Learning Common Harmonic Waves on Stiefel Manifold - A New Mathematical Approach for Brain Network Analyses

Harmonic Wavelet Neural Network for Discovering Neuropathological Propagation Patterns in Alzheimer's Disease

Emerging researchindicates that the degenerative biomarkers associated with Alzheimer's disease (AD) exhibit a non-random distribution within the cerebral cortex, instead following the structural brain network. The alterations in brain networks occur much earlier than the onset of clinical symptoms, thereby affecting the progression of brain disease. In this context, the utilization of computational methods to ascertain the propagation patterns of neuropathological events would contribute to the comprehension of the pathophysiological mechanism involved in the evolution of AD. Despite the encouraging findings achieved by existing graph-based deep learning approaches in analyzing irregular graph data, their applications in identifying the spreading pathway of neuropathology are limited due to two disadvantages. They include (1) lack of a common brain network as an unbiased reference basis for group comparison, and (2) lack of an appropriate mechanism for the identification of propagation patterns. To this end, we propose a proof-of-concept harmonic wavelet neural network (HWNN) to predict the early stage of AD and localize disease-related significant wavelets, which can be used to characterize the spreading pathways of neuropathological events across the brain network. The extensive experiments constructed on both synthetic and real datasets demonstrate that our proposed method achieves superior performance in classification accuracy and statistical power of identifying propagation patterns, compared with other representative approaches.

Brain Network Classification for Accurate Detection of Alzheimer's Disease via Manifold Harmonic Discriminant Analysis

Mounting evidence shows that Alzheimer's disease (AD) manifests the dysfunction of the brain network much earlier before the onset of clinical symptoms, making its early diagnosis possible. Current brain network analyses treat high-dimensional network data as a regular matrix or vector, which destroys the essential network topology, thereby seriously affecting diagnosis accuracy. In this context, harmonic waves provide a solid theoretical background for exploring brain network topology. However, the harmonic waves are originally intended to discover neurological disease propagation patterns in the brain, which makes it difficult to accommodate brain disease diagnosis with high heterogeneity. To address this challenge, this article proposes a network manifold harmonic discriminant analysis (MHDA) method for accurately detecting AD. Each brain network is regarded as an instance drawn on a Stiefel manifold. Every instance is represented by a set of orthonormal eigenvectors (i.e., harmonic waves) derived from its Laplacian matrix, which fully respects the topological structure of the brain network. An MHDA method within the Stiefel space is proposed to identify the group-dependent common harmonic waves, which can be used as group-specific references for downstream analyses. Extensive experiments are conducted to demonstrate the effectiveness of the proposed method in stratifying cognitively normal (CN) controls, mild cognitive impairment (MCI), and AD.

Connectome-based prediction modeling of cognitive control using functional and structural connectivity

BACKGROUND

Cognitive control involves flexibly configuring mental resources and adjusting behavior to achieve goal-directed actions. It is associated with the coordinated activity of brain networks, although it remains unclear how both structural and functional brain networks can predict cognitive control. Connectome-based predictive modeling (CPM) is a powerful tool for predicting cognitive control based on brain networks.

METHODS

The study used CPM to predict cognitive control in 102 healthy adults from the UCLA Consortium for Neuropsychiatric Phenomics dataset and further compared structural and functional connectome characteristics that support cognitive control.

RESULTS

Our results showed that both structural (r values 0.263-0.375) and functional (r values 0.336-0.503) connectomes can significantly predict individuals' cognitive control subcomponents. There is overlap between the functional and structural networks of all three cognitive control subcomponents, particularly in the frontoparietal (FP) and motor (Mot) networks, while each subcomponent also has its own unique weight prediction network. Overall, the functional and structural connectivity that supports different cognitive control subcomponents manifests overlapping and distinct spatial patterns.

CONCLUSIONS

The structural and functional connectomes provide complementary information for predicting cognitive control ability. Integrating information from both connectomes offers a more comprehensive understanding of the neural underpinnings of cognitive control.

Learning pyramidal multi-scale harmonic wavelets for identifying the neuropathology propagation patterns of Alzheimer's disease

Previous studies have established that neurodegenerative disease such as Alzheimer's disease (AD) is a disconnection syndrome, where the neuropathological burdens often propagate across the brain network to interfere with the structural and functional connections. In this context, identifying the propagation patterns of neuropathological burdens sheds new light on understanding the pathophysiological mechanism of AD progression. However, little attention has been paid to propagation pattern identification by fully considering the intrinsic properties of brain-network organization, which plays an important role in improving the interpretability of the identified propagation pathways. To this end, we propose a novel harmonic wavelet analysis approach to construct a set of region-specific pyramidal multi-scale harmonic wavelets, it allows us to characterize the propagation patterns of neuropathological burdens from multiple hierarchical modules across the brain network. Specifically, we first extract underlying hub nodes through a series of network centrality measurements on the common brain network reference generated from a population of minimum spanning tree (MST) brain networks. Then, we propose a manifold learning method to identify the region-specific pyramidal multi-scale harmonic wavelets corresponding to hub nodes by seamlessly integrating the hierarchically modular property of the brain network. We estimate the statistical power of our proposed harmonic wavelet analysis approach on synthetic data and large-scale neuroimaging data from ADNI. Compared with the other harmonic analysis techniques, our proposed method not only effectively predicts the early stage of AD but also provides a new window to capture the underlying hub nodes and the propagation pathways of neuropathological burdens in AD.

