Abstract
The recent development of neuroimaging technology and network theory allows us to visualize and characterize the whole-brain functional connectivity in vivo. The importance of conventional structural image atlas widely used in population-based neuroimaging studies has been well verified. Similarly, a “common” brain connectivity map (also called connectome atlas) across individuals can open a new pathway to interpreting disorder-related brain cognition and behaviors. However, the main obstacle of applying the classic image atlas construction approaches to the connectome data is that a regular data structure (such as a grid) in such methods breaks down the intrinsic geometry of the network connectivity derived from the irregular data domain (in the setting of a graph). To tackle this hurdle, we first embed the brain network into a set of graph signals in the Euclidean space via the diffusion mapping technique. Furthermore, we cast the problem of connectome atlas construction into a novel learning-based graph inference model. It can be constructed by iterating the following processes: (1) align all individual brain networks to a common space spanned by the graph spectrum bases of the latent common network, and (2) learn graph Laplacian of the common network that is in consensus with all aligned brain networks. We have evaluated our novel method for connectome atlas construction in comparison with non-learning-based counterparts. Based on experiments using network connectivity data from populations with neurodegenerative and neuropediatric disorders, our approach has demonstrated statistically meaningful improvement over existing methods.
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Notes
It is worth noting that the parcellation of the AAL template is defined based on anatomical structure. Although there are still quite a few fMRI studies using the AAL template, the interest is shifting towards using functional atlases which follow the insight of brain functions. However, we demonstrate the common functional brain networks using both structural and functional parcellations in order to show the proposed computational method can work with different atlases.
References
Herculano-Houzel, S. 2009 The Human Brain in Numbers: A Linearly Scaled-up Primate Brain. Front Hum Neurosci, 3(31).
Nowakowski, R. S. (2006). Stable neuron numbers from cradle to grave. Proc Natl Acad Sci U S A, 103(33), 12219–12220.
Sporns, O. (2011) Networks of the brain. MIT Press.
Sporns, O. (2013). Structure and function of complex brain networks. Dialogues Clin Neurosci, 15(3), 247–262.
Heuvel, M. P. V. D., & Sporns, O. (2011). Rich-club organization of the human connectome. J Neurosci, 31(44), 15775–15786.
Yan, C., et al. (2013). Standardizing the intrinsic brain: Towards robust measurement of inter-individual variation in 1000 functional connectomes. Neuroimage, 80(10), 246–262.
Blezek, D. J., & Miller, J. V. (2007). Atlas stratification. Med Image Anal, 11(5), 443–457.
Serag, A., Aljabar, P., Ball, G., Counsell, S. J., Boardman, J. P., Rutherford, M. A., Edwards, A. D., Hajnal, J. V., & Rueckert, D. (2012). Construction of a consistent high-definition spatio-temporal atlas of the developing brain using adaptive kernel regression. NeuroImage, 59(3), 2255–2265.
Fletcher, P. T., Venkatasubramanian, S., & Joshi, S. (2009). The geometric median on Riemannian manifolds with application to robust atlas estimation. NeuroImage, 45(1), S143–S152.
Xie, Y., Ho, J., and Vemuri, B.C. (2010) Image Atlas Construction via Intrinsic Averaging on the Manifold of Images, in IEEE Conference on Computer Vision and Pattern Recognition: San Francisco, CA.
Joshi, S., et al. (2004) Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage, 23(Supplement 1): p. S151-S160.
Avants, B. B., et al. (2008). Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain. Med Image Anal, 12(1), 26–41.
Vercauteren, T., et al. (2009) Diffeomorphic demons: efficient non-parametric image registration. NeuroImage, 45(1, Supplement 1): p. S61-S72.
Wu, G., et al. (2013) S-HAMMER: Hierarchical attribute-guided, Symmetric Diffeomorphic Registration for MR Brain Images. Human Brain Mapping.
Wu, G., Qi, F., & Shen, D. (2006). Learning-based deformable registration of MR brain images. Medical Imaging, IEEE Transactions on, 25(9), 1145–1157.
