Determination of Vascular Dementia Brain in Distinct Frequency Bands with Whole Brain Functional Connectivity Patterns

Recent studies have shown that multivariate pattern analysis (MVPA) can be useful for distinguishing brain disorders into categories. Such analyses can substantially enrich and facilitate clinical diagnoses. Using MPVA methods, whole brain functional networks, especially those derived using different frequency windows, can be applied to detect brain states. We constructed whole brain functional networks for groups of vascular dementia (VaD) patients and controls using resting state BOLD-fMRI (rsfMRI) data from three frequency bands - slow-5 (0.01∼0.027 Hz), slow-4 (0.027∼0.073 Hz), and whole-band (0.01∼0.073 Hz). Then we used the support vector machine (SVM), a type of MVPA classifier, to determine the patterns of functional connectivity. Our results showed that the brain functional networks derived from rsfMRI data (19 VaD patients and 20 controls) in these three frequency bands appear to reflect neurobiological changes in VaD patients. Such differences could be used to differentiate the brain states of VaD patients from those of healthy individuals. We also found that the functional connectivity patterns of the human brain in the three frequency bands differed, as did their ability to differentiate brain states. Specifically, the ability of the functional connectivity pattern to differentiate VaD brains from healthy ones was more efficient in the slow-5 (0.01∼0.027 Hz) band than in the other two frequency bands. Our findings suggest that the MVPA approach could be used to detect abnormalities in the functional connectivity of VaD patients in distinct frequency bands. Identifying such abnormalities may contribute to our understanding of the pathogenesis of VaD.     

Resting-state quantitative electroencephalography reveals increased neurophysiologic connectivity in depression

Symptoms of Major Depressive Disorder (MDD) are hypothesized to arise from dysfunction in brain networks linking the limbic system and cortical regions. Alterations in brain functional cortical connectivity in resting-state networks have been detected with functional imaging techniques, but neurophysiologic connectivity measures have not been systematically examined. We used weighted network analysis to examine resting state functional connectivity as measured by quantitative electroencephalographic (qEEG) coherence in 121 unmedicated subjects with MDD and 37 healthy controls. Subjects with MDD had significantly higher overall coherence as compared to controls in the delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), and beta (12-20 Hz) frequency bands. The frontopolar region contained the greatest number of "hub nodes" (surface recording locations) with high connectivity. MDD subjects expressed higher theta and alpha coherence primarily in longer distance connections between frontopolar and temporal or parietooccipital regions, and higher beta coherence primarily in connections within and between electrodes overlying the dorsolateral prefrontal cortical (DLPFC) or temporal regions. Nearest centroid analysis indicated that MDD subjects were best characterized by six alpha band connections primarily involving the prefrontal region. The present findings indicate a loss of selectivity in resting functional connectivity in MDD. The overall greater coherence observed in depressed subjects establishes a new context for the interpretation of previous studies showing differences in frontal alpha power and synchrony between subjects with MDD and normal controls. These results can inform the development of qEEG state and trait biomarkers for MDD.     

The role of corpus callosum development in functional connectivity and cognitive processing

The corpus callosum is hypothesized to play a fundamental role in integrating information and mediating complex behaviors. Here, we demonstrate that lack of normal callosal development can lead to deficits in functional connectivity that are related to impairments in specific cognitive domains. We examined resting-state functional connectivity in individuals with agenesis of the corpus callosum (AgCC) and matched controls using magnetoencephalographic imaging (MEG-I) of coherence in the alpha (8-12 Hz), beta (12-30 Hz) and gamma (30-55 Hz) bands. Global connectivity (GC) was defined as synchronization between a region and the rest of the brain. In AgCC individuals, alpha band GC was significantly reduced in the dorsolateral pre-frontal (DLPFC), posterior parietal (PPC) and parieto-occipital cortices (PO). No significant differences in GC were seen in either the beta or gamma bands. We also explored the hypothesis that, in AgCC, this regional reduction in functional connectivity is explained primarily by a specific reduction in interhemispheric connectivity. However, our data suggest that reduced connectivity in these regions is driven by faulty coupling in both inter- and intrahemispheric connectivity. We also assessed whether the degree of connectivity correlated with behavioral performance, focusing on cognitive measures known to be impaired in AgCC individuals. Neuropsychological measures of verbal processing speed were significantly correlated with resting-state functional connectivity of the left medial and superior temporal lobe in AgCC participants. Connectivity of DLPFC correlated strongly with performance on the Tower of London in the AgCC cohort. These findings indicate that the abnormal callosal development produces salient but selective (alpha band only) resting-state functional connectivity disruptions that correlate with cognitive impairment. Understanding the relationship between impoverished functional connectivity and cognition is a key step in identifying the neural mechanisms of language and executive dysfunction in common neurodevelopmental and psychiatric disorders where disruptions of callosal development are consistently identified.     

