DREAM

Rhythms of the brain are generated by neural oscillations across multiple frequencies. These oscillations can be decomposed into distinct frequency intervals associated with specific physiological processes. In practice, the number and ranges of decodable frequency intervals are determined by sampling parameters, often ignored by researchers. To improve the situation, we report on an open toolbox with a graphical user interface for decoding rhythms of the brain system (DREAM). We provide worked examples of DREAM to investigate frequency-specific performance of both neural (spontaneous brain activity) and neurobehavioral (in-scanner head motion) oscillations. DREAM decoded the head motion oscillations and uncovered that younger children moved their heads more than older children across all five frequency intervals whereas boys moved more than girls in the age of 7 to 9 years. It is interesting that the higher frequency bands contain more head movements, and showed stronger age-motion associations but weaker sex-motion interactions. Using data from the Human Connectome Project, DREAM mapped the amplitude of these neural oscillations into multiple frequency bands and evaluated their test-retest reliability. The resting-state brain ranks its spontaneous oscillation’s amplitudes spatially from high in ventral-temporal areas to low in ventral-occipital areas when the frequency band increased from low to high, while those in part of parietal and ventral frontal regions are reversed. The higher frequency bands exhibited more reliable amplitude measurements, implying more inter-individual variability of the amplitudes for the higher frequency bands. In summary, DREAM adds a reliable and valid tool to mapping human brain function from a multiple-frequency window into brain waves. Supplementary Information The online version contains supplementary material available at (10.1007/s12021-020-09500-9)

1 Introduction 2 Rhythms of the brain are generated by neural oscillations occurring across multiple 3 frequencies [5]. The natural logarithm linear law (N3L) offers a theoretical framework 4 for parcellating these brain oscillations into multiple frequency intervals linking to 5 distinct physiological roles [22]. Remarkably, when graphed on the natural logarithm 6 scale, the centers of each frequency interval fall on adjacent integer points. Thus, 7 distances between adjacent center points are isometric on the natural logarithm scale, 8 resulting in a full parcellation of the whole frequency domain where each parcel of the 9 frequencies is fixed in theory, namely frequency intervals. These frequency intervals 10 have been repeatedly observed experimentally [6]. This characteristic suggests that 11 distinct physiological mechanisms may contribute to distinct intervals. Functional 12 magnetic resonance imaging (fMRI), a non-invasive and safe technique with an 13 acceptable trade-off between spatial and temporal resolution, has the potential to 14 contribute to the study of certain neural oscillations in the human brain in vivo. In 15 early fMRI studies of the human brain, researchers tended to treat oscillations across 16 different frequencies without differentiation. Low-frequency oscillations measured by 17 resting-state fMRI (rfMRI) have been assessed primarily in the frequency range of 0.01 18 to 0.1 Hz, a range in which spontaneous brain activity has high signal amplitude [4,20]. 19 While such efforts have been somewhat informative, treating this broad frequency range 20 in a unitary manner may conceal information carried by different frequency intervals. 21 To address this issue, an early study decomposed the rfMRI signals into multiple 22 frequency intervals using the N3L theory (Slow-5: 0.01 -0.027 Hz, Slow-4: 0.027 -0.073 23 Hz, Slow-3: 0.073 -0.198 Hz, Slow-2: 0.198 -0.25 Hz) [47]. This exploration 24 demonstrated the feasibility of mapping distributional characteristics of oscillations' 25 amplitude in both space and time across multiple frequency intervals in the brain. 26 Since then, an increasing number of rfMRI studies have employed such methods by 27 directly applying these frequency intervals, and have detected frequency-dependent 28 differences in brain oscillations in patients. Specifically, these differences were mostly 29 evident between Slow-4 and Slow-5 amplitudes [14,16,19,21,28,42]. Such 30 frequency-dependent phenomena have also been explored using other rfMRI metrics 31 including regional homogeneity detected in the Slow-3 and Slow-5 frequency ranges [34]. 32 While the lower and upper bounds of the frequency intervals are fixed in theory, their 33 highest and lowest detectable frequencies and frequency resolution are determined by 34 the sampling parameters (e.g., rate and duration) in computational practice. However, 35 the above-mentioned studies applied the frequency intervals from earlier studies [8,47] 36 rather than to use those matching their actual sampling settings. To address this 37 2/20 situation, we developed an easy to use toolbox to decode the frequency intervals by 38 applying the N3L theory. This toolbox, named DREAM, is based on MATLAB with a 39 graphical user interface (GUI). Here, we introduce the N3L algorithm and its DREAM 40 implementation. Neural oscillations reflected by the human brain spontaneous activity 41 measured with resting-state functional MRI and head motion data during mock MRI 42 scans were employed as two worked examples to demonstrate the use of DREAM to 43 perform frequency analyses. 44 2 Methods and Algorithms 45 Neuronal brain signals are temporally continuous but they are almost always measured 46 as discrete data for practical reasons. The characteristics of the sampled data should 47 meet the criterion of the sampling theorem proposed by American electrical engineers 48 Harry Nyquist and Claude Shannon. The core algorithm to determine the frequency 49 boundaries of measured neuronal signals in DREAM is based on the Nyquist-Shannon 50 sampling theorem. Specifically, per the theorem, sampling frequency and sampling time 51 determine the highest and lowest frequencies that can be detected and reconstructed.

