A concise and persistent feature to study brain resting-state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

Persistent homology reveals robustness loss in inhaled substance abuse rs-fMRI networks

Analyzing functional brain activity through functional magnetic resonance imaging (fMRI) is commonly done using tools from graph theory for the analysis of the correlation matrices. A drawback of these methods is that the networks must be restricted to values of the weights of the edges within certain thresholds and there is no consensus about the best choice of such thresholds. Topological data analysis (TDA) is a recently-developed tool in algebraic topology which allows us to analyze networks through combinatorial spaces obtained from them, with the advantage that all the possible thresholds can be considered at once. In this paper we applied TDA, in particular persistent homology, to study correlation matrices from rs-fMRI, and through statistical analysis, we detected significant differences between the topological structures of adolescents with inhaled substance abuse disorder (ISAD) and healthy controls. We interpreted the topological differences as indicative of a loss of robustness in the functional brain networks of the ISAD population.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Alterations via inter-regional connective relationships in Alzheimer's disease

Disruptions in the inter-regional connective correlation within the brain are believed to contribute to memory impairment. To detect these corresponding correlation networks in Alzheimer's disease (AD), we conducted three types of inter-regional correlation analysis, including structural covariance, functional connectivity and group-level independent component analysis (group-ICA). The analyzed data were obtained from the Alzheimer's Disease Neuroimaging Initiative, comprising 52 cognitively normal (CN) participants without subjective memory concerns, 52 individuals with late mild cognitive impairment (LMCI) and 52 patients with AD. We firstly performed vertex-wise cortical thickness analysis to identify brain regions with cortical thinning in AD and LMCI patients using structural MRI data. These regions served as seeds to construct both structural covariance networks and functional connectivity networks for each subject. Additionally, group-ICA was performed on the functional data to identify intrinsic brain networks at the cohort level. Through a comparison of the structural covariance and functional connectivity networks with ICA networks, we identified several inter-regional correlation networks that consistently exhibited abnormal connectivity patterns among AD and LMCI patients. Our findings suggest that reduced inter-regional connectivity is predominantly observed within a subnetwork of the default mode network, which includes the posterior cingulate and precuneus regions, in both AD and LMCI patients. This disruption of connectivity between key nodes within the default mode network provides evidence supporting the hypothesis that impairments in brain networks may contribute to memory deficits in AD and LMCI.

Topological analysis of functional connectivity in Parkinson's disease

Parkinson's disease (PD) is a clinically heterogeneous disorder, which mainly affects patients' motor and non-motor function. Functional connectivity was preliminary explored and studied through resting state functional magnetic resonance imaging (rsfMRI). Through the topological analysis of 54 PD scans and 31 age-matched normal controls (NC) in the Neurocon dataset, leveraging on rsfMRI data, the brain functional connection and the Vietoris-Rips (VR) complex were constructed. The barcodes of the complex were calculated to reflect the changes of functional connectivity neural circuits (FCNC) in brain network. The 0-dimensional Betti number β0 means the number of connected branches in VR complex. The average number of connected branches in PD group was greater than that in NC group when the threshold δ ≤ 0.7. Two-sample Mann-Whitney U test and false discovery rate (FDR) correction were used for statistical analysis to investigate the FCNC changes between PD and NC groups. In PD group, under threshold of 0.7, the number of FCNC involved was significantly differences and these brain regions include the Cuneus_R, Lingual_R, Fusiform_R and Heschl_R. There are also significant differences in brain regions in the Frontal_Inf_Orb_R and Pallidum_R, when the threshold increased to 0.8 and 0.9 (p < 0.05). In addition, when the length of FCNC was medium, there was a significant statistical difference between the PD group and the NC group in the Neurocon dataset and the Parkinson's Progression Markers Initiative (PPMI) dataset. Topological analysis based on rsfMRI data may provide comprehensive information about the changes of FCNC and may provide an alternative for clinical differential diagnosis.