Visual working memory load-related changes in neural activity and functional connectivity

Background

Visual working memory (VWM) helps us store visual information to prepare for subsequent behavior. The neuronal mechanisms for sustaining coherent visual information and the mechanisms for limited VWM capacity have remained uncharacterized. Although numerous studies have utilized behavioral accuracy, neural activity, and connectivity to explore the mechanism of VWM retention, little is known about the load-related changes in functional connectivity for hemi-field VWM retention.

Methodology/Principal Findings

In this study, we recorded electroencephalography (EEG) from 14 normal young adults while they performed a bilateral visual field memory task. Subjects had more rapid and accurate responses to the left visual field (LVF) memory condition. The difference in mean amplitude between the ipsilateral and contralateral event-related potential (ERP) at parietal-occipital electrodes in retention interval period was obtained with six different memory loads. Functional connectivity between 128 scalp regions was measured by EEG phase synchronization in the theta- (4–8 Hz), alpha- (8–12 Hz), beta- (12–32 Hz), and gamma- (32–40 Hz) frequency bands. The resulting matrices were converted to graphs, and mean degree, clustering coefficient and shortest path length was computed as a function of memory load. The results showed that brain networks of theta-, alpha-, beta-, and gamma- frequency bands were load-dependent and visual-field dependent. The networks of theta- and alpha- bands phase synchrony were most predominant in retention period for right visual field (RVF) WM than for LVF WM. Furthermore, only for RVF memory condition, brain network density of theta-band during the retention interval were linked to the delay of behavior reaction time, and the topological property of alpha-band network was negative correlation with behavior accuracy.

Conclusions/Significance

We suggest that the differences in theta- and alpha- bands between LVF and RVF conditions in functional connectivity and topological properties during retention period may result in the decline of behavioral performance in RVF task.     

The impact of experimental instruction on changes in EEG power during verbal creative thinking in men and women

Features of EEG pattern during verbal creative thinking depending on experimental instruction were studied in men and women. Spectral power density was analyzed in six frequency bands (4-30 Hz). Performance of a creative task produced an increase in the power of theta (4-6 Hz) and beta2 (20-40 Hz) components and decrease in the power of alpha (8-13 Hz) and betal (13-20 Hz). Changes in the alpha and betal bands were observed, predominantly, in the posterior areas, whereas power of the thetal and beta2 bands increased in the anterior areas. Independently of instruction, women demonstrated greater synchronization in the theta1 band than men, whereas in men the desynchronization in the alpha2 band (10-13 Hz) was more pronounced. When the subjects were instructed to create original sentences, a widespread decrease in the EEG power was observed in the band of 8-30 Hz as compared to instruction "to create sentences". Thus, the instruction-related changes in EEG power were not gender-specific. They may reflect neural activity mediating selective attention.     

