning wide-field configurations that cannot reveal the bead depth, as optical sectioning techniques such as confocal and two-photon microscopy are usually precluded due to insufficient speed to follow rapidly diffusing particles in three dimensions. The lack of depth sectioning in widefield fluorescence imaging is problematic for cases in which the viscosity is depth dependent, such as in airway mucus, where multiple distinct biological layers are expected. For

Ó 2016 Biophysical Society.

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example, the mucins comprising periciliary gel are often tethered and differ in composition from the overlying mucus (5–7). The mucus layer also has the propensity to form an inhomogeneous mesh and mucus rafts (8,9). In addition to enabling viscoelastic quantification of small volumes of media that would be virtually impossible to obtain for measurements on a conventional cone-andplate rheometer, PTM is also advantageously flexible in terms of the size scale that can be interrogated. Mucus, for example, is composed of a matrix of long mucin chains that form a porous matrix around an aqueous medium. Larger particles at or above the characteristic pore size of a given mucus sample will encounter much greater viscous drag than smaller particles that are more free to move within the pores. Therefore, by using PTM with small beads, one can access the fluid microenvironment and assess the diffusion of particles that are similar in size to therapeutic particles that are intended to penetrate the mucus and reach the underlying epithelium (10). Various bead sizes and coatings that alter interactions with the mucus and other features of the environment can also be used to interrogate the mechanistic causes of disease (11,12). Fluorescence recovery after photobleaching has also been used to probe the fluid properties of mucus by measuring the rate of diffusion of fluorescent dyes in the mucus (13–15). Like macroscopic-scale rheometry, this modality is hindered by a mismatch of size, but in this case the dye molecules are typically too small to be significantly impeded by the mucin matrix (13,14). Therefore, the resulting diffusion constants do not reflect the mucus viscosity experienced by objects on a physiological scale. Structures such as cilia are unlikely to avoid interactions with the mucins, for example. Fluorescently labeled dextrans larger than the fluorophore molecules themselves are sometimes used as diffusants, but even these are typically much smaller than the characteristic pore size of the mucus mesh (15,16). Our laboratory has developed micron-resolution optical coherence tomography (mOCT) (17) and mOCT-based imaging and analysis methods to interrogate the airway surface environment (18). The high resolution (1–2 mm), fast frame rate (40þ frames per second (fps)), and large depth of focus (300 mm) of mOCT have enabled simultaneous and colocalized dynamic measurements of mucociliary transport, including the airway surface liquid and periciliary liquid volume, ciliary beat frequency, and rate of mucociliary transport (9,19). These same properties also enable one to track the motions of individual particles in mucus with sufficient speed and precision to quantify thermal diffusion and thereby perform PTM. Adding a PTM capability to mOCT would provide the only tool with the ability to capture mucus viscosity in the context of quantitative mucociliary transport parameters, which is critical for understanding the role of anomalous viscosity in the pathogenesis of CF and evaluating treatment strategies that aim to improve mucus clearance by reducing viscosity. Our objective in

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this study was to evaluate the feasibility of using mOCT to conduct PTM, and compare the results with those obtained by conventional methods in a range of viscosities relevant to CF.

MATERIALS AND METHODS Imaging The mOCT apparatus has been described previously (17,18). In brief, mOCT is a spectral-domain OCT technology that uses the exceptionally high bandwidth of a supercontinuum light source, centered near 800 nm, to achieve 1 mm axial (depth) resolution. A circular obscuration pupil mask is employed to achieve significant enhancement of the depth of focus, allowing a relatively high numerical aperture (NA ¼ 0.12) lens to create a small spot size (~2 mm lateral, 1 mm axial) that is maintained over a large depth. In its present configuration, the mOCT apparatus uses a SuperK Extreme OCT (NKT Photonics, Birkerød, Denmark). The usable wavelengths are limited by the chromatic limitations of the fiber (SM600) that links the spectrometer to the interferometer, as well as the associated launch and collimation optics. A custom spectrometer using a 940 lp/mm holographic grating (Wasatch Photonics, Logan, UT) and line scan camera (Sprint spL4096-140k; Basler AG, Ahrensburg, Germany) captures wavelengths from 650 nm to 950 nm. In the sample arm of the mOCT interferometer, an f ¼ 25 mm achromatic doublet lens is used as the objective lens (0.12 NA). A rod mirror produces a circular pupil obscuration corresponding to 0.06 NA. A galvo scanner enables OCT imaging with a B-scan frame rate at 40 Hz (512 lines at 20,480 Hz line rate) over a typical field of view of 500 mm. There are two identical copies of the mOCT instrument: one at Massachusetts General Hospital and one at the University of Alabama at Birmingham. The two instruments perform equivalently, and the imaging data presented in this work were acquired from either unit without distinction. The mOCT image sets used for rheology analysis were composed of a minimum of 200 frames, equal to 5 s at 40 fps. Manual operation of the mOCT controls resulted in some variability in the frame count past 200. Imaging was performed at a room temperature of ~298 K. These parameters match the settings that are typically employed for mOCT analysis of mucociliary transport. We conducted mOCT-PTM by imaging regions that contained visible microparticles with sufficient contrast and spacing to clearly distinguish individual particles from the background and from each other. We performed standard Fourier domain OCT image construction (20) using a linear intensity look-up table rather than the log-scale that is typically employed in OCT to reduce the impact of low-intensity noise on particle localization. The axial scale was corrected for the refractive index of water (1.33). Image sequences were analyzed in ImageJ using the particle-tracking plugin SpotTracker (21,22). A manually estimated initial position for each particle was given, which was used by the SpotTracker algorithm to trace a particle’s position through time with subpixel precision (localization precision of sparse particles is much smaller than the optical resolution). Up to 25 particle trajectories were computed per imaging region. The set of particle trajectories was input into a custom MATLAB (The MathWorks, Natick, MA) routine that removes the bulk motion contribution from each track. The common-mode motion for the ensemble of particles in a given region of interest was measured and subtracted from the individual tracks. The remaining motion in the corrected tracks was then plotted as the mean-squared displacement (MSD). The squared displacement of all particle positions along only the axial direction, the highest-resolution axis in mOCT, was averaged, using every combination of displacement pairs possible contained within the length of the track. The axial position is preferred because the high axial resolution of mOCT enables the greatest localization accuracy in this direction. For example, from a 5-s duration trajectory x(t), the MSD for Dt ¼ 1 s was the mean

