Arterioles

These processes converted the stitched data sets into vectors that represent short centerlines in each vessel (Fig. 1d) as well as the location of all neuronal and nonneuronal nuclei^{19 (link)}. Each centerline was associated with a specific radius, points in 1 of 26 directions, and had two neighbors everywhere except at branching points, where three adjacent centerlines overlapped to form a vertex (Fig. 1e). The radii were corrected for the eccentricity induced by differences in axial versus lateral resolution and for the estimated point spread of the focus^{19 (link)}. We automatically corrected for a small fraction of gaps, ~0.05 of all vessels, in the data set^{25 (link)}. Identification of surface and penetrating vessels as arterioles versus venules was based on tracing the surface vessels to the middle cerebral artery versus the central sinus or rhinal vein.
Cortical columns in mouse vibrissae cortex were clearly defined in layer IV by their cytoarchitectonic pattern, that is, cell somata organize around the perimeter of the column, whereas cortical and thalamo-cortical projections occupy the center^{14 (link)}. The lateral boundaries and axial extent of cortical columns were delimited by visual examination of the reconstructed volume of α-NeuN image data.

The raw data consists of successive line-scans along the central axis of an arteriole lumen (Fig. 1A). The spatial dimension, x, corresponds to the linear motion of the focal volume along the blood vessel. The required resolution along x is set by the diffraction limit. For a 40-X water-dipping lens, the lateral resolution is about 0.7 μm, yielding a sampling of Δx ≈ 0.3 μm per pixel. For a typical 150 μm field, this requires ~ 500 samples per line. At the ~ 500 μs per line scan rate of high-speed gravimeter mirror scanners (model 6110, Cambridge Technology, Lexington, MA), the sampling time is thus Δt ≈ 1 μs per pixel. An upper limit to the maximum velocity that can be determined with scanning measurements is set by (½)Δx/Δt ≈ 150 mm/s; the factor of ½ results from the use bidirectional scanning to correct for the speed of the scan mirrors. Signal-to-noise constraints may necessitate the use of slower scan rates, as discussed (Tsai and Kleinfeld, 2009 ).
From the continuous data set of Figure 1A, we select a strip along x that contains a straight, planar section of the vessel. We define this width as L ≡ N_xΔx, where N_x is the number of spatial samples; typically, L ~ 40 μm. We window the data in time intervals of T = N_t Δt separate windows, where N_t is the number of lines in the sample. We calculate the velocity for successive blocks of the windowed line-scan data, with an overlap of T/4 between blocks. Each block is denoted F_i(x, t) where i is an index that corresponds to time in units of T/4. The Nyquist frequency is (2T)⁻¹, or 10 Hz for the typical choice of T = 50 ms; this is sufficient to capture the heart-rate of the rat without aliasing.
Each windowed data block is first normalized to remove inhomogeneities in illumination in space and to remove the baseline intensity, usually using the first second, 20T of data, so that the data block has a mean value of zero, i.e.,
The Radon transform maps each windowed data block F_i(x, t) from space-time coordinates to space-velocity coordinates, F̃_i(r, θ), by
Bright points in the transformed data correspond to lines at particular angles and radii (Fig. 1B). If the original image block F_i(x, t) contains many streaks with a similar orientation, as produced by a line-scan along a blood vessel, the variance of F̃_i(r, θ) along r is maximal along the orientation of the streaks.