The brain matures with stronger functional connectivity and decreased randomness of its network

We investigated the development of the brain's functional connectivity throughout the life span (ages 5 through 71 years) by measuring EEG activity in a large population-based sample. Connectivity was established with Synchronization Likelihood. Relative randomness of the connectivity patterns was established with Watts and Strogatz' (1998) graph parameters C (local clustering) and L (global path length) for alpha (~10 Hz), beta (~20 Hz), and theta (~4 Hz) oscillation networks. From childhood to adolescence large increases in connectivity in alpha, theta and beta frequency bands were found that continued at a slower pace into adulthood (peaking at ~50 yrs). Connectivity changes were accompanied by increases in L and C reflecting decreases in network randomness or increased order (peak levels reached at ~18 yrs). Older age (55+) was associated with weakened connectivity. Semi-automatically segmented T1 weighted MRI images of 104 young adults revealed that connectivity was significantly correlated to cerebral white matter volume (alpha oscillations: r = 33, p<01; theta: r = 22, p<05), while path length was related to both white matter (alpha: max. r = 38, p<001) and gray matter (alpha: max. r = 36, p<001; theta: max. r = 36, p<001) volumes. In conclusion, EEG connectivity and graph theoretical network analysis may be used to trace structural and functional development of the brain.     

Frequency Dependent Alterations in Regional Homogeneity of Baseline Brain Activity in Schizophrenia

Low frequency oscillations are essential in cognitive function impairment in schizophrenia. While functional connectivity can reveal the synchronization between distant brain regions, the regional abnormalities in task-independent baseline brain activity are less clear, especially in specific frequency bands. Here, we used a regional homogeneity (ReHo) method combined with resting-state functional magnetic resonance imaging to investigate low frequency spontaneous neural activity in the three different frequency bands (slow-5∶0.01–0.027 Hz; slow-4∶0.027–0.08 Hz; and typical band: 0.01–0.08 Hz) in 69 patients with schizophrenia and 62 healthy controls. Compared with controls, schizophrenia patients exhibited decreased ReHo in the precentral gyrus, middle occipital gyrus, and posterior insula, whereas increased ReHo in the medial prefrontal cortex and anterior insula. Significant differences in ReHo between the two bands were found in fusiform gyrus and superior frontal gyrus (slow-4> slow-5), and in basal ganglia, parahippocampus, and dorsal middle prefrontal gyrus (slow-5> slow-4). Importantly, we identified significant interaction between frequency bands and groups in the inferior occipital gyrus and caudate body. This study demonstrates that ReHo changes in schizophrenia are widespread and frequency dependent.     

Frequency-Dependent Changes in the Regional Amplitude and Synchronization of Resting-State Functional MRI in Stroke

Resting-state functional magnetic resonance imaging (R-fMRI) has been intensively used to assess alterations of inter-regional functional connectivity in patients with stroke, but the regional properties of brain activity in stroke have not yet been fully investigated. Additionally, no study has examined a frequency effect on such regional properties in stroke patients, although this effect has been shown to play important roles in both normal brain functioning and functional abnormalities. Here we utilized R-fMRI to measure the amplitude of low-frequency fluctuations (ALFF) and regional homogeneity (ReHo), two major methods for characterizing the regional properties of R-fMRI, in three different frequency bands (slow-5: 0.01-0.027 Hz; slow-4: 0.027-0.73 Hz; and typical band: 0.01-0.1 Hz) in 19 stroke patients and 15 healthy controls. Both the ALFF and ReHo analyses revealed changes in brain activity in a number of brain regions, particularly the parietal cortex, in stroke patients compared with healthy controls. Remarkably, the regions with changed activity as detected by the slow-5 band data were more extensive, and this finding was true for both the ALFF and ReHo analyses. These results not only confirm previous studies showing abnormality in the parietal cortex in patients with stroke, but also suggest that R-fMRI studies of stroke should take frequency effects into account when measuring intrinsic brain activity.     

Intrinsic Patterns of Coupling between Correlation and Amplitude of Low-Frequency fMRI Fluctuations Are Disrupted in Degenerative Dementia Mainly due to Functional Disconnection