Particle-Tracking Microrheology with mOCT of the squared displacements between every pair of points that were 1 s apart, i.e., x(1) – x(0), x(1.025) – x(0.025), x(1.05) – x(0.05), etc., through x(5) – x(4). Curve-fitting (described in the following section) was performed to mitigate noise, to produce a smooth MSD as a function of time.

Corrections for randomness and noise Brownian motion is an entropy-driven thermal phenomenon, and reliance on measurements of such random motion is inevitably subject to statistical variance. Additionally, image noise causes a random variation in particle position measurements, termed localization noise or error (23), that is independent of time and is common to both mOCT and fluorescence forms of PTM. The instantaneous slope of the MSD used in the algebraic StokesEinstein equation (3) is highly sensitive to noise. Therefore, a smooth curve must be fit to the observed MSD to mitigate this effect. The effect of localization noise is also evident on the MSD curve as a discontinuity at time zero: all particles appear to move by an amount determined by the localization noise, even if no time has passed to allow real Brownian motion. The vertical offset of the MSD, which appears as a nonzero y intercept, is therefore representative of the localization noise amplitude (24,25). Consequently, the y intercept of MSD fitting was set to zero to avoid this spurious contribution. The corrected MSD was converted to frequency-dependent dynamic viscoelasticity using the generalized Stokes-Einstein relation and Laplace transform approximations as described by Mason et al. (3). In cases where the viscous loss is frequency dependent, the MSD is nonlinear, necessitating the use of higher-order fitting functions. However, polynomial fits are not generally monotonic, whereas the expected value of MSD must strictly increase in time. A decrease in the observed MSD as a function of time may result occasionally from random behavior and noise, but a high-order polynomial that could capture such a decrement in its fit would produce a nonphysical dynamic viscosity result. To prevent nonmonotonic fits while preserving higher-order dynamics, we utilized a three-term fit of shifted and scaled error functions with additional linear and offset terms:

MSDfit ðtÞ ¼ c1 t þ c0 þ

3 X

an erf ðt  bn Þ;

(1)

n¼1

where an, bn, c0, and c1 are fitting parameters that were computed using publicly available MATLAB source code (26). Since the error functions were monotonic, because the set of an and c1 was constrained to be positive definite, the fit output MSDfit was certain to be monotonically increasing, preventing nonphysical occurrences of negative slope. Additionally, c0 was defined such that MSDfit(0) ¼ 0, annulling the offset artifact caused by localization noise.

Numerical analysis of sensitivity Even with curve-fitting designed to mitigate the effects of noise, the fit parameters themselves are subject to error, since both localization noise and the inherent randomness of Brownian motion contribute to uncertainty in the MSD slope fit. The diffusion constant of a given particle size in a particular medium is proportional to the slope of the MSD. Therefore, a minimum diffusion sensitivity exists, below which a measured diffusion constant is not statistically distinguishable from zero due the variance in the MSD fit. Since viscosity is inversely related to the amplitude of diffusion, this minimum diffusion translates to a maximum viscosity that can be measured by PTM. The effect of both localization noise and randomness of diffusion has been extensively analyzed by others (23–25,27). In particular, Michalet (24) derived an analytical expression of the variance in the MSD slope fit as a function of both sources of error. Although the full equation is too

cumbersome to reproduce here (see Eq. F.23 in (24)), we numerically computed the minimum amplitude of diffusion (viscosity) that results in an MSD of particles in a purely viscous medium that is distinguishable from zero slope, using both a 1 standard deviation (1s and 2s confidence interval. We analyzed the results for our typical imaging conditions as well as a range of particle-track counts and durations. To confirm the accuracy of the predicted maximum sensitivity, we also simulated 1000 sets of 25 diffusing particles, with the noise amplitude set to equal to the amount of noise observed from mOCT particle localization. The Brownian motion amplitude was simulated to match the viscosity of the critical value predicted by the Michalet model, so that the expected value of the MSD slope would be 2s over zero.

Static sample localization error We quantified the MSD offset due to pure localization error by performing mOCT-PTM on 500 nm polystyrene beads solidly embedded in a cured transparent epoxy with an index of refraction of 1.33 to match that of a typical aqueous medium (MY Polymers Ltd., Nes Ziona, Israel). Because particle diffusion was negligible in this solid sample, stochastic error was eliminated and the effect of localization error was isolated, causing the vertical offset in the resulting time-dependent MSD.

