Flow velocity summary statistics were generated by analyzing within a region of interest that was manually drawn within of the dorsal luminal surface. Our primary summary statistic was average flow speed. Average flow speed estimates were generated by analyzing histograms of and . These histograms bin all measurements across and in the scalar component function over 100 frames (6 s acquisition period). A representative raw histogram of is shown in Fig. 1(b). Our scalar vector-component histograms typically showed a larger than expected number of counts centered at zero velocity. We attributed these peaks at zero velocity to (1) misidentification of portions of the stationary trachea as particles that are not moving and (2) particles that become stuck to the tracheal wall. In order to account for these artifacts, we replaced the zero-velocity histogram bin with the average of the two neighboring bins [Fig. 1(c)]. Our processing also addresses three sources of uncertainty that influence histogram width: (1) spatial heterogeneity of flow speeds over the region of interest, (2) Brownian motion, and (3) measurement uncertainty (e.g., uncertainty in the centroiding process used in particle tracking and failure of particle matching in-between frames). Since the latter two factors are expected to be zero-mean processes, vector component values within the region of interest, were estimated using . Here, is the vector component direction ( or ), is the center value of the bin, and is the number of counts in the ’th bin. In this formulation of , additive sources of zero-mean noise should tend to zero. In contrast, calculating average speed values from individual particle velocities propagates the zero-mean noise forward when summing the squares of the vector components for each ’th particle (i.e., ). Finally, our summary statistic of average speed was then estimated using .