Persistent homology-based functional connectivity and its association with cognitive ability: Life-span study

Brain-segregation attributes in resting-state functional networks have been widely investigated to understand cognition and cognitive aging using various approaches [e.g., average connectivity within/between networks and brain system segregation (BSS)]. While these approaches have assumed that resting-state functional networks operate in a modular structure, a complementary perspective assumes that a core-periphery or rich club structure accounts for brain functions where the hubs are tightly interconnected to each other to allow for integrated processing. In this article, we apply a novel method, persistent homology (PH), to develop an alternative to standard functional connectivity by quantifying the pattern of information during the integrated processing. We also investigate whether PH-based functional connectivity explains cognitive performance and compare the amount of variability in explaining cognitive performance for three sets of independent variables: (1) PH-based functional connectivity, (2) graph theory-based measures, and (3) BSS. Resting-state functional connectivity data were extracted from 279 healthy participants, and cognitive ability scores were generated in four domains (fluid reasoning, episodic memory, vocabulary, and processing speed). The results first highlight the pattern of brain-information flow over whole brain regions (i.e., integrated processing) accounts for more variance of cognitive abilities than other methods. The results also show that fluid reasoning and vocabulary performance significantly decrease as the strength of the additional information flow on functional connectivity with the shortest path increases. While PH has been applied to functional connectivity analysis in recent studies, our results demonstrate potential utility of PH-based functional connectivity in understanding cognitive function.

Application of data harmonization and tract-based spatial statistics reveals white matter structural abnormalities in pediatric patients with focal cortical dysplasia

Our study assessed diffusion tensor imaging (DTI) metrics of fractional anisotropy (FA), mean diffusivity (MD), and radial diffusivity (RD) in pediatric subjects with epilepsy secondary to Focal Cortical Dysplasia (FCD) to improve our understanding of structural network changes associated with FCD related epilepsy. We utilized a data harmonization (DH) approach to minimize confounding effects induced by MRI protocol differences. We also assessed correlations between DTI metrics and neurocognitive measures of the fluid reasoning index (FRI), verbal comprehension index (VCI), and visuospatial index (VSI). Data (n = 51) from 23 FCD patients and 28 typically developing controls (TD) scanned clinically on either 1.5T, 3T, or 3T-wide-bore MRI were retrospectively analyzed. Tract-based spatial statistics (TBSS) with threshold-free cluster enhancement and permutation testing with 100,000 permutations were used for statistical analysis. To account for imaging protocol differences, we employed non-parametric data harmonization prior to permutation testing. Our analysis demonstrates that DH effectively removed MRI protocol-based differences typical in clinical acquisitions while preserving group differences in DTI metrics between FCD and TD subjects. Furthermore, DH strengthened the association between DTI metrics and neurocognitive indices. Fractional anisotropy, MD, and RD metrics showed stronger correlation with FRI and VSI than VCI. Our results demonstrate that DH is an integral step to reduce the confounding effect of MRI protocol differences during the analysis of white matter tracts and highlights biological differences between FCD and healthy control subjects. Characterization of white matter changes associated with FCD-related epilepsy may better inform prognosis and treatment approaches.

Topological analysis of brain dynamics in autism based on graph and persistent homology

Autism spectrum disorder (ASD) is a heterogeneous disorder with a rapidly growing prevalence. In recent years, the dynamic functional connectivity (DFC) technique has been used to reveal the transient connectivity behavior of ASDs' brains by clustering connectivity matrices in different states. However, the states of DFC have not been yet studied from a topological point of view. In this paper, this study was performed using global metrics of the graph and persistent homology (PH) and resting-state functional magnetic resonance imaging (fMRI) data. The PH has been recently developed in topological data analysis and deals with persistent structures of data. The structural connectivity (SC) and static FC (SFC) were also studied to know which one of the SC, SFC, and DFC could provide more discriminative topological features when comparing ASDs with typical controls (TCs). Significant discriminative features were only found in states of DFC. Moreover, the best classification performance was offered by persistent homology-based metrics and in two out of four states. In these two states, some networks of ASDs compared to TCs were more segregated and isolated (showing the disruption of network integration in ASDs). The results of this study demonstrated that topological analysis of DFC states could offer discriminative features which were not discriminative in SFC and SC. Also, PH metrics can provide a promising perspective for studying ASD and finding candidate biomarkers.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

A Spatiotemporal Brain Network Analysis of Alzheimer's Disease Based on Persistent Homology