mOCT-PTM of dextran standards Aqueous solutions of dextran, a high-molecular-weight polysaccharide with a strong viscosity dependence on concentration (28,29), are often used as viscosity test solutions (30,31). We used four concentrations (5%, 12%, 20%, and 30% w/v) of dextran (molecular mass ¼ 500 kD; Sigma-Aldrich, St. Louis, MO). Each solution was measured three times at ambient room temperature with each of three methods: mOCT-PTM, fluorescence microscopy PTM, and a standard cone-and-plate rheometer (Discovery HR2; TA Instruments, New Castle, DE). For both mOCT-PTM and fluorescence PTM, 500 nm uncoated fluorescent polystyrene beads (Invitrogen, Eugene, OR) were introduced into the dextran solutions at a 1:300 dilution from stock (2% solids) and homogenized by a vortex mixer. Samples were placed between a glass slide and coverslip separated by a 500 mm rubber spacer for imaging. mOCT data were acquired at 40 Hz for 5% and 12% dextran, and at 20 Hz for 20% and 30% dextran. Fluorescence images were acquired on a standard epifluorescence upright microscope (BX61; Olympus, Tokyo, Japan) with 200 frames at 27.3 fps using a 20 objective (NA ¼ 0.4). Fluorescence was excited by a 470 nm LED and a GFP filter cube (Thorlabs, Newton, NJ), and images were captured by a CCD camera (Pilot piA1000-60gm; Basler). Twenty-five particle trajectories were generated for PTM analysis from each of n ¼ 3 image sets for each modality.

mOCT-PTM of mucus We utilized mOCT-PTM to compare the viscosities of mucus generated by human bronchial epithelial (HBE) primary cultures from non-CF and CF donors. Previously described methods (18,32,33) were utilized to generate n ¼ 4 each of non-CF HBE cultures (P1) from one healthy donor and DF508 homozygous HBE cultures (P2) from one CF donor. An aqueous suspension of 500 nm particles was added to the apical surface of each culture. A 0.01% benzalkonium chloride media mixture was added for 1 h to immobilize cilia. The cells were washed in media for 15 min and then allowed to equilibrate in a 37 incubator for 3 h. The samples were then brought to room temperature and each sample was imaged in five separate regions, for a total of 40 regions imaged. The goal for each well was 25 trajectories acquired from each of five regions of interest (125 tracks per well), but insufficiencies of mucus or visible particles prevented us from reaching the target number in most cases, particularly in the CF samples. The following numbers of tracks and regions were used in each well: CF well 1: 56 tracks

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Chu et al. (five regions); CF well 2: 39 tracks (five regions); CF well 3:28 tracks (five regions); CF well 4: 40 tracks (five regions); non-CF well 1: 125 tracks (five regions); non-CF well 2: 90 tracks (five regions); non-CF well 3: 28 tracks (three regions); and non-CF well 4: 83 tracks (five regions). Because the viscosity of CF mucus in particular is not necessarily normally distributed, a nonparametric test is necessary to determine statistical significance. We utilized the two-sample Kolmogorov-Smirnov test to compare non-CF and CF mucus.

RESULTS Static sample localization error Fig. 1 shows the MSD of 25 particle trajectories derived from 500 nm polystyrene beads embedded in low-index cured epoxy, which was designed to match the index of refraction from water to accurately simulate mOCT signal intensity from beads in an aqueous medium. Because the solid epoxy medium prevents diffusion, the MSD does not change appreciably with time. The vertical offset of ~0.04 mm2 indicates the amount of localization error. This result is a key input to the numerical analysis of sensitivity in the sections below. Numerical simulation analysis Fig. 2 shows the maximum viscosity measurable by mOCTPTM as computed by numerical simultations as a function of varying the number of available particle tracks (Fig. 2 A) and the time duration of the particle tracks (Fig. 2 B). Each of these plots appears to be linear on a log-log plot (with the exception of very low particle counts in Fig. 2 A), indicating a power law relationship between each parameter and the maximum viscosity. This relationship can be quantified phenomenologically by computing the log-log fit slope. The slope of the fits indicates a track count dependence power of 0.56, and the corresponding power for track duration was 1.6. The base parameters of mOCT rheology (25 tracks, 200 frames at 40 fps, and 0.04 mm2 noise measured MSD offset) produced a maximum

sensitivity of ~4600 centipoise (cP) at the 2s margin. In addition to these phenomenological fits, the localization noise amplitude was analytically related to the maximum viscosity by a power of 1, and the frame rate interval power (with total number of frames held constant) was 1. Based on these fits to the simulated data, the maximum measurable viscosity can be modeled to be (at the 2s margin) n 0:56 n 1:6 particles frames hmax ¼ 4600cP , 25 200   1  (2) ε Dt  ; 0:04 mm2 25 ms where hmax is the maximum viscosity, nparticles is the number of particles tracked, nframes is the number of frames in one trajectory, ε is the MSD vertical offset resulting from localization error, and Dt is the interval between successive mOCT frames. This model indicates that the duration of the particle tracks in frames can be most profitably increased to improve viscosity sensitivity, and conversely that a reduction in frame count incurs a severe penalty. The number of particles tracked exhibits a comparatively weak effect on sensitivity. The frame rate can also be decreased (thereby increasing the interframe interval Dt) in favor of higher viscosity sensitivity. If the slow-moving particles in highly viscous media are allowed to diffuse for a longer period of time, the MSD may be elevated above the noise floor. Fig. 3 shows the histogram of MSD slopes derived from 1000 sets of 25 simulated particles in 4600 cP medium, with noise matching the measured MSD offset of 0.04 mm2. From the simulated results, the measured slope mean was 1.1  103 mm2/s, and the standard deviation s was 0.58  103 mm2/s. The mean is indeed ~2s above zero, which confirms the maximum measurable viscosity of 4600 cP predicted using the Michalet (24) equations. Additionally, assuming the use of standard mOCT settings and procedures as defined above, the error fraction of the viscosity measurement as a function of the viscosity was plotted (Fig. 4). At low viscosities (<1000 cP), the error is dominated by the randomness of the MSD for rapidly diffusing particles, resulting in a nearly constant ratio of noise to diffusion amplitude and a relatively low dependence on viscosity. At high viscosities (>1000 cP), the amplitude of localization noise overtakes the slow diffusion of particles and becomes the limiting factor. As the error fraction rises above 0.5, the slope fit is no longer 2s greater than zero, which was previously used as the definition for maximum measurable viscosity (4600 cP, standard parameters). The 2s and 1s cutoff lines, where the error fraction is respectively 0.5 and 1, are drawn in Fig. 4. Validation against standard modalities

FIGURE 1 Time-dependent mOCT-PTM MSD resulting from 25 tracked particles in a static epoxy sample. A lack of time dependence indicates nondiffusing beads. A vertical offset of ~0.04 mm2 reflects localization error.

