Mapping fMRI-BOLD nonlinear dynamics to transcriptional gradients via Koopman similarity analysis
Poster No:
1657
Submission Type:
Abstract Submission
Authors:
Nghi Nguyen1, Jingxuan Bao2, Jiong Chen2, Trang Cao3, Bojian Hou2, Shu Yang2, Yize Zhao4, Christos Davatzikos2, Li Shen2, Duy Duong-Tran2
Institutions:
1Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, 2Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, 3Monash Biomedical Imaging, Monash University, Clayton, Victoria, 4School of Public Health, Yale University, New Haven, CT
First Author:
Co-Author(s):
Introduction:
Human brain functions are increasingly understood through gradients derived from fMRI-BOLD via diffusion mapping (Bernhardt, 2022). While effective at capturing macro-scale functional connectivity and its alignment with the spatial distribution of 24 cell types (Zhang, 2024), it remains unclear how this approach elucidates the emergence of the macroscopic BOLD variance that cannot be explained by these broad cell types alone. We propose that diffusion mapping using linear correlations overlooks associations with finer neurobiological variations. Using similarity analysis of Koopman operators (Kamiy, 2024; Ostrow, 2024), we show that nonlinear BOLD features strongly align with transcriptional gradients of numerous genes, clusters of which are enriched in functions underpinning macroscopic BOLD variance.
Methods:
We used resting-state fMRI data from the Max Planck Institute Leipzig Mind-Brain-Body Dataset (LEMON) (Babayan, 2019), preprocessed by Jimenez-Marin et al. (2024). For alignment with transcriptomic data from the Allen Human Brain Atlas (Shen, 2012), fMRI images were parcellated into 391 regions using the Initial Parcellation Atlas (Jimenez-Marin, 2024).
Participants aged 20–30 were split into two groups: one (30 subjects) for hyperparameter tuning and another (106 subjects) for analysis. For each subject, Koopman operators were estimated for 391 BOLD time courses using a Nystroem-accelerated RBF approach (Meanti, 2024). Pairwise L2-Wasserstein distances between the singular value spectra of Koopman estimators yielded a 391-by-391 distance matrix M per subject, which embeds nonlinear BOLD dynamics. Hyperparameters of the estimators were tuned by minimizing normalized eigenvalue sums (NeSUM) of each embedding matrix M (He, 2022). Principal components (PCs) of the group-averaged embedding were extracted using multidimensional scaling.
We assessed alignment between each PC and gene transcription via Spearman correlation, testing significance with a spatially constrained Moran spectral randomization. Genes with Bonferroni-corrected significance were used to construct an interaction network with STRING, where clusters were identified by Louvain community detection. We manually labeled each cluster using the Gene Ontology (GO) enrichment terms assigned to its constituent genes.
Participants aged 20–30 were split into two groups: one (30 subjects) for hyperparameter tuning and another (106 subjects) for analysis. For each subject, Koopman operators were estimated for 391 BOLD time courses using a Nystroem-accelerated RBF approach (Meanti, 2024). Pairwise L2-Wasserstein distances between the singular value spectra of Koopman estimators yielded a 391-by-391 distance matrix M per subject, which embeds nonlinear BOLD dynamics. Hyperparameters of the estimators were tuned by minimizing normalized eigenvalue sums (NeSUM) of each embedding matrix M (He, 2022). Principal components (PCs) of the group-averaged embedding were extracted using multidimensional scaling.
We assessed alignment between each PC and gene transcription via Spearman correlation, testing significance with a spatially constrained Moran spectral randomization. Genes with Bonferroni-corrected significance were used to construct an interaction network with STRING, where clusters were identified by Louvain community detection. We manually labeled each cluster using the Gene Ontology (GO) enrichment terms assigned to its constituent genes.
Results:
We identified three PCs of the embedding manifold, each roughly organizing the brain along a major functional axis described in previous studies (Cross, 2021): Multiple Demand-Limbic, Transmodal-Sensory, and Somatomotor-Visual (Figure 1A, B, C). The Transmodal-Sensory axis significantly aligned with 667 genes, forming 26 clusters significantly enriched in GO processes linked to neurotransmission, cell morphology, and neurovascular coupling (Figure 1D, E). The other PCs showed weaker alignment with gene expression: the Multiple Demand-Limbic axis is correlated with just 6 genes, and the Somatomotor-Visual axis with 36 genes.
Applying the same transcriptomic alignment to diffusion mapping eigenvectors from the functional connectome (via the Pearson correlation matrix) showed far fewer significant gene correlations: 6, 18, and 7 genes for the first three eigenvectors. Network and enrichment analysis of these genes showed no significantly enriched clusters.
Applying the same transcriptomic alignment to diffusion mapping eigenvectors from the functional connectome (via the Pearson correlation matrix) showed far fewer significant gene correlations: 6, 18, and 7 genes for the first three eigenvectors. Network and enrichment analysis of these genes showed no significantly enriched clusters.
·Major axes of the BOLD embedding and gene clusters associated with the Transmodal-Sensory axis.
Conclusions:
Our findings suggest that nonlinear embeddings of BOLD dynamics, derived using Koopman operators, reveal a closer alignment between transcriptional gradients and large-scale functional axes than diffusion mapping based on linear correlations. By linking molecular and cellular processes to BOLD variance in unprecedented detail, our approach underscores the potential of Koopman frameworks in neuroimaging, paving the way for future studies on neurogenomic factors driving nonlinear BOLD dynamics and functional connectivity patterns.
Genetics:
Transcriptomics
Modeling and Analysis Methods:
fMRI Connectivity and Network Modeling
Methods Development 2
Task-Independent and Resting-State Analysis 1
Physiology, Metabolism and Neurotransmission:
Neurophysiology of Imaging Signals
Keywords:
Data analysis
FUNCTIONAL MRI
Other - Transcriptomics; Diffusion Mapping; Nonlinear Dynamics; Koopman
1|2Indicates the priority used for review
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Provide references using APA citation style.
Bernhardt, B. C. (2022). Gradients in brain organization. NeuroImage, 251, 118987.
Cross, N. (2021). Cortical gradients of functional connectivity are robust to state-dependent changes following sleep deprivation. NeuroImage, 226, 117547.
He, B. (2022, June). Exploring the gap between collapsed & whitened features in self-supervised learning. In International Conference on Machine Learning (pp. 8613-8634). PMLR.
Jimenez-Marin, A. (2024). Open datasets and code for multi-scale relations on structure, function and neuro-genetics in the human brain. Scientific Data, 11(1), 256.
Kamiya, S. (2024, March). Koopman Operator Based Dynamical Similarity Analysis for Data-driven Quantification of Distance between Dynamics. In ICLR 2024 Workshop on Representational Alignment.
Meanti, G. (2024). Estimating Koopman operators with sketching to provably learn large scale dynamical systems. Advances in Neural Information Processing Systems, 36.
Ostrow, M. (2024). Beyond geometry: Comparing the temporal structure of computation in neural circuits with dynamical similarity analysis. Advances in Neural Information Processing Systems, 36.
Shen, E. H. (2012). The Allen Human Brain Atlas: comprehensive gene expression mapping of the human brain. Trends in Neurosciences, 35(12), 711-714.
Zhang, X.-H. (2024). The cell-type underpinnings of the human functional cortical connectome. Nature Neuroscience.