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Sampling data retains most of the information contained in the original signals if the 53 sampling frequency is at least twice the maximum frequency of the continuous signals.

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As for neuronal signals, the highest frequency that could be detected and reconstructed 55 is determined by the sampling frequency, or by the sampling interval which is equal to 56 the reciprocal of the sampling frequency, as shown in formula (1) where f max represents the highest frequency that could be detected in the neuronal 58 signal and T R represents the sampling interval.

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The lowest frequency in neuronal signals that could be detected depends on the 60 sampling time. As shown in formula (2), in order to distinguish the lowest frequency in 61 neuronal signals, the sampling time should be equal to or larger than the reciprocal of 62 two times the lowest frequency 63 T ≥ 1 2f min (2) where T represents the sampling time, and f min represents the lowest frequency in 64 neuronal signals that could be distinguished.

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Since the sampling time is equal to the number of samples multiplied by the 66 sampling interval, the lowest frequency can be calculated by formula (3): where N represents the number of samples.

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According to the N3L theory, neural oscillations in mammalian brain formed a linear 69 hierarchical organization of multiple frequency bands when regressed on a natural 70 logarithmic scale. The center of each band would fall on each integer of the natural 71 logarithmic scale ( Fig. 1-1). Thus, adjacent bands have constant intervals that equals to 72 one, which correspond to the approximately constant ratios of adjacent bands on the 73 linear scale ( Fig. 1-2). With the highest and lowest frequencies reconstructed, N3L can 74 derive the number of decoded frequencies and the boundaries of each frequency interval 75 ( Fig. 1-3). Accordingly, when graphed on the natural log scale, the center of each  Computation System [36]. the data selected (the right side).

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We introduce how to use the graphical interface step by step in below. The circled 119 numbers in Figure 4 correspond to the analyzing steps in this section.

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• Step 4 -set up sampling rate: Enter the sampling interval in seconds (T R ) in 127 the input box (in some cases, this can be automatically extracted from the header 128 information).

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• Step 5 (optional) -data directory: If the data are stored in a sub-folder inside 130 the subject directory, type the name of the data directory in the input box.

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After all the above parameters are set up, data meeting the requirement will appear 132 in the list-box ( Fig. 4-6), from where the user can remove unwanted data by selecting 133 the file name and clicking the Remove button. Finally, by clicking the Divide button, 134 a user can start the decoding program. The outputs contain a set of decoded files and a 135 csv file that records the boundary frequencies of each decoded band. The outcomes can 136 be directly used for subsequent analyses. the effects of motion on fMRI results such as increases of short-distance correlations and 142 decreases of long-distance correlations in rfMRI-derived connectivity metrics [23,27,38]. 143 Researchers have proposed various methods to correct motion effects in fMRI studies.