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mOCT-PTM measurements of four dextran-500 solutions of varying concentration are shown in comparison with

Particle-Tracking Microrheology with mOCT

FIGURE 2 (A and B) Numerical solutions for maximum measurable viscosity as a function of (A) particle track count (40 fps, 200 total frames, 0.04 mm2 noise MSD offset) and (B) duration (40 fps, 25 particle tracks, 0.04 mm2 noise MSD offset), using both 1s and 2s thresholds of detection. Results are based on equations derived in (24). To see this figure in color, go online.

gold-standard cone-and-plate rheometer and conventional fluorescence microscopy PTM results in Fig. 5. A 25-particle set in a single imaging field of view is defined to be one sample for both mOCT and fluorescence PTM. Dynamic viscosity is generally frequency dependent, and the results in Fig. 4 were sampled at 1 Hz to represent a physiologically relevant frequency that would be expected in vivo. The Newtonian behavior of the dextran samples yielded nearly uniform slopes in the MSD (Fig. 6 A) and constant viscosity as a function of frequency (Fig. 6 B) as measured by mOCTPTM. The dynamic viscosity of each concentration was drawn from 75 particle tracks each (three image sets, 25 particles each).

(Fig. 8 A), which are similar to previously reported values derived from fluorescence microscopy PTM (19). The nonparametric, two-sample Kolmogorov-Smirnov test indicated a significant difference between CF and non-CF viscosities (p < 0.05). Fig. 8 B illustrates a single representative particle trajectory from both normal and CF mucus as measured by mOCT and the SpotTracker plugin. Fig. 8 C depicts the CF and normal MSDs from a single region containing the tracks shown in Fig. 8 B, and Fig. 8 D shows the frequencydependent dynamic viscosity derived from the MSDs. DISCUSSION

A representative mOCT sequence that includes images of 500 nm polystyrene beads suspended in the airway surface liquid of an HBE culture is shown in Fig. 7. The mOCT-PTM results for HBE mucus are shown in Fig. 8. The CF HBE viscosity was 184 5 29 cP (SEM) and the non-CF HBE viscosity was 17.7 5 4.3 cP (SEM)

The low amplitude of Brownian motion combined with the coarse resolution of typical OCT systems has likely impeded the development of OCT particle-tracking rheology. To our knowledge, the mOCT-PTM approach presented here is the most sensitive OCT-based PTM method reported to date. In 2002, Popescu et al. (34) utilized low-coherence interferometry to perform rheology on a small volume of scatterers, but the indicated viscosities were limited to a few centipoise. Another method based on correlation statistics of diffusers

FIGURE 3 MSD slopes from simulated sets of 25 particles, each in 4600 cP medium, which was predicted to yield an MSD slope 2s above zero given the observed mOCT noise. The distribution of the slopes resulting from n ¼ 1000 sets closely matches the model’s prediction. The MSD slope was found to be negative in 21 sets (2.1%), compared with 2.23% predicted by the normal distribution for z ¼ 2.

FIGURE 4 Numerical solutions for the standard error fraction of the MSD slope, representing the error fraction of measured viscosity, using standard mOCT procedures (500 nm particles, 25 particles, 200 frames at 40 fps). The 1s and 2s cutoff lines are shown, indicating the noise fraction levels at which the slope is 1s and 2s above 0, respectively. Results are based on equations derived in (24). To see this figure in color, go online.

mOCT-PTM of mucus

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FIGURE 5 (A and B) The viscosities of varying dextran concentrations (5%, 12%, 20%, and 30% w/v) measured by mOCT-PTM, fluorescence PTM, and cone-and-plate rheometer are shown with standard errors (n ¼ 3), unnormalized (A) and normalized to the gold-standard cone-and-plate value for each dextran concentration (B). To see this figure in color, go online.

was recently reported by Chhetri et al. (35), but it requires the application of gold nanorods. Oldenburg et al. (36) used OCT to track macroscopic particle motion for measurement of mucociliary transport in airways, but they did not perform viscoelastic measurements. The vertical offset on MSD plots using mOCT of 0.5 mm polystyrene spheres was found to be ~0.04 mm2, corresponding to a root mean-square (RMS) error of 0.2 mm for each observation of the bead. The mOCT axial sampling for these images was 0.8 mm/px, and thus the localization error was 0.25 px, which is comparable to the RMS error levels of ~0.2 px reported by Sage et al. (22) using the SpotTracker algorithm in high-SNR imaging for fluorescence PTM. The localization precision is therefore superior to both the pixel size and the optical resolution. The centroid of a distribution of intensity counts is the result of the average of

many counts, allowing the position to be computed with subpixel precision, a phenomenon that is leveraged by superresolution microscopies based on sparse particle localization (37,38). Given this level of noise, which is a function of our mOCT system performance and therefore is relatively fixed, we sought to determine the impact of imaging parameters that can be modified by choice, i.e., the number of particles to be tracked, the time duration of tracking, and the frame rate. The mathematics underlying particle-tracking rheology is very difficult to solve analytically as a function of these parameters. Fortunately, Michalet (24) provided highly detailed derivations of numerical solutions, which are highly general but difficult to interpret analytically. We therefore computed solutions to Michalet’s results in a parameter space that matches the ranges expected for

FIGURE 6 (A and B) MSDs (A, left) and frequency-dependent dynamic viscosities (B, right) of varying dextran concentrations (5%, 12%, 20%, and 30% w/v) measured by mOCT-PTM. A total of 75 particle tracks (3 image sets, 25 particles each) were analyzed for each concentration. A constant MSD slope and uniform frequency response indicate Newtonian behavior. To see this figure in color, go online.