Estimating Outlier-Immunized Common Harmonic Waves for Brain Network Analyses on the Stiefel Manifold

Since brain network organization is essentially governed by the harmonic waves derived from the Eigen-system of the underlying Laplacian matrix, discovering the harmonic-based alterations provides a new window to understand the pathogenic mechanism of Alzheimer's disease (AD) in a unified reference space. However, current reference (common harmonic waves) estimation studies over the individual harmonic waves are often sensitive to outliers, which are obtained by averaging the heterogenous individual brain networks. To address this challenge, we propose a novel manifold learning approach to identify a set of outlier-immunized common harmonic waves. The backbone of our framework is calculating the geometric median of all individual harmonic waves on the Stiefel manifold, instead of Fréchet mean, thus improving the robustness of learned common harmonic waves to the outliers. A manifold optimization scheme with theoretically guaranteed convergence is tailored to solve our method. The experimental results on synthetic data and real data demonstrate that the common harmonic waves learned by our approach are not only more robust to the outliers than the state-of-the-art methods, but also provide a putative imaging biomarker to predict the early stage of AD.

Characterizing the propagation pathway of neuropathological events of Alzheimer's disease using harmonic wavelet analysis

Empirical imaging biomarkers such as the level of the regional pathological burden are widely used to measure the risk of developing neurodegenerative diseases such as Alzheimer's disease (AD). However, ample evidence shows that the brain network (wirings of white matter fibers) plays a vital role in the progression of AD, where neuropathological burdens often propagate across the brain network in a prion-like manner. In this context, characterizing the spreading pathway of AD-related neuropathological events sheds new light on understanding the heterogeneity of pathophysiological mechanisms in AD. In this work, we propose a manifold-based harmonic network analysis approach to explore a novel imaging biomarker in the form of the AD propagation pattern, which eventually allows us to identify the AD-related spreading pathways of neuropathological events throughout the brain. The backbone of this new imaging biomarker is a set of region-adaptive harmonic wavelets that represent the common network topology across individuals. We conceptualize that the individual's brain network and its associated pathology pattern form a unique system, which vibrates as do all natural objects in the universe. Thus, we can computationally excite such a brain system using selected harmonic wavelets that match the system's resonance frequency, where the resulting oscillatory wave manifests the system-level propagation pattern of neuropathological events across the brain network. We evaluate the statistical power of our harmonic network analysis approach on large-scale neuroimaging data from ADNI. Compared with the other empirical biomarkers, our harmonic wavelets not only yield a new imaging biomarker to potentially predict the cognitive decline in the early stage but also offer a new window to capture the in-vivo spreading pathways of neuropathological burden with a rigorous mathematics insight.

Gating attractor dynamics of frontal cortex under acupuncture via recurrent neural network

Acupuncture can regulate the functions of human body and improve the cognition of brain. However, the mechanism of acupuncture manipulations remains unclear. Here, we hypothesis that the frontal cortex plays a gating role in information routing of brain network under acupuncture. To that end, the gating effect of frontal cortex under acupuncture is analyzed in combination with EEG data of acupuncture at Zusanli acupoints. In addition, recurrent neural network (RNN) is used to reproduce the dynamics of frontal cortex under normal state and acupuncture state. From low-dimensional view, it is shown that the brain networks under acupuncture state can show stable attractor cycle dynamics, which may explain the regulation effect of acupuncture. Comparing with different manipulations, we find that the attractor of low-dimensional trajectory varies under different frequencies of acupuncture. Besides, a strip gated band of neural dynamics is found by changing the frequency of stimulation and excitatory-inhibitory balance of network. The attractor state is found to transport in the gating area under different stimulation frequencies, and the probability of attractor migration is different across acupuncture manipulations. This reverse engineering of brain network indicates that the differences among acupuncture manipulations are caused by interaction and separation in the neural activity space between attractors that encode acupuncture function. Consequently, our results may provide help for quantitative analysis of acupuncture, and benefit for the clinical guidance of acupuncture clinicians.

Learning dynamic graph embeddings for accurate detection of cognitive state changes in functional brain networks

Mounting evidence shows that brain functions and cognitive states are dynamically changing even in the resting state rather than remaining at a single constant state. Due to the relatively small changes in BOLD (blood-oxygen-level-dependent) signals across tasks, it is difficult to detect the change of cognitive status without requiring prior knowledge of the experimental design. To address this challenge, we present a dynamic graph learning approach to generate an ensemble of subject-specific dynamic graph embeddings, which allows us to use brain networks to disentangle cognitive events more accurately than using raw BOLD signals. The backbone of our method is essentially a representation learning process for projecting BOLD signals into a latent vertex-temporal domain with the greater biological underpinning of brain activities. Specifically, the learned representation domain is jointly formed by (1) a set of harmonic waves that govern the topology of whole-brain functional connectivities and (2) a set of Fourier bases that characterize the temporal dynamics of functional changes. In this regard our dynamic graph embeddings provide a new methodology to investigate how these self-organized functional fluctuation patterns oscillate along with the evolving cognitive status. We have evaluated our proposed method on both simulated data and working memory task-based fMRI datasets, where our dynamic graph embeddings achieve higher accuracy in detecting multiple cognitive states than other state-of-the-art methods.