静息态功能磁共振影像（resting-state functional magnetic resonance imaging，r-fMRI）技术的发展使得研究者能够非侵入地探究活体人脑自发的活动。研究表明，人脑是由空间上广泛分布的脑区相互连接而组成的具有良好组织规则的复杂网络。通过r-fMRI数据和基于图论的复杂网络分析方法，研究者能够重构人脑大尺度功能连接组（即脑功能网络）进而解析其固有的连接模式。研究发现，人脑功能网络上存在着具有稠密功能连接的枢纽脑区，主要位于内外侧的额叶、顶叶皮层以及外侧的颞叶皮层，这些枢纽脑区在人脑功能网络的信息传递和信息整合过程中起到至关重要的作用，但是它们在功能网络中的配置会因疾病引起的脑网络连接异常而发生改变。对脑功能网络的枢纽脑区进行研究对于深入理解健康人群和脑疾病中的脑网络工作机制及评估具有重要的科学和应用价值。现有的静息态脑功能网络的研究大多关注血氧水平依赖信号的低频成分，即先验的设定0.01-0.08Hz或者0.01-0.1Hz的频段来构建人脑功能网络，将低频以外的信息归于受非神经元信号引起的生理噪声影响的噪声信号。越来越多的证据表明，健康人群和脑疾病患者的脑功能连接都具有频段依赖性，即使在低频段的0.01-0.027Hz和0.027-0.073Hz频段具有不同的脑连接特征，在高频段（>0.1Hz）同样存在枢纽脑区以及组织良好的功能脑网络，且与低频带存在空间分布上的差异，为理解脑的功能组织原则提供了更为丰富的信息。然而，以往针对脑功能枢纽频率依赖分布特点的研究多直接观测先验的低频带（0.01-0.08Hz或者0.01-0.1Hz）划分下的空间分布特点，并未考虑脑功能网络连接在不同频带存在差异的属性。同时，频率依赖功能枢纽的空间分布在多次脑影像扫描下的稳定性和不同数据集的可重复性尚不明确。本论文围绕脑功能枢纽的频率依赖特点这一重要科学问题，采用r-fMRI和复杂网络分析技术，针对健康人脑功能连接枢纽脑区空间分布模式的频带依赖特征、枢纽脑区频率依赖性的重测信度与可重复性特征，以及抑郁症脑功能网络频率依赖的枢纽分布异常特性三个方面开展了系统研究：

基于多频率的静息态人脑连接组枢纽脑区的研究（研究一）：人脑功能连接组中存在具有稠密连接的枢纽脑区，这些枢纽脑区在脑功能网络的全局信息整合中起到关键作用，但是研究者对功能枢纽脑区在不同频段下的空间分布特征仍然知之甚少。本研究基于57名健康被试的r-fMRI数据，将脑功能影像数据在0.01-0.24 Hz范围细分为10个子频段，在不同频段下对每个被试都构建了基于体素的高分辨率的脑功能网络，进而计算每个体素节点的连接强度的空间分布图，在此基础上利用聚类算法获得空间分布差异性较大的三个子频带。研究发现，在典型采样频率0.5Hz（TR=2秒）以下，可获取的频段0.01Hz-0.24Hz可以被分类成三个具有不同空间分布模式的频段，即低频段0.01-0.06Hz，中频段0.06-0.16Hz和高频段0.16-0.24Hz。单因素重复测量方差分析揭示了最为显著的频段之间的功能连接差异位于内外侧额顶皮层、海马旁回等区域。其中，在低频段，功能枢纽脑区主要位于内外侧的额叶顶叶皮层，在中频段，功能网络枢纽脑区主要位于内侧额顶皮层和顶下小叶区域。此外，在中频段和高频段，具有一些共同的功能枢纽脑区，主要位于颞上回、旁海马回、杏仁核以及小脑区域。该研究通过建立高分辨率脑功能网络和频段细分方法，为人脑静息态自发活动的枢纽脑区的频域依赖性提供了实验证据，建立的频段划分方法为研究正常和疾病状态的脑功能网络提供了方法学依据。

基于多频率的静息态人脑连接组枢纽脑区的重测信度与可重复性研究（研究二）：脑网络指标的可重测信度以及跨样本的可重复性，是开展统计推断以及作为潜在临床生物学标志物的重要前提。该研究中，进一步探索了在研究一中建立的脑功能连接组的频段划分方法和识别的频率依赖的功能枢纽脑区是否具有较好的可重测性和可重复性。该研究采用了研究一的入组被试在第一次与第二次随访的r-fMRI数据，采用与研究一相同的数据分析流程，探究不同频段下功能枢纽脑区空间分布情况，通过聚类分析得到了与研究一相同的三个特征频段。并结合类内相关系数计算各频段下功能连接强度分布的重测信度，发现了特征频段的枢纽脑区空间分布具有良好的可重测信度。同时，为了进一步验证功能枢纽频率依赖的空间分布在不同的数据集上的稳定性，研究采用一个独立r-fMRI数据集（48名年轻健康被试），探索了三个特征频段的可重复性。结果表明，在独立数据集上同样可以获得相同的三个特征频段，并且三个特征频段下枢纽脑区与研究一中相对应特征频段的枢纽脑区有很高的空间相似性。这些结果表明建立的脑功能网络频段划分方法和脑网络枢纽脑区的频域特性具有高的可重测性和可重复性，为探索正常和疾病状态的脑功能网络频率特性提供了稳定可靠的计算方法。