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Particle-Tracking Microrheology with mOCT

FIGURE 7 Single frame from mOCT image sequence showing a crosssectional view of HBE cells (non-CF) grown on a polycarbonate Transwell filter. Polystyrene microspheres (500 nm) used for mOCT-PTM were suspended in the mucus. Scale bar, 20 mm. Please see Movie S1 for full video. To see this figure in color, go online.

mOCT-PTM of normal and CF mucus to predict how our choice of settings would affect noise and sensitivity. We expressed these predictions in terms of the maximum detectable viscosity, which scales inversely with the mOCTPTM sensitivity of detection for diffusive motion. We consid-

ered both 1s and 2s thresholds of sensitivity, where s is the standard deviation of the MSD slope resulting from both the stochastic nature of diffusion and the error of localization. The effect of frame interval (the inverse of frame rate) is evident from the model: waiting a longer period of time between acquisitions results in more diffusion between time samples, and is equivalent to lowering viscosity by a proportional amount. Localization noise likewise has a directly observable proportional impact. The effects of the number of frames over which a particle is tracked or the number of particles that are tracked were more complex and required us to compute numerical solutions, which, unsurprisingly, demonstrated that an increase in either factor will improve the sensitivity of PTM (Fig. 2). Tracking particles over a longer period of time allows the low-amplitude Brownian motion in high-viscosity media to accumulate enough to be detected. Tracking more particles allows stochastic variations endemic to thermally driven diffusion to be averaged over more samples.

FIGURE 8 (A) Viscosity of CF and normal mucus measured in situ on HBE cell cultures using mOCT-PTM. (B) Representative track of a 500 nm particle over 5 s in the airway surface liquid overlying normal and CF HBE cell cultures. Note the greater precision in the vertical/axial direction compared with the horizontal/lateral direction. (C) Averaged MSD of five regions from one well each of normal and CF HBE cultures. (D) Corresponding averaged frequencydependent dynamic viscosity. In (C) and (D), SEM margins are indicated by the thin lines bracketing the data curves. To see this figure in color, go online.

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Both particle count and track duration appear to have a geometric power relationship with maximum viscosity, as indicated by their linear appearance on a log-log plot, although their different slopes indicate an unequal dependence. The dependencies on each evaluated factor (number of particles, number of time samples, localization noise, and frame interval) were aggregated into Eq. 1, which centers around the 4600 cP level that results from our standard mOCT rheology parameters (25 particles, 200 time samples, 0.04 mm2 localization variance, 25 ms frame interval). The more conservative 2s threshold of detection was applied, which determined the base hmax of 4600 cP. As previously noted, increasing the number of tracked particles has a positive but relatively weak (power ¼ 0.56) effect on sensitivity. The track duration in time samples has a far greater effect, although practical limits due to excessive sample motion often prevent arbitrarily long tracking periods. Notably, increasing the sampling rate while preserving the time duration of the imaging sequence (increasing nframes and decreasing Dt) has a net positive effect, with power ¼ 0.6. Higher frame rates should therefore result in better sensitivity. These numerical results of Michalet’s (24) equations are encapsulated in Eq. 2. The power of each term’s exponent helps to predict the consequences of abnormal experimental conditions. For example, Eq. 2 predicts the loss of maximum detectible viscosity when fewer than 25 bead trajectories can be derived from an image sequence, as may be encountered when little airway surface liquid exists. These results also indicate how one can improve the sensitivity to achieve higher-viscosity measurements: a longer duration of tracking is the simplest option, but an increased frame rate is even more effective. However, little can be done if there are too few trackable particles owing to a low level of mucus, in which case the analysis will instead describe the loss of sensitivity attributable to insufficient mucus. Additionally, the proximity of surfaces to any diffusing particles that may exist in an extremely thin layer of mucus may create boundary conditions that could confound the PTM analysis. It should also be noted that although mOCT-PTM suffers from the same limitations as other PTM techniques based on en face imaging, in contrast to those techniques, the mucus layer thickness on mOCT images is readily apparent (as in Fig. 7), which allows us to reject potentially spurious data arising from samples with insufficient mucus. The results from 1000 simulated sets of mOCT particle tracks of maximum detectable viscosity (Fig. 3) confirm that the mean measured MSD slope lies 2s above zero. The probability of measuring a zero or negative slope at this viscosity is an acceptably low 2%. The plot of error fraction as a function of viscosity (Fig. 4) also shows 2 error rising above the mean at 4600 cP, but also illustrates the behavior of noise under lower-viscosity conditions. The noise fraction is nearly constant at low viscosities and does not decline for further decreases in viscosity; a roughly 20% error fraction persists. This low viscosity range repre-