Current brain network studies based on persistent homology mainly focus on the spatial evolution over multiple spatial scales, and there is little research on the evolution of a spatiotemporal brain network of Alzheimer's disease (AD). This paper proposed a persistent homology-based method by combining multiple temporal windows and spatial scales to study the spatiotemporal evolution of brain functional networks. Specifically, a time-sliding window method was performed to establish a spatiotemporal network, and the persistent homology-based features of such a network were obtained. We evaluated our proposed method using the resting-state functional MRI (rs-fMRI) data set from Alzheimer's Disease Neuroimaging Initiative (ADNI) with 31 patients with AD and 37 normal controls (NCs). In the statistical analysis experiment, most network properties showed a better statistical power in spatiotemporal networks than in spatial networks. Moreover, compared to the standard graph theory properties in spatiotemporal networks, the persistent homology-based features detected more significant differences between the groups. In the clustering experiment, the brain networks on the sliding windows of all subjects were clustered into two highly structured connection states. Compared to the NC group, the AD group showed a longer residence time and a higher window ratio in a weak connection state, which may be because patients with AD have not established a firm connection. In summary, we constructed a spatiotemporal brain network containing more detailed information, and the dynamic spatiotemporal brain network analysis method based on persistent homology provides stronger adaptability and robustness in revealing the abnormalities of the functional organization of patients with AD.

Repeated anodal high-definition transcranial direct current stimulation over the left dorsolateral prefrontal cortex in mild cognitive impairment patients increased regional homogeneity in multiple brain regions

Transcranial direct current stimulation (tDCS) can improve cognitive function. However, it is not clear how high-definition tDCS (HD-tDCS) regulates the cognitive function and its neural mechanism, especially in individuals with mild cognitive impairment (MCI). This study aimed to examine whether HD-tDCS can modulate cognitive function in individuals with MCI and to determine whether the potential variety is related to spontaneous brain activity changes recorded by resting-state functional magnetic resonance imaging (rs-fMRI). Forty-three individuals with MCI were randomly assigned to receive either 10 HD-tDCS sessions or 10 sham sessions to the left dorsolateral prefrontal cortex (L-DLPFC). The fractional amplitude of low-frequency fluctuation (fALFF) and the regional homogeneity (ReHo) was computed using rs-fMRI data from all participants. The results showed that the fALFF and ReHo values changed in multiple areas following HD-tDCS. Brain regions with significant decreases in fALFF values include the Insula R, Precuneus R, Thalamus L, and Parietal Sup R, while the Temporal Inf R, Fusiform L, Occipital Sup L, Calcarine R, and Angular R showed significantly increased in their fALFF values. The brain regions with significant increases in ReHo values include the Temporal Inf R, Putamen L, Frontal Mid L, Precentral R, Frontal Sup Medial L, Frontal Sup R, and Precentral L. We found that HD-tDCS can alter the intensity and synchrony of brain activity, and our results indicate that fALFF and ReHo analysis are sensitive indicators for the detection of HD-tDCS during spontaneous brain activity. Interestingly, HD-tDCS increases the ReHo values of multiple brain regions, which may be related to the underlying mechanism of its clinical effects, these may also be related to a potential compensation mechanism involving the mobilization of more regions to complete a function following a functional decline.

Promises and pitfalls of topological data analysis for brain connectivity analysis

Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in neuroscience. We conjecture its prominent tool of persistent homology may benefit from going beyond analysing structural and functional connectivity to effective connectivity graphs capturing the direct causal interactions or information flows. Therefore, we assess the potential of persistent homology to directed brain network analysis by testing its discriminatory power in two distinctive examples of disease-related brain connectivity alterations: epilepsy and schizophrenia. We estimate connectivity from functional magnetic resonance imaging and electrophysiology data, employ Persistent Homology and quantify its ability to distinguish healthy from diseased brain states by applying a support vector machine to features quantifying persistent homology structure. We show how this novel approach compares to classification using standard undirected approaches and original connectivity matrices. In the schizophrenia classification, topological data analysis generally performs close to random, while classifications from raw connectivity perform substantially better; potentially due to topographical, rather than topological, specificity of the differences. In the easier task of seizure discrimination from scalp electroencephalography data, classification based on persistent homology features generally reached comparable performance to using raw connectivity, albeit with typically smaller accuracies obtained for the directed (effective) connectivity compared to the undirected (functional) connectivity. Specific applications for topological data analysis may open when direct comparison of connectivity matrices is unsuitable - such as for intracranial electrophysiology with individual number and location of measurements. While standard homology performed overall better than directed homology, this could be due to notorious technical problems of accurate effective connectivity estimation.