Low frequency fluctuations (LFFs) of the BOLD signal are a major discovery in the study of the resting brain with functional magnetic resonance imaging (fMRI). Two fMRI-based measures, functional connectivity (FC), a measure of signal synchronicity, and the amplitude of LFFs (ALFF), a measure of signal periodicity, have been proved to be sensitive to changes induced by several neurological diseases, including degenerative dementia. In spite of the increasing use of these measures, whether and how they are related to each other remains to be elucidated. In this work we used voxel-wise FC and ALFF computed in different frequency bands (slow-5: 0.01-0.027 Hz; slow-4: 0.027-0.073 Hz; and full-band: 0.01-0.073 Hz), in order to assess their relationship in healthy elderly as well as the relevant changes induced by Alzheimer’s Disease (AD) and Mild Cognitive Impairment (MCI). We found that in healthy elderly subjects FC and ALFF are positively correlated in anterior and posterior cingulate cortex (full-band, slow-4 and slow-5), temporal cortex (full-band and slow-5), and in a set of subcortical regions (full-band and slow-4). These correlation patterns between FC and ALFF were absent in either AD or MCI patients. Notably, the loss of correlation between FC and ALFF in the AD group was primarily due to changes in FC rather than in ALFF. Our results indicate that degenerative dementia is characterized by a loss of global connection rather than by a decrease of fluctuation amplitude.     

Frontal bilateral synchronous theta waves and the resting EEG coherence in children aged 7–8 and 9–10 with learning difficulties

The resting state cortical functional connectivity was studied in children of 7–8 (N = 29) and 9–10 (N = 23) years with learning difficulties whose EEG showed the frontal bilateral synchronous theta waves (FTW) and in the control children of 7–8 (N = 32) and 9–10 (N = 16) years who did not experience school difficulties and whose EEG did not show signs of abnormality. The functional connectivity was estimated in the θ, α₁, α₂, and β₁ frequency bands via measuring the coherence for the resting EEG that was free from any abnormal patterns. Compared to control children, there was a reduction in the strength of the functional coupling between the frontal and anterior temporal cortices found predominantly in the left hemisphere of FTW children. The relative weakness of the coupling between the frontal cortex and the other cortical areas was more pronounced in children of 7–8 than in children of 9–10 years. These between-group differences were unaffected by the frequency band or gender factors.     

A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

Background

Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them.

Methods

We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects.

Results

Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as “hubs” for the outflow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property.In particular, a higher local efficiency E _l can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz).By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of “activation” Ω within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions.

Conclusions

The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

     

Halteria grandinella: a rapid swimming ciliate with a high frequency of ciliary beating

A ciliated protozoan, Halteria grandinella, swam backward rapidly with a migration distance per second attaining 100 times the cell size. This high swimming velocity was accompanied by a high frequency of ciliary beating. Recordings with a high-speed digital video (10(3) frames/s) revealed that the frequency during forward and backward swimming was, respectively, 105 +/- 10 Hz and 260 +/- 30 Hz. These frequencies are the highest among cilia and flagella reported to date. Electron microscopic observation of the ciliary structure confirmed normal 9 + 2 arrangements of the axoneme except that cilia for migration are bundled into membranelles. Ciliary beating of saponin-treated cells was reactivated by the addition of Mg2+ -ATP, although the beating amplitude was smaller than that of intact cells. Kinetic analysis of the ATP-dependent increase of beating frequency revealed that the maximal frequency in the presence of free Ca2+ and 0.9 microM Ca2+ was approximately 60 and 110 Hz, respectively. A possible mechanism to increase beating frequency with Ca2+ is discussed.     

Electroencephalographic characteristic of cognitive-specific alerting attention in verbal learning--III: Localized characteristics of EEG spatial synchronization

Electroencephalograms (EEG) were recorder in 19 standard derivations in 88 healthy subjects, while they were in the states: rest with eyes open; memorization (learning) of verbal bilingual semantic pairs (Latin and Russian languages); the retrieval of the rote information from memory (control). We compared estimates of EEG coherence in these states for the frequency bands theta (4-7 Hz), alpha-1 (7-10 Hz), alpha-2 (10-13 Hz), beta-1 (13-18 Hz), beta-2 (18-30 Hz), gamma (30-40 Hz). When compared with the rest most strongly expressed: for memorization a decrease of coherence in the pairs of derivations from frontal and central areas of the cortex in the EEG frequency bands; for retrieval an increase of coherence in interhemispheric derivation pairs of pariental-occipital region in majority of the frequency bands. For the retrieval also increases of coherence in the beta2 and gamma bands, along with coherence decreases at low frequencies take place in pairs formed by derivations from the parieto-occipital region with derivations from the frontal and the central ones. Dynamics of EEG coherence in comparisons of memorization and retrieval from the rest and each are expressed significantly more in the interhemispheric and crosshemispheric pairs of derivations than in the intrahemispheric pairs. Revealed topographic specificity of the dynamics of EEG coherence by changing the states is considered in terms of ideas about cognitive-specific forms of sustained goal-directed mental attention.     