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sents the regime in which the inherently stochastic behavior of particle diffusion dominates the error of localization, which can be expected for the large diffusion amplitudes of low-viscosity media. This is an inherent limitation in using a relatively small number (n ¼ 25) of tracked particles for PTM employing both mOCT and conventional fluorescence microscopy. We validated our mOCT and fluorescence PTM methods against a gold-standard cone-and-plate rheometer with four dextran solutions of varying concentration (Fig. 5). Both PTM-based methods exhibited higher variability with repeated measurements, as predicted above. Most importantly, however, each method yielded close agreement with each other and the gold standard, confirming the accuracy of PTM. The limitations imposed by stochastic diffusion in both PTM forms are evident: the error bars are generally wider than those obtained for the cone-and-plate measurements, and variation is high due to the relatively low number of particle sets (n ¼ 3). The unity slopes in the log-log plots of MSD and the flatness of the dynamic frequency response shown in Fig. 6 also indicate that the Newtonian behavior of the dextran solution is correctly captured across the frequency range. Finally, our application of mOCT-PTM to mucus in situ on human airway cultures (Fig. 8) revealed a significant difference in viscosity between mucus derived from cells of a healthy donor and that obtained from cells of a CF patient. The representative particle trajectories shown in Fig. 8 B clearly show much more suppressed Brownian motion in the CF case compared with the normal cells. These trajectories also show the disparity in localization accuracy in the horizontal and vertical directions resulting from the superiority of the mOCT axial resolution (1 mm) compared with the lateral resolution (2 mm). Other sources of lateral error, including galvanometer scan error, may contribute to the poorness of the lateral precision, and the total lateral error dominates the amplitude of diffusion. Therefore, only the more accurate axial position data are utilized to compute viscosity. This choice optimizes the sensitivity of mOCTPTM but requires the assumption that the viscoelasticity is isotropic, i.e., it can be represented as a scalar field. Fig. 8 C shows the MSD evolution as a function of time for one region, which is nearly linear in trend for both CF and normal mucus, but with reduced diffusion in the CF mucus. Note also that the MSD appears to decrease approaching 5 s in the CF case. This is an artifact of the fact that noise at large time displacements is relatively high as a result of fewer pairs of particle positions being averaged. When localization noise dominates the true diffusive motion, the amount of particle motion will likely be overestimated, resulting in the viscosity being underestimated. Additionally, some of the CF regions contained few traceable particles, which also elevates noise. Fig. 8 D shows the frequency-dependent dynamic viscosity corresponding to this MSD, which also illustrates an elevated overall

Particle-Tracking Microrheology with mOCT

viscosity for CF mucus. The increased noise level seen at the higher frequencies results from errors in MSD offset correction through error function fitting, which are small but represent a large fraction of the MSD at the short time intervals corresponding to higher frequencies. One limitation of mOCT-PTM is that the high lateral resolution constrains imaging to a thin cross section of the mucus, essentially 2 mm thick. As particle diffusion occurs in three dimensions, some particles may depart the field during the imaging time and thus will be untraceable. Since particle diffusion is assumed to be isotropic, the motion of particles in the axial dimension, as tracked by mOCT-PTM, can be used to represent the motion in the out-of-plane direction as well. Thus, as the MSD approaches 4 mm2 (and the RMS particle motion begins to exceed the 2 mm slice width), particle departure becomes a significant factor. Therefore, particle departure predominantly affects measurements of low viscosity, and may be thought of as a form of saturation. A viscosity of 6.5 cP causes the MSD to reach 4 mm2 in our standard imaging time of 5 s, which can be defined as the lower bound of measurable viscosity resulting from this saturation, thus providing a dynamic range bookend to the maximum measurable viscosity of 4600 cP discussed above. Another restriction of this study is the immobilization of cilia in the HBE cultures before imaging. Mucociliary transport greatly reduces the available tracking time of particles as they are carried out of the field of view. Because the sensitivity of mOCT-PTM is highly dependent on the particle count, we chose to arrest the transport to maximize accuracy for this first mOCT-PTM study. To compensate for common motion of particles caused by transport, we implemented a common-mode motion removal routine, which was active in this experiment to help combat any residual bulk motion. Rheological studies on tracheobronchial mucus from healthy human lung airways have been limited due to the difficulty of collecting samples, since sputum cannot be spontaneously expectorated in normal patients without induction, which dilutes mucus with saline. However, studies of human CF sputum using macroviscosity techniques have determined viscosities to be 7  104 times the viscosity of water (1 cP) at a shear rate of 0.2 s1 (39). Microrheological studies of CF sputum showed 15- and 7-fold lower viscosities than the macroviscosities probed by 100- and 200-nm particles, respectively (39), or ~4500–10,000 cP, which TABLE 1

verges on the maximum of the mOCT-PTM range. Any significant reduction in viscosity induced by mucus-thinning therapies would be detectable. Additionally, the viscosity measurements we obtained in mucus produced by CF HBE cells, using both mOCT and fluorescence PTM methods, were <1000 cP on average. Further, the viscosity of specimens obtained from airway diseases with less severe obstruction (e.g., non-CF bronchiectasis, chronic obstructive pulmonary disease, and asthma) is expected to be far lower. We therefore expect that our calculated maximum detectable viscosity of 4600 cP will be sufficient to capture a useful range of physiological conditions in studies of mucus viscosities in situ. As both techniques rely on the same physics of thermal diffusion, the mOCT-PTM and conventional fluorescence microscopy PTM results are analyzed identically. The only difference is in the modality used to image the particles. However, simply using a cross-sectional imaging technique such as mOCT is advantageous. Particles can be tracked in a depth-dependent fashion, preventing particles that are trapped on the cell surface, for example, from contributing spuriously to the results. Furthermore, mOCT is already capable of providing many other measurements relevant to airway microfunction, and introducing mOCT viscosity measurements adds key data that can be acquired simultaneously and colocalized with the epithelium and mucus transport apparatus. However, the 1 mm resolution of mOCT, albeit high for OCT, remains short of what most research-grade fluorescence microscopes offer. In situations where viscosity sensitivity is paramount and the application is amenable to fluorescence microscopy, conventional fluorescence PTM may be preferable. This may also be the case for samples in which the mucus layer is thin and largely homogeneous, where a wide-field configuration may more easily yield a larger area encompassing more particles. Like fluorescence PTM, mOCT-PTM computes the complex shear modulus, which contains measures of both viscosity and elasticity. However, in this work we focused on validating measurements of viscosity. At this time, we have not fully explored the accuracy of mOCT-PTM for assessing the energy storage capacity of complex viscoelastic fluids such as mucus. Table 1 below summarizes the qualitative attributes of both PTM techniques in addition to cone-and-plate rheometry.