Zitová, B., & Flusser, J. (2003). Image registration methods: A survey. Image Vis Comput, 21(11), 977–1000.
Shi, F., Wang, L., Wu, G., Li, G., Gilmore, J. H., Lin, W., & Shen, D. (2014). Neonatal atlas construction using sparse representation. Hum Brain Mapp, 35(9), 4663–4677.
Shattuck, D. W., Mirza, M., Adisetiyo, V., Hojatkashani, C., Salamon, G., Narr, K. L., Poldrack, R. A., Bilder, R. M., & Toga, A. W. (2008). Construction of a 3D probabilistic atlas of human cortical structures. NeuroImage, 39(3), 1064–1080.
Shi, F., Yap, P. T., Wu, G., Jia, H., Gilmore, J. H., Lin, W., & Shen, D. (2011). Infant brain atlases from neonates to 1- and 2-year-olds. PLoS One, 6(4), e18746.
Bassett, D. S., & Bullmore, E. (2006). Small-world brain networks. Neuroscientist, 12(6), 512–523.
Fan, L., Li, H., Zhuo, J., Zhang, Y., Wang, J., Chen, L., Yang, Z., Chu, C., Xie, S., Laird, A. R., Fox, P. T., Eickhoff, S. B., Yu, C., & Jiang, T. (2016). The human Brainnetome atlas: A new brain atlas based on connectional architecture. Cereb Cortex, 26(8), 3508–3526.
Shen, X., Tokoglu, F., Papademetris, X., & Constable, R. T. (2013). Groupwise whole-brain parcellation from resting-state fMRI data for network node identification. Neuroimage, 82(11), 403–415.
Wig, G. S., Laumann, T. O., Cohen, A. L., Power, J. D., Nelson, S. M., Glasser, M. F., Miezin, F. M., Snyder, A. Z., Schlaggar, B. L., & Petersen, S. E. (2013). Parcellating an individual Subject's cortical and subcortical brain structures using snowball sampling of resting-state correlations. Cereb Cortex, 24(8), 2036–2054.
Arsigny, V., Fillard, P., Pennec, X., & Ayache, N. (2006). Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn Reson Med, 56(2), 411–421.
Rekik, I., et al. (2017) Estimation of Brain Network Atlases using Diffusive-Shrinking Graphs: Application to Developing Brains, in International Conference on Information Processing in Medical Imaging. p. 385–397.
Wang, B., Mezlini, A. M., Demir, F., Fiume, M., Tu, Z., Brudno, M., Haibe-Kains, B., & Goldenberg, A. (2014a). Similarity network fusion for aggregating data types on a genomic scale. Nat Methods, 11, 333–337.
Coifman, R. R., & Lafon, S. (2006). Diffusion maps. Appl Comput Harmon Anal, 21(1), 5–30.
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013a). The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process Mag, 30(3), 83–98.
Talmon, R., Cohen, I., Gannot, S., & Coifman, R. R. (2013). Diffusion maps for signal processing: A deeper look at manifold-learning techniques based on kernels and graphs. IEEE Signal Process Mag, 30(4), 75–86.
Hlinka, J., et al. (2011). Functional connectivity in resting-state fMRI: Is Llinear correlation sufficient. Neuroimage, 54(3), 2212–2225.
Hutchison, R. M., Womelsdorf, T., Allen, E. A., Bandettini, P. A., Calhoun, V. D., Corbetta, M., Della Penna, S., Duyn, J. H., Glover, G. H., Gonzalez-Castillo, J., Handwerker, D. A., Keilholz, S., Kiviniemi, V., Leopold, D. A., de Pasquale, F., Sporns, O., Walter, M., & Chang, C. (2013). Dynamic functional connectivity: Promise, issues, and interpretations. NeuroImage, 80(10), 360–378.
Chung, M.K., et al. (2017) Topological Distances Between Brain Networks, in International Workshop on Connectomics in NeuroImaging. LNCS, springer: Quebec City, Canada.
Lee, H., et al., Computing the shape of brain network using graph filtration and Gromov-Haudorff metric, in MICCAI 2011.