The effect of sinus node depression on heart rate variability in humans using zatebradine, a selective bradycardic agent

Zatebradine is a bradycardic agent with a selective effect on the pacemaker current in the sinus node. The effect of such drugs on heart rate variability is not known. Thirty-six patients without structural heart disease were randomly assigned to receive 10 mg of zatebradine i.v. (n = 24) or isotonic saline (n = 12). Heart rate variability (HRV) was recorded as power in the very low frequency (VLF, 0.003-0.040 Hz), low frequency (LF, 0.040-0.150 Hz), and high frequency (HF, 0.150-0.400 Hz) spectral bands as well as total power (TP, 0.003-0.400 Hz) during 5-min ECG acquisitions at baseline, 30, and 60 min following the start of the infusion. No change in heart rate variability was detected in the control group. Zatebradine significantly reduced heart rate variability at 60 min in all frequency bands: VLF (-12+/-4%, p<0.001), LF (-19+/-4%, p<0.001), and HF (-26+/-5%, p<0.001). The reduction in HRV following zatebradine is due to depression of sinus node response to all external stimuli and underscores the need for documentation of normal sinus node function in HRV research.     

Motor Network Plasticity and Low-Frequency Oscillations Abnormalities in Patients with Brain Gliomas: A Functional MRI Study

Brain plasticity is often associated with the process of slow-growing tumor formation, which remodels neural organization and optimizes brain network function. In this study, we aimed to investigate whether motor function plasticity would display deficits in patients with slow-growing brain tumors located in or near motor areas, but who were without motor neurological deficits. We used resting-state functional magnetic resonance imaging to probe motor networks in 15 patients with histopathologically confirmed brain gliomas and 15 age-matched healthy controls. All subjects performed a motor task to help identify individual motor activity in the bilateral primary motor cortex (PMC) and supplementary motor area (SMA). Frequency-based analysis at three different frequencies was then used to investigate possible alterations in the power spectral density (PSD) of low-frequency oscillations. For each group, the average PSD was determined for each brain region and a nonparametric test was performed to determine the difference in power between the two groups. Significantly reduced inter-hemispheric functional connectivity between the left and right PMC was observed in patients compared with controls (P<0.05). We also found significantly decreased PSD in patients compared to that in controls, in all three frequency bands (low: 0.01–0.02 Hz; middle: 0.02–0.06 Hz; and high: 0.06–0.1 Hz), at three key motor regions. These findings suggest that in asymptomatic patients with brain tumors located in eloquent regions, inter-hemispheric connection may be more vulnerable. A comparison of the two approaches indicated that power spectral analysis is more sensitive than functional connectivity analysis for identifying the neurological abnormalities underlying motor function plasticity induced by slow-growing tumors.     

Developmental trends of theta–beta interelectrode power correlation during resting state in normal children

The possibility that power-to-power (theta–beta) frequency coupling increases during development was analyzed. Three minutes of spontaneous EEG in an open eyes condition were recorded in a sample of 160 subjects ranging from 6 to 26 years old. Theta (4–7 Hz) and beta band (15–20 Hz) power was calculated in a trial-by-trial basis. Inter-electrode power correlations (IPC) were computed in each subject as the correlation between the power of two frequency bands recorded in two electrodes. An increase in theta–beta IPC with age was obtained. IPCs were higher when theta was seeded in posterior regions than in anterior or central regions. Moreover, the significant correlations between each individual IPC and age were calculated, making it possible to draw IPC versus age correlation maps in order to capture the IPC development topography. An increase was found in significant correlations in the left hemisphere compared to the right hemisphere. There were no differences in the inter-hemispheric versus intra-hemispheric IPC maturation spatial patterns. An increase in power-to-power–frequency coupling in theta–beta occurs during development, suggesting an increase in functional connectivity with age. Frequency coupling between theta and beta rhythms would be one of the mechanisms facilitating integration of long distance functional networks during development.     