Disrupted metabolic connectivity in dopaminergic and cholinergic networks at different stages of dementia from 18F-FDG PET brain persistent homology network

Dementia is related to the cellular accumulation of β-amyloid plaques, tau aggregates, or α-synuclein aggregates, or to neurotransmitter deficiencies in the dopaminergic and cholinergic pathways. Cellular and neurochemical changes are both involved in dementia pathology. However, the role of dopaminergic and cholinergic networks in metabolic connectivity at different stages of dementia remains unclear. The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. The sums of the network distances revealed significant differences between the network connectivity evident in the Alzheimer's disease and mild cognitive impairment cohorts. A larger distance between brain regions can indicate poorer efficiency in the integration of information. PHN analysis revealed the structural properties of and changes in the dopaminergic and cholinergic metabolism networks in patients with different stages of dementia at a range of thresholds. This method was thus able to identify dysregulation of dopaminergic and cholinergic networks in the pathology of dementia.

Altered Frequency-Dependent Brain Activation and White Matter Integrity Associated With Cognition in Characterizing Preclinical Alzheimer's Disease Stages

Background

Subjective cognitive decline (SCD), non-amnestic mild cognitive impairment (naMCI), and amnestic mild cognitive impairment (aMCI) are regarded to be at high risk of converting to Alzheimer's disease (AD). Amplitude of low-frequency fluctuations (ALFF) can reflect functional deterioration while diffusion tensor imaging (DTI) is capable of detecting white matter integrity. Our study aimed to investigate the structural and functional alterations to further reveal convergence and divergence among SCD, naMCI, and aMCI and how these contribute to cognitive deterioration.

Methods

We analyzed ALFF under slow-4 (0.027-0.073 Hz) and slow-5 (0.01-0.027 Hz) bands and white matter fiber integrity among normal controls (CN), SCD, naMCI, and aMCI groups. Correlation analyses were further utilized among paired DTI alteration, ALFF deterioration, and cognitive decline.

Results

For ALFF calculation, ascended ALFF values were detected in the lingual gyrus (LING) and superior frontal gyrus (SFG) within SCD and naMCI patients, respectively. Descended ALFF values were presented mainly in the LING, SFG, middle frontal gyrus, and precuneus in aMCI patients compared to CN, SCD, and naMCI groups. For DTI analyses, white matter alterations were detected within the uncinate fasciculus (UF) in aMCI patients and within the superior longitudinal fasciculus (SLF) in naMCI patients. SCD patients presented alterations in both fasciculi. Correlation analyses revealed that the majority of these structural and functional alterations were associated with complicated cognitive decline. Besides, UF alterations were correlated with ALFF deterioration in the SFG within aMCI patients.

Conclusions

SCD shares structurally and functionally deteriorative characteristics with aMCI and naMCI, and tends to convert to either of them. Furthermore, abnormalities in white matter fibers may be the structural basis of abnormal brain activation in preclinical AD stages. Combined together, it suggests that structural and functional integration may characterize the preclinical AD progression.

Effect of APOE ε4 on multimodal brain connectomic traits: a persistent homology study

BACKGROUND

Although genetic risk factors and network-level neuroimaging abnormalities have shown effects on cognitive performance and brain atrophy in Alzheimer's disease (AD), little is understood about how apolipoprotein E (APOE) ε4 allele, the best-known genetic risk for AD, affect brain connectivity before the onset of symptomatic AD. This study aims to investigate APOE ε4 effects on brain connectivity from the perspective of multimodal connectome.

RESULTS

Here, we propose a novel multimodal brain network modeling framework and a network quantification method based on persistent homology for identifying APOE ε4-related network differences. Specifically, we employ sparse representation to integrate multimodal brain network information derived from both the resting state functional magnetic resonance imaging (rs-fMRI) data and the diffusion-weighted magnetic resonance imaging (dw-MRI) data. Moreover, persistent homology is proposed to avoid the ad hoc selection of a specific regularization parameter and to capture valuable brain connectivity patterns from the topological perspective. The experimental results demonstrate that our method outperforms the competing methods, and reasonably yields connectomic patterns specific to APOE ε4 carriers and non-carriers.

CONCLUSIONS

We have proposed a multimodal framework that integrates structural and functional connectivity information for constructing a fused brain network with greater discriminative power. Using persistent homology to extract topological features from the fused brain network, our method can effectively identify APOE ε4-related brain connectomic biomarkers.

