Fig. S7

Fig. S7

Optimal intensity threshold for the computation of cross-­ correlation functions on xy-images

(a) Raw raster-‐scanned xy-­image acquired by detecting the photoluminescence signal of 5-nm Quantum Dots (QDs) (two-­‐photon excitation at λ_exc =900 nm, detection bandwidth=640-­690 nm) in a sinusoid of the hepatic microcirculatory system; f_line= 1370 Hz, δx= 0.026 µm, scale bar= 3 µm; intensity calibration bar on the bottom in arbitrary units (a.u.). QDs appear as the brightest diagonal lines in the xy-image, separated by low-­intensity diagonal stripes produced by non-fluorescent flowing red blood cells. Due to auto-­fluorescence contributions and to the scattering processes that inevitably occur in a thick living biological sample, the separation of alternating streaks is rather unclear. Cross-­correlation functions are better computed after a threshold has been applied to the intensity counts in the pixels of the xy-­image. The threshold is inserted in the same Python code used for the computation of the CCFs: for each pixel, the detected intensity is unaltered if it exceeds the threshold and it is set to zero otherwise, so that the threshold defines a minimum photoluminescence intensity F_min; if it is properly chosen, the background is effectively removed without altering the estimate of the blood flow speed recovered from the diagonal lines produced by QDs. (b)-­(d) Three exemplifying threshold values are evaluated for the image of panel a: F_min=1000 a.u. in b, 1528 a.u. in c and 2000 a.u. in d. The pixels in which the detected intensity exceeds the threshold F_min (and that therefore remain unchanged for the computation of the CCFs) are uniformly green-colored; otherwise they are shown with the same LUT of panel a. For a too low threshold value (panel b) the background is not suppressed, whereas for a much higher value (panel d) too many pixels acquire a null intensity prior to the derivation of the CCFs. An intermediate, reasonable threshold is shown in panel c. (e) Histogram of the intensity counts for the image shown in a. The threshold F_min=1528 a.u. adopted for panel c corresponds to the center x_c=1528±9 a.u. of the histogram, as obtained from its Gaussian best fit (the first peak of the histogram is ascribed to the low intensity values detected outside the vessel and is therefore neglected). Inset: the threshold F_min=1528 determined from the histogram is adopted to derive the experimental cross-­correlation functions from the image in a for increasing column distances J - I in the range 10-­90 pixels (10-­pixels step). (f) Effect of various threshold values on experimental CCFs for the image in a. CCFs are computed for a fixed column distance J-­I=100 pixels and for increasing threshold values in the range 0-­2600 a.u.. The higher the threshold, the higher is the amplitude of the CCF and the more discernible is its peak; no variation in the peak lag time τ_max is found, so that the flow speed measurement is not affected by the threshold: the global fit (eq. S.23) of six CCFs (1528 a.u.< F_min < 2600 a.u.) provides a shared speed (|v|=494±3 µm/s for all the curves. Inset: CCFs are normalized to highlight the independence of the peak time τ_max on the threshold value. The threshold only affects the width of the diagonal lines produced by flowing objects in the xy-­image: the higher the adopted value for F_min the thinner is each diagonal stripe (pixels on the border are more likely affected by the threshold) and this leads in turn to a reduced width of the recovered cross-­correlation function. This effect can be quantified by the (narrow) range a=1.9-­‐2.7 µm for the radius of flowing objects provided by the fits of the CCFs (we recall that, according to eq. S.23, the width of the CCF is directly proportional to the squared radius a²). Globally the previously adopted value F_min=1528 a.u. allows a reliable computation of the cross-correlation functions (inset of panel e) without largely affecting the width of the CCFs (and the resulting estimates of the radius a and of the diffusion coefficient D of the flowing objects). (g)-­(j) The choice and the effect of the threshold are tested on the image analysed extensively in Figure 3 (ROI 2, frame 5). Here even the CCFs computed with F_min=0 a.u. allow the recovery of the blood flow speed and they provide therefore a reference value to validate the independence of the estimated speed |v| on the selected threshold value. (g) Raw raster-­scanned xy-­image (see acquisition parameters in Figure 3; calibration bar on the left in arbitrary units, scale bar, 5 µm) acquired by detecting the photoluminescence signal of 5-­nm QDs. In the inset, the pixels having an intensity exceeding the chosen threshold F_min=5855 a.u. (i.e, pixels kept unchanged for the computation of the CCFs) are uniformly green-­colored. The threshold is assigned by the center of the histogram of the intensity counts (shown in h with its Gaussian fit) as previously discussed. (i),(j) Effect of various threshold values on experimental cross-correlation functions for the image in g. CCFs are computed for a fixed column distance J − I=20 pixels in i and for J - I=40 pixels in j, for increasing threshold values in the range 0-­8300 a.u. (same color code in both panels). As before, the amplitude of the CCFs increases for increasing values of F_min while the position of the peak time τ_max remains unchanged. The global fit, performed according to eq. (S.23) on the two CCFs derived for a column distance (J − I) of 20 and 40 pixels with F_min=0 a.u., leads to a speed |v| =242±8 µm/s, in agreement with the result |v| =235±3 µm/s obtained for F_min=5855 a.u. (reported in Figure 3e). This also confirms that, even when not mandatory, the introduction of the threshold does not alter the obtained results. Inset: CCFs for J − I=20 pixels have been normalized to highlight the slight reduction of the correlation width for increasing F_min and the independence of the peak time τ_max on the threshold value.