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In contrast, studying head motion as a neurobehavioral trait has long been overlooked 145 (see an exception in [41]), especially in children. Here, we use DREAM to quantify head 146 motion data acquired from preschool and school children in a mock scanner using a 147 novel multi-frequency perspective. We hypothesized that: 1) head motion is a 148 behavioral trait associated with age; 2) there are sex differences in head motion in 149 children; and 3) the head motion effects are frequency-dependent. normative research for lifespan development of mind and brain (CLIMB) [9]. All 154 participants were from groups visiting during the Public Science Open Day of the 155 Chinese Academy of Sciences, with the approval of at least one legal guardian.

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The experiment was performed in a mock MRI scanner at the site of the MRI Research 157 Center of the Institute of Psychology, Chinese Academy of Sciences. The mock scanner 158 was built by PST (Psychology Software Tools, Inc.) using a 1:1 model of the GE MR750 159 3T MRI scanner in use at the institute. It is used for training young children to lie still 160 in a scanner before participating the actual MRI scanning session. It is decorated with 161 cartoon stickers to provide a children-friendly atmosphere. Head motion data were on the head motion data, we first converted the head motion data using the natural 194 logarithm transformation and then assess the relationship between FD and age by using 195 linear regression models to fit the FD data in each frequency interval with age. We 196 conducted this regression for boys and girls, respectively, and tested whether the slopes 197 and intercepts are significantly different between boys and girls. Of note, this method is 198 equivalent to an Analysis of Covariance (ANCOVA) [29]. These analyses were also 199 applied to the standard deviation of FD time series to test the stability of head motion. 200

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Six participants were excluded from further data analysis due to sampling periods less 202 than three minutes. Another four participants were excluded because their mean FD 203 values were three standard deviations higher than the mean value of the whole group 204 (i.e., outliers). Total 42 boys (age: 3 -14 years, 8.7 ± 3.0) and 42 girls (age: 4 -16 years, 205 8.4 ± 3.1) were included in our final analyses. No significant differences in age were 206 found between males and females. All the findings derived with the head motion data 207 without despike preprocessing are highly similar to those of using despike, which are 208 reported as following. Meanwhile, all the results derived from the linear regression     The relationship between age and mean FD values are plotted in Figure 7, indicating 228 that younger children tend to move more than older ones, and this trait correlation held 229 in both boys and girls. We also performed a similar linear regression analysis between 230 the standard deviations of decoded FD values and age, and observed similar outcomes 231 that the standard deviations were significantly negatively correlated with age across 232 frequency bands and sexes. This showed older children are more stable with their head 233 motion than younger children. 234 We further tested if the two lines are different between boys and girls. Statistical Inspired by the trend that sex-related differences in mean FD are smaller in higher 242 frequency bands, especially evident for early stages, we thus divided all the participants 243 into three age groups (3 to 6 years: 14 boys, 18 girls; 7 to 9 years: 14 boys, 15 girls; 10 244 to 16 years: 14 boys, 9 girls) and compared mean FD values between males and females 245 in each age group using two-way (sex and frequency band) ANOVA with repeated 246 measures. Figure 8   Mean FD (logmm) The amplitude of low frequency fluctuation (ALFF) is a common metric used in fMRI 255 studies that reflects regional amplitude of the signal intensity's fluctuations in a 256 10/20 frequency range [40]. Previous studies revealed variations of ALFF in both spatial and 257 frequency domains in the resting-state brain. From the perspective of spatial 258 distribution, in the typical resting-state frequency range (e.g., 0.01-0.1 Hz), the neural 259 oscillations showed higher ALFF in grey matter than white matter [4,32]. It is noted 260 that ALFF reaches its peaks in visual areas [17], posterior structures along brain 261 midline [4,44] and in cingulate and medial prefrontal cortices [12]. In frequency domain, 262 BOLD oscillations distributed to grey matter were mainly in Slow-4 and Slow-5, while 263 its white matter oscillations were dominated by Slow-3 and Slow-2 [47]. Specifically, 264 higher ALFF in Slow-4 was detected in the bilateral thalamus and basal ganglia 265 whereas the slow-5 oscillators exhibited higher ALFF in the ventromedial prefrontal 266 cortex, precuneus and cuneus (replicated in [37]). These findings revealed the For each rfMRI scan, we first extracted the representative time series for each of the 400 292 parcels [31] by averaging all the preprocessed time series within a single parcel. DREAM 293 decomposed the time series into its components across the potential frequency bands. 294 We performed ALFF analysis for all the bands of each run and each subject according 295 to [47] implemented by CCS [36]. Subject-level parcel-wise ALFF maps for each 296 frequency band were standardized into subject-level Z-score maps (i.e., by subtracting 297 the mean parcel-wise ALFF of the entire cortical surface, and dividing by the standard 298 deviation). The two standardized ALFF maps in the same session were then averaged, 299 resulting in two (test versus retest) standardized ALFF maps per frequency band for 300 each subject. To investigate the test-retest reliability of ALFF across the five frequency 301 bands, we calculated the parcel-wise intraclass correlation (ICC) based upon the two 302 ALFF maps [35,49]. We averaged the two standardized ALFF maps of all the subjects 303 to obtain the group-level standardized ALFF maps. In order to evaluate the spatial 304 distribution of the ALFF values for each parcel, we assigned its rank of ALFF values to 305 11/20 the parcel (from 1 to 400). All the above analyses were done for each of the five 306 frequency bands, leading to an ALFF ranking map for each frequency band.   Figure 10. Test-retest reliability of ALFF across six frequency bands.