Comparison of mOCT-PTM, Fluorescence PTM, and Cone-and-Plate Rheometry

Minimum sampling volume Differentiates measurements by depth Combinable with correlated mucociliary transport measurement Stochastic noise from quantized particle tracks In situ capable Typical limiting factor

mOCT-PTM

Fluorescence PTM

Cone-and-Plate

none yes yes

none no no

~200 mL no no

yes yes thin mucus layers may not contain enough particles

yes yes lack of depth-resolved information

no no large volume required, analysis cannot be done in situ

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Chu et al.

CONCLUSIONS

ACKNOWLEDGMENTS

We have demonstrated that mOCT imaging can resolve particles with sufficient SNR and stability to be used for PTM, which can be applied for in situ measurements of mucus viscosity, a key disease parameter in a variety of conditions. Our measurements are accurate for a vast range of physiologically relevant viscosities. Our analysis demonstrates that mOCT images that are acquired over 5 s at 40 fps, and include 25 tracked particles, can measure viscosity up to 4600 cP. We validated our mOCT-PTM measurements against fluorescence PTM as well as gold-standard cone-and-plate rheometry using dextran solutions. Our in situ mOCT-PTM analysis of CF and normal mucus from primary cultures of HBE cells confirms that a statistically significant elevation of viscosity exists in CF. Our work in this study was focused on validating viscosity measurements, although mOCT-PTM measures the complex shear modulus, which includes both viscosity and elasticity. PTM allows very small volumes of mucus or sputum to be interrogated, overcoming a major limiting factor in CF mucus studies. Unlike fluorescence PTM, mOCT-PTM allows particles to be filtered by depth, restricting analysis of potentially heterogeneous mucus to targeted layers. However, the key advantage of mOCT-PTM is that it provides the ability to colocalize rheological information with mOCT quantification of the functional microanatomy of the respiratory epithelium. Many questions regarding CF still revolve around the interplay between viscosity and other factors involving mucociliary transport and airway hydration. mOCT-PTM offers the potential to correlate viscoelasticity with measurements of airway surface liquid and periciliary liquid volume and mucociliary transport, all of which we have previously measured in situ with mOCT. With the additional capability of PTM, mOCT can be used as an integrated tool to study the pathogenic role of mucus viscosity in CF, to test experimental therapeutics intended to improve mucus clearance by reducing viscosity, and, when implemented in vivo, to evaluate individual patients’ responses to treatments.

This work was supported by the National Institutes of Health (R01 HL116213), the Cystic Fibrosis Foundation (Mucociliary Clearance Consortium), and the Flatley Foundation.

SUPPORTING MATERIAL One movie is available at http://www.biophysj.org/biophysj/supplemental/ S0006-3495(16)30586-0.

AUTHOR CONTRIBUTIONS All authors reviewed and contributed to the writing of the manuscript. K.K.C., L.L., S.M.R., and G.J.T. designed the experiments. K.K.C., D.M., C.F., L.L., and E.J.W. carried out imaging experiments. D.M., S.E.B., and C.F. prepared samples. K.K.C., D.M., C.F., Y.L., E.J.W., S.E.B., and H.B. performed data analysis. K.K.C., L.L., and B.D. wrote analysis software. K.K.C. performed numerical simulations. G.M.S. and S.M.R. contributed physiological expertise. B.S.S. and J.H. provided expertise with particle-tracking algorithms. S.M.R. and G.J.T. jointly supervised the project.