Lee, H., Kang, H., Chung, M. K., Kim, B. N., & Lee, D. S. (2012a). Persistent brain network homology from the perspective of dendrogram. IEEE Trans on Medical Imaging, 31(12), 2267–2277.
Edelsbrunner, H., & Harer, J. (2008). Persistent homology -- a survey. Contemp Math, 453, 257–282.
Cox, T.F. and Cox, M.A.A. (2001) Multidimensional Scaling: Chapman and Hall.
Shimada, Y., Ikeguchi, T., & Shigehara, T. (2012). From Networks to time series. Phys Rev Lett, 109(15), 158701.
Shuman, D., et al. (2013b). The emergence field of signal processing on graphs. IEEE Signal Process Mag, 30(3), 83–90.
Kalofolias, V., How to learn a graph from smooth signals, in The 19th International Conference on Artificial Intelligence and Statistics (AISTATS 2016). 2016: Cadiz, Spain.
Komodakis, N., & Pesquet, J.-C. (2015). Playing with duality: An overview of recent primal?Dual approaches for solving large-scale optimization problems. IEEE Signal Process Mag, 32(6), 31–54.
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., & Joliot, M. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, 15(1), 273–289.
Destrieux, C., Fischl, B., Dale, A., & Halgren, E. (2010). Automatic parcellation of human cortical gyri and sulci using standard anatomical nomenclature. Neuroimage, 53(1), 1–15.
Guo, C. C., Kurth, F., Zhou, J., Mayer, E. A., Eickhoff, S. B., Kramer, J. H., & Seeley, W. W. (2012). One-year test–retest reliability of intrinsic connectivity network fMRI in older adults. NeuroImage, 61(4), 1471–1483.
Liu, K., et al. (2017) Structural Brain Network Changes across the Adult Lifespan. Front Aging Neurosci, 9(275).
Geerligs, L., Renken, R. J., Saliasi, E., Maurits, N. M., & Lorist, M. M. (2015). A brain-wide study of age-related changes in functional connectivity. Cereb Cortex, 25, 1987–1999.
Lee, H., et al. (2012b). Persistent brain network homology from the perspective of dendrogram. IEEE Trans Med Imaging, 31(12), 1387–1402.
Guimerà, R., & Nunes Amaral, L. A. (2005). Functional cartography of complex metabolic networks. Nature, 433(7028), 895–900.
van den Heuvel, M. P., & Sporns, O. (2013). Network hubs in the human brain. Trends Cogn Sci, 17(12), 683–696.
Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: Uses and interpretations. NeuroImage, 52(3), 1059–1069.
Wang, B., Mezlini, A. M., Demir, F., Fiume, M., Tu, Z., Brudno, M., Haibe-Kains, B., & Goldenberg, A. (2014b). Similarity network fusion for aggregating data types on a genomic scale. Nat Methods, 11(1), 333–337.
Huang, H., et al. (2013) A New Sparse Simplex Model for Brain Anatomical and Genetic Network Analysis, in MICCAI. Nagoya, Japan.
Zu, C., et al. 2018 Identifying disease-related Connectome biomarkers by sparse Hypergraph learning. Brain Imaging and Behavior.
Acknowledgments
This work was supported in part by NIH R21AG059065 and K01AG049089.
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Appendix
Appendix
To solve Eq. 12, we need to determine the proximity operator for h1 and h2, and the derivative of h3 as follows:
Besides, we introduce a step-size variable τ ∈ (0, 1 + ζ + ‖K‖2) to control the convergence, where \( {\left\Vert K\right\Vert}_2=2\sqrt{\frac{N\left(N-1\right)}{2}} \). The primal dual algorithm for Eq. 12 is summarized below:
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Kim, M., Yan, C., Yang, D. et al. Constructing Connectome Atlas by Graph Laplacian Learning. Neuroinform 19, 233–249 (2021). https://doi.org/10.1007/s12021-020-09482-8
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DOI: https://doi.org/10.1007/s12021-020-09482-8