Multi-dimensional persistent feature analysis identifies connectivity patterns of resting-state brain networks in Alzheimer's disease

OBJECTIVE

The characterization of functional brain network is crucial to understanding the neural mechanisms associated with Alzheimer's disease (AD) and mild cognitive impairment (MCI). Some studies have shown that graph theoretical analysis could reveal changes of the disease-related brain networks by thresholding edge weights. But the choice of threshold depends on ambiguous cognitive conditions, which leads to the lack of interpretability. Recently, persistent homology (PH) was proposed to record the persistence of topological features of networks across every possible thresholds, reporting a higher sensitivity than graph theoretical features in detecting network-level biomarkers of AD. However, most research on PH focused on 0-dimensional features (persistence of connected components) reflecting the intrinsic topology of the brain network, rather than 1-dimensional features (persistence of cycles) with an interesting neurobiological communication pattern. Our aim is to explore the multi-dimensional persistent features of brain networks in the AD and MCI patients, and further to capture valuable brain connectivity patterns.

APPROACH

We characterized the change rate of the connected component numbers across graph filtration using the functional derivative curves, and examined the persistence landscapes that vectorize the persistence of cycle structures. After that, the multi-dimensional persistent features were validated in disease identification using a K-nearest neighbor algorithm. Furthermore, a connectivity pattern mining framework was designed to capture the disease-specific brain structures.

MAIN RESULTS

We found that the multi-dimensional persistent features can identify statistical group differences, quantify subject-level distances, and yield disease-specific connectivity patterns. Relatively high classification accuracies were received when compared with graph theoretical features.

SIGNIFICANCE

This work represents a conceptual bridge linking complex brain network analysis and computational topology. Our results can be beneficial for providing a complementary objective opinion to the clinical diagnosis of neurodegenerative diseases.

Default Mode Network Analysis of APOE Genotype in Cognitively Unimpaired Subjects Based on Persistent Homology

Current researches on default mode network (DMN) in normal elderly have mainly focused on finding some dysfunctional areas with decreased or increased connectivity. The global network dynamics of apolipoprotein E (APOE) e4 allele group is rarely studied. In our previous brain network study, we have demonstrated the advantage of persistent homology. It can distinguish robust and noisy topological features over multiscale nested networks, and the derived properties are more stable. In this study, for the first time we applied persistent homology to analyze APOE-related effects on whole-brain functional network. In our experiments, the risk allele group exhibited lower network radius and modularity in whole brain DMN based on graph theory, suggesting the abnormal organization structure. Moreover, two suggested measures from persistent homology detected significant differences between groups within the left hemisphere and in the whole brain in two datasets. They were more statistically sensitive to APOE genotypic differences than standard graph-based measures. In summary, we provide evidence that the e4 genotype leads to distinct DMN functional alterations in the early phases of Alzheimer's disease using persistent homology approach. Our study offers a novel insight to explore potential biomarkers in healthy elderly populations carrying APOE e4 allele.

White Matter Brain Network Research in Alzheimer's Disease Using Persistent Features

Despite the severe social burden caused by Alzheimer’s disease (AD), no drug than can change the disease progression has been identified yet. The structural brain network research provides an opportunity to understand physiological deterioration caused by AD and its precursor, mild cognitive impairment (MCI). Recently, persistent homology has been used to study brain network dynamics and characterize the global network organization. However, it is unclear how these parameters reflect changes in structural brain networks of patients with AD or MCI. In this study, our previously proposed persistent features and various traditional graph-theoretical measures are used to quantify the topological property of white matter (WM) network in 150 subjects with diffusion tensor imaging (DTI). We found significant differences in these measures among AD, MCI, and normal controls (NC) under different brain parcellation schemes. The decreased network integration and increased network segregation are presented in AD and MCI. Moreover, the persistent homology-based measures demonstrated stronger statistical capability and robustness than traditional graph-theoretic measures, suggesting that they represent a more sensitive approach to detect altered brain structures and to better understand AD symptomology at the network level. These findings contribute to an increased understanding of structural connectome in AD and provide a novel approach to potentially track the progression of AD.

Functional network topology associated with apathy in Alzheimer's disease

BACKGROUND

Apathy, a common neuropsychiatric (NPS) in patients with mild cognitive impairment (MCI) and Alzheimer's disease (AD), is associated with structural and metabolic brain changes. However, functional connectivity changes across the brain in association with apathy remain unclear. In this study, graph theoretical measures of integration and segregation from resting state functional connectivity in MCI and AD patients with low depression scores, and healthy controls.

METHODS

In MCI and AD patients with low depression scores, graph theoretical measures of integration and segregation were derived from resting state functional connectivity in patients, which were compared between those with apathy (NPS_A, n = 21) to those without NPS (NPS_None, n = 28) and those with NPS other than apathy (NPS_NA, n = 38). Additionally, the same measures were compared between AD patients and healthy controls (amyloid uptake below threshold levels).