重性抑郁障碍患者频率依赖的人脑连接组改变特征研究（研究三）：脑功能连接组的研究表明重性抑郁障碍患者脑网络存在广泛的功能连接异常。然而，以往多数研究基于预设的低频带通滤波（0.01-0.08Hz或者0.01-0.1Hz）进行，抑郁症脑功能连接是否存在频率依赖的异常特征尚不清楚。为了回答该问题，本研究使用来自7个独立中心的大样本静息态功能磁共振数据集（1002名重性抑郁障碍患者和924名健康被试）对脑功能连接强度进行分频率解析，三个频段的划分基于研究一的结果，即0.01-0.06Hz、0.06-0.16Hz、以及0.16-0.24Hz。研究发现重性抑郁障碍患者脑功能连接强度在左侧顶下皮层、颞下皮层、中央前皮层、梭状回皮层以及双侧的楔前叶等区域存在显著的频率依赖性改变。通过对功能连接强度具备显著频率依赖的区域进行细化的功能连接分析，研究发现这些依赖于频率的连接强度改变主要由中长距离连接的出现异常导致，并且这些连接的改变是依赖于脑功能系统的。研究发现在高频滤波（0.16-0.24Hz）条件下，患者左侧楔前叶的连接强度异常降低与病程显著负相关。这些结果揭示了重性抑郁障碍患者脑功能网络中存在频率依赖的功能连接异常，为从较宽的频段上研究重性抑郁障碍患者的连接组改变提供了实验证据，也为研究一和研究二建立的脑网络频率依赖性计算方法的适用性提供了疾病模型验证。

综上所述，本论文基于静息态功能磁共振影像技术，结合脑连接组学和复杂网络分析方法，系统揭示了健康人群脑功能枢纽脑区的空间分布具备频率依赖性，并且不同频带下的空间分布模式具备较高的重测信度和可重复性。同时，通过将该发现用于抑郁症脑网络研究，发现重性抑郁障碍中功能枢纽脑区的分布同样存在频率依赖的异常。这些发现为我们深入理解人脑自发活动的脑网络频率特性，以及探索健康和疾病状态下的脑网络连接组织架构和工作机制提供了重要的方法学和实验证据。

The development of resting-state functional magnetic resonance imaging (r-fMRI) technology has provided researchers with a non-invasive way to explore the spontaneous or intrinsic activity of the human brain in vivo. Studies have shown that the human brain consists of a complex network of spatially distributed brain regions that are interconnected with optimized configurations. By using r-fMRI data and graph theoretical complex network analysis methods, researchers have been able to reconstruct the large-scale functional connectome or functional network of the human brain and resolve its intrinsic connectivity patterns. It has been found that there are several hub regions with dense functional connectivity in the human brain functional network, mainly located in the medial and lateral frontal parietal cortices and the lateral temporal cortex. These functional hubs play a crucial role in information transfer and integration in the human brain functional network, but their configuration can be altered by disease-induced abnormalities in brain network connectivity. The study of hub regions in the functional brain network is of great scientific value for understanding the mechanisms of functioning of healthy and diseased brains and implementing interventions. Most existing studies on the resting-state functional brain network have focused on the low-frequency component of the spontaneous oxygen level dependent signals, i.e., the 0.01-0.08 Hz or 0.01-0.1 Hz band set a priori to identify hub regions in the functional brain network. However, this approach risks relegating information beyond the low frequencies to noisy signals influenced by physiological noise not caused by neuronal signals. There is growing evidence that functional connectivity in both healthy and diseased brains is frequency-dependent, with different brain connectivity characteristics even in different low-frequency bands (e.g., 0.01-0.027 Hz and 0.027-0.073 Hz). In the high-frequency band (>0.1 Hz), there are also hub regions and well-organized functional brain networks with spatial distribution differences from the low-frequency band, indicating that the high-frequency band may provide new clues for exploring the organizational principles of healthy and diseased brains. However, previous studies on the frequency-dependent distribution of functional hubs have mainly observed spatial distribution under a prior low-frequency band (0.01-0.08 Hz or 0.01-0.1 Hz), without considering that functional brain network connections differ in different frequency bands. Additionally, it is unclear whether the frequency-dependent spatial distribution of functional hubs is stable under multiple brain imaging scans and reproducible across different data sets. This paper employs r-fMRI and complex network analysis techniques to investigate the frequency-dependent spatial distribution patterns of functional hubs in healthy human brains and their test-retest reliability and reproducibility. It further examines the abnormal distribution of frequency-dependent functional hubs in the depressed brain.

