Neuronal Origin of the Temporal Dynamics of Spontaneous BOLD Activity Correlation

Resting-state functional connectivity (FC) has become a major functional magnetic resonance imaging method to study network organization of human brains. There has been recent interest in the temporal fluctuations of FC calculated using short time windows ("dynamic FC") because this method could provide information inaccessible with conventional "static" FC, which is typically calculated using the entire scan lasting several tens of minutes. Although multiple studies have revealed considerable temporal fluctuations in FC, it is still unclear whether the fluctuations of FC measured in hemodynamics reflect the dynamics of underlying neural activity. We addressed this question using simultaneous imaging of neuronal calcium and hemodynamic signals in mice and found coordinated temporal dynamics of calcium FC and hemodynamic FC measured in the same short time windows. Moreover, we found that variation in transient neuronal coactivation patterns was significantly related to temporal fluctuations of sliding window FC in hemodynamics. Finally, we show that the observed dynamics of FC cannot be fully accounted for by simulated data assuming stationary FC. These results provide evidence for the neuronal origin of dynamic FC and further suggest that information relevant to FC is condensed in temporally sparse events that can be extracted using a small number of time points.

fluctuations of FC calculated using short time-windows ("dynamic FC") because it 23 could provide information inaccessible with conventional "static" FC that is typically 24 calculated using the entire scan lasting several tens of minutes. Although multiple 25 studies have revealed considerable temporal fluctuations in FC, it is still unclear 26 whether the fluctuations of FC measured in hemodynamics reflect the dynamics of 27 underlying neural activity. We addressed this question using simultaneous imaging of 28 neuronal calcium and hemodynamic signals in mice, and found coordinated temporal 29 dynamics of calcium FC and hemodynamic FC measured in the same short time 30 windows. Moreover, we found that variation in transient neuronal coactivation patterns 31 (CAPs) was significantly related to temporal fluctuations of sliding window FC in 32 hemodynamics. Finally, we show that observed dynamics of FC cannot be fully 33 accounted for by simulated data assuming stationary FC. These results provide evidence 34 for the neuronal origin of dynamic FC and further suggest that information relevant to 35 FC is condensed in temporally sparse events that can be extracted using a small number  Several studies have also questioned whether the apparent "dynamics" of FC 70 calculated using the sliding window method is related to temporal instability of hemodynamic images were then coregistered by rigid-body transformation using 138 manually selected anatomical landmarks that were visible in both images (e.g., 139 branching points of blood vessels). All of the images were then spatially down-sampled 140 by a factor of two. Pixels within the cortex (at this point including large blood vessels 141 including the sinus) were extracted manually. For both calcium and hemodynamics, 142 slow drift in each pixel's time course was removed using a high-pass filter (> 0.01 Hz, 143 second order Butterworth. No low-pass filter was used). After filtering, each pixel's 144 time course was normalized by subtracting the mean across time and then dividing by 145 the standard deviation across time. Global signal regression was conducted by 146 regressing out the time course of average signal within the brain from each pixel's time 147 course. Finally, hemodynamic signal was multiplied by -1 to set the polarity of the 148 activity change equal to that in the calcium signal. 149

Extraction of Region-of-Interest (ROI) Time Courses 151
Selection of ROI and time courses are conducted as described previously (

Cluster Analysis and Kurtosis Analysis 201
For the state analysis of sliding window FC, we adopted the k-means clustering Correlation distance (1-r) was used to compute the separation between each window's 204 FC-matrix (using all 38 ROIs) and the k-means clustering was iterated 100 times with 205 random centroid positions to avoid local minima. The windowed FC-matrices were 206 mean-centered by scan to eliminate scan-level and subject-level features from 207 contributing the clustering result. K-means clustering was applied in the same manner to 208 the simulated data that was matched in size to the real data. The cluster validity index 209 was used to evaluate the quality of clustering for the range of cluster numbers (k = 2-10). 210 The cluster validity index was computed as the average ratio of within-cluster distance 211 to between-cluster distance. 212 Non-stationarity of spontaneous neuronal signal correlation was assessed by 213 calculating multivariate kurtosis using the same procedure as described by Laumann 214 and colleagues (Laumann et al. 2016). One value of kurtosis was calculated for each 215 FC-matrix (using all 38 ROIs) obtained each scan. The same procedure was applied to 216 the simulated data that was matched in size to the real data. 217 218