Traveling waves in the prefrontal cortex during working memory

Neural oscillations are evident across cortex but their spatial structure is not well- explored. Are oscillations stationary or do they form “traveling waves”, i.e., spatially organized patterns whose peaks and troughs move sequentially across cortex? Here, we show that oscillations in the prefrontal cortex (PFC) organized as traveling waves in the theta (4-8Hz), alpha (8-12Hz) and beta (12-30Hz) bands. Some traveling waves were planar but most rotated. The waves were modulated during performance of a working memory task. During baseline conditions, waves flowed bidirectionally along a specific axis of orientation. Waves in different frequency bands could travel in different directions. During task performance, there was an increase in waves in one direction over the other, especially in the beta band.     

A solid state NMR study of locust bean gum galactomannan and Konjac glucomannan gels

This paper describes a ¹³C solid state NMR study of hydrated powders and gels of locust bean gum galactomannan-LBG and Konjac glucomannan-KGM. Changes in relative spectral intensities, cross-polarization dynamics (T_CH, T_1ρH) and relaxation times (T_1C, T_1H, T_2H) show that hydration (0–90%) of LBG powders increases the 10⁸ Hz frequency molecular motions, probably reflecting the enhanced motion of non-aggregating segments and chain ends. Slower motions (10⁴–10⁵ Hz) are enhanced only slightly at 90% hydration. LBG gel shows higher spatial distinction between aggregated and non-aggregated segments than the hydrated powder and relaxation times indicate higher mobility for galactose-ramified segments, compared to linear mannose segments. While the dynamics of KGM hydration is similar to that of LBG, i.e. mainly affecting fast 10⁸ Hz motions, the gel is significantly more rigid. Both spectra and relaxation times show that glucose residues in KGM gel are particularly hindered, probably due to their preferential involvement in chain aggregation.     

Analysis and modeling of time-variant amplitude–frequency couplings of and between oscillations of EEG bursts

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.     

Oscillator decomposition of infant fNIRS data

The functional near-infrared spectroscopy (fNIRS) can detect hemodynamic responses in the brain and the data consist of bivariate time series of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) on each channel. In this study, we investigate oscillatory changes in infant fNIRS signals by using the oscillator decompisition method (OSC-DECOMP), which is a statistical method for extracting oscillators from time series data based on Gaussian linear state space models. OSC-DECOMP provides a natural decomposition of fNIRS data into oscillation components in a data-driven manner and does not require the arbitrary selection of band-pass filters. We analyzed 18-ch fNIRS data (3 minutes) acquired from 21 sleeping 3-month-old infants. Five to seven oscillators were extracted on most channels, and their frequency distribution had three peaks in the vicinity of 0.01-0.1 Hz, 1.6-2.4 Hz and 3.6-4.4 Hz. The first peak was considered to reflect hemodynamic changes in response to the brain activity, and the phase difference between oxy-Hb and deoxy-Hb for the associated oscillators was at approximately 230 degrees. The second peak was attributed to cardiac pulse waves and mirroring noise. Although these oscillators have close frequencies, OSC-DECOMP can separate them through estimating their different projection patterns on oxy-Hb and deoxy-Hb. The third peak was regarded as the harmonic of the second peak. By comparing the Akaike Information Criterion (AIC) of two state space models, we determined that the time series of oxy-Hb and deoxy-Hb on each channel originate from common oscillatory activity. We also utilized the result of OSC-DECOMP to investigate the frequency-specific functional connectivity. Whereas the brain oscillator exhibited functional connectivity, the pulse waves and mirroring noise oscillators showed spatially homogeneous and independent changes. OSC-DECOMP is a promising tool for data-driven extraction of oscillation components from biological time series data.