Frequency-dependent hub of the resting state human brain functional network (Study 1): The human functional network contains several functionally densely connected hub regions, which play a crucial role in global information integration. However, the spatial distribution of these functional hubs at different frequency bands remains poorly understood. In this study, r-fMRI data from 57 healthy subjects were used to preprocess functional MRI data into 10 subdivided frequency bands between 0.01-0.24 Hz. A high-resolution voxel-based functional brain network was constructed, and the functional connectivity strength (FCS) map for each subject was generated at different frequency bands. Results showed that the available frequency band (0.01 Hz-0.24 Hz) below the typical sampling frequency of 0.5 Hz (TR = 2 sec) could be classified into three frequency bands with different FCS spatial distribution patterns: low frequency band (0.01-0.06 Hz), middle frequency band (0.06-0.16 Hz), and high-frequency band (0.16-0.24 Hz). One-way repeated measures ANOVA revealed significant frequency-dependent differences in functional connectivity primarily located in the medial and lateral frontoparietal cortices and the parahippocampus. In the low-frequency band, functional hub regions were mainly located in the medial and lateral frontoparietal cortices, while in the middle-frequency band, functional network hubs were mainly located in the medial frontoparietal cortex and subparietal lobule regions. Additionally, in the middle and high-frequency bands, there were some common functional hubs, mainly located in the superior temporal gyrus, parahippocampal gyrus, amygdala, and cerebellar regions. This study provides experimental evidence for the frequency-dependence of the functional hub distribution derived from resting-state spontaneous activity in the human brain by establishing high-resolution functional brain networks and frequency band segmentation methods. The established frequency band segmentation methods provide a methodological basis for studying brain functional networks in healthy and disease states. 

Test-retest reliability and reproducibility of frequency-dependent hub regions in resting state human brain functional network (Study 2): Test-retest reliability and reproducibility of brain network indicators are important prerequisites for statistical inference and potential clinical biomarkers. In this study, we further explored whether the frequency-band identification method of the functional connectomes and the frequency-dependent functional hubs shown in Study 1 have good test-retest reliability and reproducibility. This study used test-retest resting-state fMRI data from the same group of subjects as in Study 1. The same data processing procedures were conducted to explore the spatial distribution of functional hubs at different frequency bands. Through clustering analysis, the study obtained the same three characteristic frequency bands as in Study 1.The test-retest reliability of the functional connectivity strength distribution at each frequency band was calculated using intra-class correlation coefficient. The results showed that the functional hubs at each characteristic frequency band were highly retestable.Further more, to verify whether the frequency-dependent spatial distribution of functional hubs is stable across different datasets, the study explored the reproducibility of the three characteristic frequency bands using a second independent dataset with 48 healthy subjects. Results showed that the same three feature frequency bands were also available in the independent dataset, and the hub regions under the three feature frequency bands showed high spatial similarity to the hub regions in the corresponding feature frequency bands in Study 1. These results indicate that the established frequency band delineation method and the frequency-dependent characteristics of the functional brain network hubs are highly reliable and reproducible. This provides a stable and reliable computational method for exploring the frequency characteristics of functional brain networks in both normal and disease states.

Frequency-dependent alterations in the brain connectome in major depressive disorder (Study 3): Studies of the functional connectome have shown the presence of a wide range of functional connectivity abnormalities in brain networks of patients with major depressive disorder (MDD). However, most previous studies were conducted based on pre-determined low-frequency band-pass filtering (0.01-0.08 Hz or 0.01-0.1 Hz), and it is unclear whether depressed brain functional connectivity is characterized by frequency-dependent abnormalities. To address this issue, the present study used a large sample of resting-state functional MRI datasets from seven independent centers (1002 patients with MDD and 924 healthy subjects) to investigate alterations in functional connectivity strength at different frequency bands (0.01-0.06 Hz, 0.06-0.16 Hz, and 0.16-0.24 Hz). Results showed significant frequency-dependent changes in functional connectivity strength in the left inferior parietal cortex, inferior temporal cortex, precentral cortex, cingulate gyrus, and bilateral precuneus. Further seed-based functional connectivity analysis in regions with significant frequency-dependent functional connectivity strength differences revealed that these frequency-dependent changes in connectivity strength were mainly driven by abnormalities in medium- and long-range connections, and that these connectivity changes were dependent on the functional system. Additionally, reductions in functional connectivity strength in the left precuneus were significantly negatively correlated with the severity of the disease at high frequency band (0.16-0.24 Hz). These results shed light on the presence of frequency-dependent functional connectivity abnormalities in the functional brain network of patients with MDD, providing experimental evidence for studying the altered connectome in patients with MDD over a wider frequency band and validating the disease model using frequency-dependent computational approaches to brain networks established in Studies 1 and 2.

In summary, this paper uses r-fMRI technology and complex network analysis methods of brain connectomics to systematically reveal that the spatial distribution of functional connectivity strength in the healthy brain is frequency-dependent, and the spatial distribution patterns in different frequency bands have high test-retest reliability and reproducibility. Moreover, by applying this methodology to studying depression brain network, we found that the distribution of functional hub regions in MDD also had frequency-dependent abnormalities. These results provide important methodological and empirical evidence for a deeper understanding of the frequency properties of spontaneous activity in the human brain, as well as for a better understanding of the organizational architecture and working mechanisms in healthy and diseased states.