Time Course Simulation 219
To obtain a null dataset to evaluate the non-stationarity of the real data, we constructed data. This procedure produces simulated data that are stationary by construction but 226 matched to real data in the covariance structure and mean spectral content. 227

Consistent FC dynamics in calcium and hemodynamic signals 230
Transgenic mice expressing GCaMP in neocortical neurons were used to simultaneously If the dynamics of FC in calcium and hemodynamics were matched, the similarity 251 between calcium and hemodynamic FC in the same time window should be higher than 252 that calculated using different time windows (e.g., similarity between Ca-FCwindow#1 and 253 Hemo-FCwindow#1 would be higher than the similarity between Ca-FCwindow#1 and 254 Hemo-FCwindow#2). Otherwise, the similarity between FC-matrices in calcium and 255 hemodynamics merely reflects the overall similarity of FC in calcium and 256 hemodynamics but not the coordinated dynamics of calcium and hemodynamic FC. 257 Across all the data, we found that the distribution of the correlation coefficient between 258 the FC-matrices in calcium and hemodynamics was shifted toward positive values 259 compared with that calculated with the scan-shifted data (P < 10 -14 , 260 Kolmogorov-Smirnov test; Fig. 2C). The difference between the real data and the 261 sign-rank test; Fig. 2D) and was seen across various window sizes ranging from 1 sec to 263 60 sec (Fig. 2E). Together these results suggest that temporal variability in 4A). We found that the distribution of the correlation between ∆CAP and ∆FC for the 306 real data was shifted toward positive values whereas the same distribution calculated 307 using trial-shifted data was centered near zero (P < 10 -30 , Kolmogorov-Smirnov test; Fig.  308 4B). Furthermore, the correlation between ∆CAP and ∆FC was consistently positive 309 across all animals (P < 0.156, n = 7 mice, sign rank test; Fig. 4C) and was seen across 310 various sizes of time-windows ranging from 1 to 60 sec (Fig. 4D). Taken  both calcium and hemodynamic signals, we found cluster validity index of real data to 325 be significantly smaller than that of simulated data (Fig. 5B), suggesting that the real 326 data had cluster structure that could not be fully accounted for by sampling error. 327 If the kurtosis of real data were larger than that of simulated data that is stationary by 329 construction, the non-stationarity of the real data is implied. We found that the kurtosis 330 of the real data was significantly higher than that of the simulated data (P < 10 -11 for 331 both, sign rank test, n = 64 scans; Fig. 5C). Together, these results suggest that 332 dynamics of FC arise from non-stationarity of spontaneous neuronal activity, and 333 analyses based on sliding window correlation have the potential to detect 334 non-stationarity. 335 In the present study, we used simultaneous imaging of calcium and hemodynamic ways. Since LFP recordings were limited from a small number of recording sites 357 whereas EEG recording did not have enough spatial resolution, evidence directly 358 linking global spatial pattern of neuronal activity with hemodynamic FC has been 359 lacking. Using simultaneous imaging of calcium and hemodynamic signals, the present 360 study provides evidence suggesting that temporal variability of hemodynamic FC and 361 its time-to-time spatial patterns reflect spatial patterns of large-scale neuronal activity. 362 Moreover, since the present study used anesthetized and head-fixed mice, the results are 363 unlikely to be attributable to head motion.  Correlation between FC matrices for calcium and hemodynamics was larger for the data 641 than for the trial-shifted control significantly across animals. (E) Correlation between 642 FC matrices of calcium and hemodynamics was larger for the data than the trial-shifted 643 control across different window-sizes (1, 2, 3, 5, 6, 10, 12, 15, 20, 30 and 60 sec). Error 644 bars indicate s.e.m. across animals (n = 7). 645  Hemo-FC that were calculated using the entire scan, in which the 30-sec window 669 belongs to, were subtracted to obtain maps of ∆CAP and ∆FC, respectively. Finally, 670 values of ∆CAP and ∆FC were compared across ROI pairs similarly as in Figure 3B.