-16 years old -6 years old
Test-retest reliability maps of ALFF are also generated (Fig. 10)  Nyquist-Shannon sampling theorem and the brain oscillation theory [6]. Such a theory 365 has been proven of great potentials to understand the brain dynamics as well as their 366 behavioral correspondences. From a theoretical perspective, the oscillation theory can 367 be independent of any modalities (e.g., EEG, MEG, ECoG, TMS, fMRI, fNIRS, eye 368 tracking, etc.) for measuring these oscillations as windows into brain waves [3].

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DREAM is thus applicable for multiple forms of discrete sampling data, as long as the 370 data are entered in the supported format. Currently, DREAM can process both NIFTI 371 formatted neuroimaging data and text file formatted behavioral data while more other 372 formats will be supported in its forthcoming releases.

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As a demonstration of its utility, the results derived with DREAM for pure 374 behavioral recordings suggest that head motion may be a behavioral feature reflecting 375 both state and trait of individuals. We showed that head movements in the high 376 frequency bands are more evident than those in the low frequency bands. This could be 377 a behavioral reflection of the hierarchical organization of brain oscillations for their 378 synchronization at multiple scales in space. Neural oscillations of the higher 379 frequency-bands are related to more local information processing while the lower 380 frequency-bands are for more distant communications in the brain. Our findings are 381 consistent with the previous observation that the head motion had more impacts on the 382 short-distance brain connectivity. While the head motion during fMRI scanning has 383 been treated an important confounding factor in the neural signal [27], some recent work 384 also argued its neurobiological components related to individual traits of the motor 385 behaviors (e.g., [41,43]). The current researh offers data for an alternative explanation 386 on such neurobehavioral trait likely driven by brain systems operating within a 387 multi-band frequency landscape. In the context of development, as we expected, 388 younger children moved more than older children across all the slow frequency bands.

