OCT particle tracking velocimetry of biofluids in a microparallel plate strain induction chamber

Abstract. Significance: Imaging biofluid flow under physiologic conditions aids in understanding disease processes and health complications. We present a method employing a microparallel plate strain induction chamber (MPPSIC) amenable to optical coherence tomography to track depth-resolved lateral displacement in fluids in real time while under constant and sinusoidal shear. Aim: Our objective is to track biofluid motion under shearing conditions found in the respiratory epithelium, first validating methods in Newtonian fluids and subsequently assessing the capability of motion-tracking in bronchial mucus. Approach: The motion of polystyrene microspheres in aqueous glycerol is tracked under constant and sinusoidal applied shear rates in the MPPSIC and is compared with theory. Then 1.5 wt. % bronchial mucus samples considered to be in a normal hydrated state are studied under sinusoidal shear rates of amplitudes 0.7 to 3.2  s−1. Results: Newtonian fluids under low Reynolds conditions (Re∼10−4) exhibit velocity decreases directly proportional to the distance from the plate driven at both constant and oscillating velocities, consistent with Navier–Stokes’s first and second problems at finite depths. A 1.5 wt. % mucus sample also exhibits a uniform shear strain profile. Conclusions: The MPPSIC provides a new capability for studying biofluids, such as mucus, to assess potentially non-linear or strain-rate-dependent properties in a regime that is relevant to the mucus layer in the lung epithelium.


Experimental Procedure
Table S1 provides a detailed list of key imaging parameters for the constant velocity and sinusoidal velocity experiments over all frequencies. For the tilt adjustment method, the user initially marks approximate locations of the top and bottom surfaces of the fluid. For each surface, a line is extrapolated through the user-defined points, then a 10-pixel vertical window searched to locate pixels in each column with maximum intensity. Then, new lines are fit through the intensity maxima, which are used to define the top and bottom of the sample region as well as the angles of the top and bottom plates relative to horizontal. The separation distance H between the top and bottom surfaces is measured at the center of the image. Distortion, Daxial and Dtransverse, is accounted for in the height calculation. The surfaces are only segmented for one frame in each stack as there is negligible movement of the plates between frames.

Decimation Technique
Decimation is used to exaggerate motion in regions of low velocity, such as near the top plate, where displacements between successive frames can be less than a single pixel.

Constant Velocity
Frames corresponding to turn around points in velocity (velocity extrema) are identified by an initial sweep of xshift (using Eqn. (5)) over successive frames of an ROI in the bottom row (ROIN,j) and by subsequently plotting the cumulative displacement. The chosen number of 2 frames padding the extrema was based on the mechanical turn-around time of the nanopositioner.
Because we expect the velocity to decrease linearly between the bottom and top plates, we determine a row (i) dependent decimation value, ki, based upon an initial estimate of the velocity within that row, vi (in pixels / frame). Initial velocity is computed by linear regression of the depth and velocity of the bottom ROIN,j and the top of the sample region, where we expect a velocity of zero. To target a displacement of at least 3 pixels, we define ki as 3 or 1, whichever is larger. In high velocity regions ki will equal 1 (no decimation) and displacements will typically be much larger than 3 pixels. In very low velocity regions, if ki is larger than F, the number of frames in one sweep, it is set to F-1 to enable at least one measurement per sweep.

Sinusoidal Velocity
We define frame decimation vector as: where xshift(k)i is the theoretical pixel displacements over frames in ROIi,j. The maximum frame decimation number is capped at a user defined number based on a maximum phase angle of the waveform to search over: = 2π 10 , so that the velocity is not changing significantly over the decimation range.
Note that the velocity of a time point must be calculated as the average velocity between two equally distant frames. We perform normalized cross correlations using the decimation frame pairs of each row and store the ℎ values in a master (NMQ) matrix. The velocity is calculated by dividing each ℎ by total number of frames between the two time points.
The outcome velocities have units of pixels per frame. The results of the decimation technique are displayed in Figure S1. Figure S1: (a) Pre-decimation traces of lateral particle displacements in a Newtonian sample driven by a sinusoidal waveform. (b) Pre-decimation traces of lateral particle displacements in a mucus sample driven by a sinusoidal waveform. : (c) Post-decimation traces of lateral particle displacements in a Newtonian sample driven by a sinusoidal waveform. (d) Post-decimation traces of lateral particle displacements in a mucus sample driven by a sinusoidal waveform. Traces are shown at multiple depths in the sample, offset by their depth position for clarity (5 of 6 waveforms shown). For visual purposes, not all ROI depths were plotted.