Synchronized renal blood flow dynamics mapped with wavelet analysis of laser speckle flowmetry data

Abstract

Full-field laser speckle microscopy provides real-time imaging of superficial blood flow rate. Here we apply continuous wavelet transform to time series of speckle-estimated blood flow from each pixel of the images to map synchronous patterns in instantaneous frequency and phase on the surface of rat kidneys. The regulatory mechanism in the renal microcirculation generates oscillations in arterial blood flow at several characteristic frequencies. Our approach to laser speckle image processing allows detection of frequency and phase entrainments, visualization of their patterns, and estimation of the extent of synchronization in renal cortex dynamics.

Figure 1. Fourier representation of the TGF oscillations.

(A) Time-averaged LSF image of a rat kidney. Blue regions are masked and excluded from analysis. (B) Fourier power spectra averaged over all the non-masked pixels of the original (gray) and spatially downsampled (black) data. (C) Location of the main Fourier peak in the TGF band mapped across a kidney surface. (D) Log peak intensities of Fourier power spectrum mapped across the kidney surface. Time series from each pixel were normalized to their standard deviation.

Figure 2. Mapping intensity of TGF oscillations in 6 animals.

Grayscale images show LSF frames, pseudo-colors represent the log peak power of the Fourier spectrum in the TGF band . Time series from each pixel were normalized to their standard deviation. Areas where the value was lower than 95%-confidence interval, estimated from Monte-Carlo simulations, are transparent.

Figure 3. CWT-based identification of the instantaneous frequency and phase of the dominant rhythm for an example pixel in a LSF data (the same preparations as in Figure 1).

(A) time-averaged LSF frame. (B) Top, blood flow signal extracted from the yellow mark in (A) and normalized to its standard deviation; middle: wavelet spectrogram of the normalized signal, ridges of wavelet modulus maxima (blue) and the dominant ridge (red); bottom: time-frequency representation of the wavelet phase, the dominant rhythm is show with the red line (same as above). (C) Map of the mean frequencies of the main rhythm, identified in each pixel of the kidney image.

Figure 4. Collective changes in the dominant rhythm frequency (preparation 4 shown in Figure 2).

(A) Map of time-averaged frequencies of the dominant rhythm across the kidney surface. (B) Time dynamics of the dominant rhythm frequency in each pixel within square areas in (A), after re-ordering to a 1D line. Frequency is shown as color. Changes in frequency tend to coincide in populations of pixels.

Figure 5. Organized spatial phase dynamics.

(A) Phase maps for a short time interval (the same preparation as in Figure 4), every 4th frame is shown. Wrapped phase is color-coded from to . Each row of 10 frames roughly corresponds to one period of TGF oscillation. Maps in each column tend to reproduce their phase pattern for 4 periods. (B) First four empirical spatial eigenmodes (PC1–PC4) for the time period from 900 to 1100 seconds and the corresponding paired phase plots, displaying how coefficients for the pairs of modes change with time in relation to another mode. Clear oscillatory behaviour is seen for the first two eigenmodes, which correspond to concentric phase wave-like pattern. (inset) Cumulative fraction of variance explained by the first 20 modes; first two modes capture around 45% of the variation in the data. (C) Dynamics of the fraction of variance explained by the first 4 modes in moving 250 s-wide time windows for the 6 experiments shown in Figure 2. (D) boxplots that summarize the values shown in (C), phase delays are highly spatially organized over the whole experiment.

Figure 6. Local coherence maps for the preparations shown in Figure 2.

Areas of highly locally coherent dynamics can be seen in all preparations, even in the one where only small fraction of the kidney surface showed significant TGF peak in Fourier spectrum. White square in the lower left corner show the span of the neighborhood area.

Figure 7. Clusters of coherent pixels.

Taking peaks of local coherence maps as tentative cluster centers, each pixel was affiliated according to the center it was most coherent with. Different clusters are shown in different colors. If phase coherence of a pixel was less then 0.5 with any of the cluster centers, it was considered unclustered (shown as gray).