RESULTS

Altered whole brain global efficiency and reduced local efficiency were found in NPS_A compared to NPS_None and NPS_NA. In similar contrasts, apathy was associated with increased participation coefficient in the frontoparietal and cingulo-opercular template-based networks. A study-specific network definition also showed similar results. In comparison, AD patients showed higher modularity compared to controls at the whole brain level and higher participation coefficient in the ventral attention network.

LIMITATIONS

The severity and dimensions of apathy were not assessed.

CONCLUSIONS

Loss of segregation in the frontoparietal and cingulo-opercular network, which are involved in the control of goal-directed behavior, was associated with apathy in MCI/AD. The results also suggest that network-level changes in AD patients may underlie specific NPS.

A UNIVARIATE PERSISTENT BRAIN NETWORK FEATURE BASED ON THE AGGREGATED COST OF CYCLES FROM THE NESTED FILTRATION NETWORKS

A threshold-free feature in brain network analysis can help circumvent the curse of arbitrary network thresholding for binary network conversions. Here, Persistent Homology is the inspiration for defining a new aggregation cost based on the number of cycles, or for tracking the first Betti number in a nested filtration network within the graph. Our theoretical analysis shows that the proposed aggregated cost of cycles (ACC) is monotonically increasing and thus we define a univariate persistent feature based on the shape of ACC. The proposed statistic has advantages compared to the First Betti Number Plot (BNP1), which only tracks the total number of cycles at each filtration. We show that our method is sensitive to both the topology of modular networks and the difference in the number of cycles in a network. Our method outperforms its counterparts in a synthetic dataset, while in a real-world one it achieves results comparable with the BNP1. Our proposed framework enriches univariate measures for discovering brain network dissimilarities for better categorization of distinct stages in Alzheimer's Disease (AD).

Metabolic Brain Network Analysis of FDG-PET in Alzheimer's Disease Using Kernel-Based Persistent Features

Recent research of persistent homology in algebraic topology has shown that the altered network organization of human brain provides a promising indicator of many neuropsychiatric disorders and neurodegenerative diseases. However, the current slope-based approach may not accurately characterize changes of persistent features over graph filtration because such curves are not strictly linear. Moreover, our previous integrated persistent feature (IPF) works well on an rs-fMRI cohort while it has not yet been studied on metabolic brain networks. To address these issues, we propose a novel univariate network measurement, kernel-based IPF (KBI), based on the prior IPF, to quantify the difference between IPF curves. In our experiments, we apply the KBI index to study fluorodeoxyglucose positron emission tomography (FDG-PET) imaging data from 140 subjects with Alzheimer's disease (AD), 280 subjects with mild cognitive impairment (MCI), and 280 healthy normal controls (NC). The results show the disruption of network integration in the progress of AD. Compared to previous persistent homology-based measures, as well as other standard graph-based measures that characterize small-world organization and modular structure, our proposed network index KBI possesses more significant group difference and better classification performance, suggesting that it may be used as an effective preclinical AD imaging biomarker.

A concise and persistent feature to study brain resting-state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

Alzheimer's disease (AD) is the most common type of dementia in the elderly with no effective treatment currently. Recent studies of noninvasive neuroimaging, resting-state functional magnetic resonance imaging (rs-fMRI) with graph theoretical analysis have shown that patients with AD and mild cognitive impairment (MCI) exhibit disrupted topological organization in large-scale brain networks. In previous work, it is a common practice to threshold such networks. However, it is not only difficult to make a principled choice of threshold values, but also worse is the discard of potential important information. To address this issue, we propose a threshold-free feature by integrating a prior persistent homology-based topological feature (the zeroth Betti number) and a newly defined connected component aggregation cost feature to model brain networks over all possible scales. We show that the induced topological feature (Integrated Persistent Feature) follows a monotonically decreasing convergence function and further propose to use its slope as a concise and persistent brain network topological measure. We apply this measure to study rs-fMRI data from the Alzheimer's Disease Neuroimaging Initiative and compare our approach with five other widely used graph measures across five parcellation schemes ranging from 90 to 1,024 region-of-interests. The experimental results demonstrate that the proposed network measure shows more statistical power and stronger robustness in group difference studies in that the absolute values of the proposed measure of AD are lower than MCI and much lower than normal controls, providing empirical evidence for decreased functional integration in AD dementia and MCI.