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REFERENCES 1. Jayaraman, S., N. S. Joo, ., A. S. Verkman. 2001. Submucosal gland secretions in airways from cystic fibrosis patients have normal [Na(þ)] and pH but elevated viscosity. Proc. Natl. Acad. Sci. USA. 98:8119– 8123. 2. Rogers, D. F. 2000. Mucus pathophysiology in COPD: differences to asthma, and pharmacotherapy. Monaldi Arch. Chest Dis. 55:324–332. 3. Mason, T. G., K. Ganesan, ., S. C. Kuo. 1997. Particle tracking microrheology of complex fluids. Phys. Rev. Lett. 79:3282–3285. 4. Lai, S. K., Y. Y. Wang, ., J. Hanes. 2009. Micro- and macrorheology of mucus. Adv. Drug Deliv. Rev. 61:86–100. 5. Derichs, N., B. J. Jin, ., A. S. Verkman. 2011. Hyperviscous airway periciliary and mucous liquid layers in cystic fibrosis measured by confocal fluorescence photobleaching. FASEB J. 25:2325–2332. 6. Button, B., L. H. Cai, ., M. Rubinstein. 2012. A periciliary brush promotes the lung health by separating the mucus layer from airway epithelia. Science. 337:937–941. 7. Kesimer, M., C. Ehre, ., R. J. Pickles. 2013. Molecular organization of the mucins and glycocalyx underlying mucus transport over mucosal surfaces of the airways. Mucosal Immunol. 6:379–392. 8. Hattrup, C. L., and S. J. Gendler. 2008. Structure and function of the cell surface (tethered) mucins. Annu. Rev. Physiol. 70:431–457. 9. Liu, L., S. Shastry, ., G. J. Tearney. 2014. An autoregulatory mechanism governing mucociliary transport is sensitive to mucus load. Am. J. Respir. Cell Mol. Biol. 51:485–493. 10. Lai, S. K., Y. Y. Wang, and J. Hanes. 2009. Mucus-penetrating nanoparticles for drug and gene delivery to mucosal tissues. Adv. Drug Deliv. Rev. 61:158–171. 11. Schuster, B. S., J. S. Suk, ., J. Hanes. 2013. Nanoparticle diffusion in respiratory mucus from humans without lung disease. Biomaterials. 34:3439–3446. 12. Lai, S. K., Y. Y. Wang, ., J. Hanes. 2009. Altering mucus rheology to ‘‘solidify’’ human mucus at the nanoscale. PLoS One. 4:e4294. 13. Radomsky, M. L., K. J. Whaley, ., W. M. Saltzman. 1990. Macromolecules released from polymers: diffusion into unstirred fluids. Biomaterials. 11:619–624. 14. Olmsted, S. S., J. L. Padgett, ., R. A. Cone. 2001. Diffusion of macromolecules and virus-like particles in human cervical mucus. Biophys. J. 81:1930–1937. 15. Tang, X. X., L. S. Ostedgaard, ., M. J. Welsh. 2016. Acidic pH increases airway surface liquid viscosity in cystic fibrosis. J. Clin. Invest. 126:879–891. 16. Suk, J. S., S. K. Lai, ., J. Hanes. 2009. The penetration of fresh undiluted sputum expectorated by cystic fibrosis patients by non-adhesive polymer nanoparticles. Biomaterials. 30:2591–2597. 17. Liu, L., J. A. Gardecki, ., G. J. Tearney. 2011. Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography. Nat. Med. 17:1010–1014. 18. Liu, L., K. K. Chu, ., G. J. Tearney. 2013. Method for quantitative study of airway functional microanatomy using micro-optical coherence tomography. PLoS One. 8:e54473. 19. Birket, S. E., K. K. Chu, ., S. M. Rowe. 2014. A functional anatomic defect of the cystic fibrosis airway. Am. J. Respir. Crit. Care Med. 190:421–432. 20. Wojtkowski, M., V. Srinivasan, ., J. Duker. 2004. Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation. Opt. Express. 12:2404–2422.

Particle-Tracking Microrheology with mOCT 21. Sage, D. SpotTracker. http://bigwww.epfl.ch/sage/soft/spottracker/. Accessed on March 9, 2015.

low- and high-viscosity dextran and a low-viscosity Hb-based O2 carrier. Am. J. Physiol. Heart Circ. Physiol. 287:H363–H373.

22. Sage, D., F. R. Neumann, ., M. Unser. 2005. Automatic tracking of individual fluorescence particles: application to the study of chromosome dynamics. IEEE Trans. Image Process. 14:1372–1383.

32. Van Goor, F., S. Hadida, ., P. Negulescu. 2009. Rescue of CF airway epithelial cell function in vitro by a CFTR potentiator, VX-770. Proc. Natl. Acad. Sci. USA. 106:18825–18830.

23. Savin, T., and P. S. Doyle. 2005. Static and dynamic errors in particle tracking microrheology. Biophys. J. 88:623–638.

33. Rowe, S. M., L. C. Pyle, ., J. P. Clancy. 2010. DeltaF508 CFTR processing correction and activity in polarized airway and non-airway cell monolayers. Pulm. Pharmacol. Ther. 23:268–278.

24. Michalet, X. 2010. Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82:041914. 25. Berglund, A. J. 2010. Statistics of camera-based single-particle tracking. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82:011917. 26. D’Errico, J. 2002. Splines for monotonic approximations. http://www. mathworks.com/matlabcentral/newsreader/view_thread/34206. 27. Qian, H., M. P. Sheetz, and E. L. Elson. 1991. Single particle tracking. Analysis of diffusion and flow in two-dimensional systems. Biophys. J. 60:910–921. 28. Caligur, V. 2008. Dextran and related polysaccharides. BioFiles. 3.10:17. 29. Jeanes, A., C. A. Wilham, and J. C. Miers. 1948. Preparation and characterization of dextran from Leuconostoc mesenteroides. J. Biol. Chem. 176:603–615. 30. Andrade, Y. N., J. Fernandes, ., M. A. Valverde. 2005. TRPV4 channel is involved in the coupling of fluid viscosity changes to epithelial ciliary activity. J. Cell Biol. 168:869–874. 31. Cabrales, P., A. G. Tsai, and M. Intaglietta. 2004. Microvascular pressure and functional capillary density in extreme hemodilution with

34. Popescu, G., A. Dogariu, and R. Rajagopalan. 2002. Spatially resolved microrheology using localized coherence volumes. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65:041504. 35. Chhetri, R. K., R. L. Blackmon, ., A. L. Oldenburg. 2014. Probing biological nanotopology via diffusion of weakly constrained plasmonic nanorods with optical coherence tomography. Proc. Natl. Acad. Sci. USA. 111:E4289–E4297. 36. Oldenburg, A. L., R. K. Chhetri, ., B. Button. 2012. Monitoring airway mucus flow and ciliary activity with optical coherence tomography. Biomed. Opt. Express. 3:1978–1992. 37. Betzig, E., G. H. Patterson, ., H. F. Hess. 2006. Imaging intracellular fluorescent proteins at nanometer resolution. Science. 313:1642–1645. 38. Rust, M. J., M. Bates, and X. Zhuang. 2006. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods. 3:793–795. 39. Dawson, M., D. Wirtz, and J. Hanes. 2003. Enhanced viscoelasticity of human cystic fibrotic sputum correlates with increasing microheterogeneity in particle transport. J. Biol. Chem. 278:50393–50401.

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