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The stability of head motion during the experiment also varied with age, with head 390 motion becoming less variable or more stable in older children. This is more evident in 391 higher frequency bands, an implication that more sudden and sharp movements in 392 younger children. Moreover, in a specific age range (7 -9 years), boys moved more than 393 girls across Slow-6 to Slow-1 bands but such differences vanished in the delta 394 frequencies. This age range is a critical period for developing the ability to apply 395 effective cognitive control (i.e., cognitive flexibility during executive function) [1], and 396 our findings might reflect the sex differences in the cognitive development. In summary, 397 our results demonstrate the necessity to study the frequency-specific characteristics of 398 head motion, especially a perspective on understanding the neurobiological mechanism 399 behind these behavior-related oscillations. This is of great potential to enrich our 400 14/20 knowledge on the lifespan development such as children, the elderly and patients with 401 neurologic or psychiatric conditions where both distance-related brain and the head 402 motion measurements have been observed to correlate with each other [2,10,11,30]. 403 Differences in head motion across ages or between cohorts may reflect differences of 404 certain traits, which may co-vary with detected brain signals and behavioral outcomes. 405 The different properties of head motion in different frequency bands show that there 406 may be different mechanisms associated with different frequencies. Head motion at 407 higher frequencies varies more with age, and this may reflect that cognitive control 408 associated with higher frequencies develops better with age. Of note, interpolation 409 analyses indicated that this observation is not related to an issue of better 410 signal-to-noise ratio at higher frequencies because there are more events per unit time. 411 Within the narrow age range of 7 to 9 years old, boys moved more than girls in most 412 frequency bands, although sex differences were larger at lower frequencies. This may 413 indicate that the development of controlling system associated with lower frequencies 414 may have larger sex-related differences for this age range. The above results lead us to 415 speculate that there may be two control systems that are associated with different 416 frequency bands of head motion which develop differently with age and between boys 417 and girls. More detailed experimental studies deserved to test this postulation in future. 418 The strategies of dealing with head motion issues in human brain mapping may also 419 need updates regarding its measurement reliability and validity in terms of the possible 420 neurobiological correlates [35,46,50]. One promising direction is to separate various 421 sources of the head movements by using additional recordings or developing novel 422 motion metrics (e.g., the recent progress in [24][25][26]). These efforts identified seven kinds 423 of in-scanner motion in resting-state fMRI scans, and five of them related to respiration. 424 Some pseudomotion occurred only in the phase encode direction and was a function of 425 soft tissue mass, not lung volume. Using the Mock scanning experimental design as in 426 the present work, together with the aforementioned approaches, could be of high value 427 in further understanding neurobiobehavioral underpins of the human head movements. 428 Using fast fMRI from HCP, at the first time, we revealed the spatially configuring 429 pattern of ALFF ranking gradually from low to high frequency bands. This indicates a 430 trend along the two orthogonal axes. Along the dorsal-ventral axis, higher ALFF ranks 431 were moving from the ventral occipital and the ventral temporal lobe up to regions in 432 the parietal lobe as the frequency increasing. Along the anterior-posterior axis, from 433 lower to higher bands, higher ALFF ranks were walking from the posterior to the 434 anterior regions in the ventral part. This frequency-dependent ALFF pattern is similar 435 to the findings of previous studies on the association between brain structure and gene 436 expression, which also reported orthogonal gradations of brain organization and the 437 associated genetic gradients [7,18]. The underlying physiological mechanism and 438 functional significance of the frequency-dependent ALFF patterns deserve further 439 investigations. It is interesting that the frequency-dependent pattern of ICC is quite 440 uniform across the brain and as the frequency increased, its reliability increased suggest that both Slow-2 and Slow-1 ALFF could be the usable and reliable marker of 447 the brain oscillations for these applications. It is noticed that the reliability of Slow-1 448 ALFF is slightly lower than those of Slow-2 ALFF, and this may be an indication on 449 the limited Slow-1 band here compared to its theoretical range (around 0.6065 − 1.6487 450 Hz). While studies of the very fast sampled fMRI signals such as HCP are sparse, it is 451 quite promising for future studies with multiple neuroimaging modalities (e.g., [3,15] coming with more and more fMRI and EEG datasets openly shared as well as their 455 applications (e.g., [45]