Abstract
A long-standing challenge in multimodal brain network analyses is to integrate topologically different brain networks obtained from diffusion and functional MRI in a coherent statistical framework. Existing multimodal frameworks will inevitably destroy the topological difference of the networks. In this paper, we propose a novel topological learning framework that integrates networks of different topology through persistent homology. Such challenging task is made possible through the introduction of a new topological loss that bypasses intrinsic computational bottlenecks and thus enables us to perform various topological computations and optimizations with ease. We validate the topological loss in extensive statistical simulations with ground truth to assess its effectiveness of discriminating networks. Among many possible applications, we demonstrate the versatility of topological loss in the twin imaging study where we determine the extend to which brain networks are genetically heritable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Becker, C.O., et al.: Spectral mapping of brain functional connectivity from diffusion imaging. Sci. Rep. 8(1), 1–15 (2018)
Blokland, G., McMahon, K., Thompson, P., Martin, N., de Zubicaray, G., Wright, M.: Heritability of working memory brain activation. J. Neurosci. 31, 10882–10890 (2011)
Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)
Chiang, M.C., et al.: Genetics of white matter development: a DTI study of 705 twins and their siblings aged 12 to 29. NeuroImage 54, 2308–2317 (2011)
Cho, M., Lee, J., Lee, K.M.: Reweighted random walks for graph matching. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6315, pp. 492–505. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15555-0_36
Chung, M.K., Huang, S.G., Gritsenko, A., Shen, L., Lee, H.: Statistical inference on the number of cycles in brain networks. In: 16th International Symposium on Biomedical Imaging, pp. 113–116. IEEE (2019)
Chung, M.K., Lee, H., DiChristofano, A., Ombao, H., Solo, V.: Exact topological inference of the resting-state brain networks in twins. Network Neurosci. 3, 674 (2019)
Chung, M.K., Xie, L., Huang, S.-G., Wang, Y., Yan, J., Shen, L.: Rapid acceleration of the permutation test via transpositions. In: Schirmer, M.D., Venkataraman, A., Rekik, I., Kim, M., Chung, A.W. (eds.) CNI 2019. LNCS, vol. 11848, pp. 42–53. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32391-2_5
Clough, J.R., Oksuz, I., Byrne, N., Schnabel, J.A., King, A.P.: Explicit topological priors for deep-learning based image segmentation using persistent homology. In: Chung, A.C.S., Gee, J.C., Yushkevich, P.A., Bao, S. (eds.) IPMI 2019. LNCS, vol. 11492, pp. 16–28. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-20351-1_2
Cohen-Steiner, D., Edelsbrunner, H., Harer, J., Mileyko, Y.: Lipschitz functions have Lp-stable persistence. Found. Comput. Math. 10, 127 (2010). https://doi.org/10.1007/s10208-010-9060-6
Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61–75 (2008)
Glahn, D., et al.: Genetic control over the resting brain. Proc. Nat. Acad. Sci. 107, 1223–1228 (2010)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 377–388 (1996)
Honey, C.J., Kötter, R., Breakspear, M., Sporns, O.: Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proc. Nat. Acad. Sci. 104(24), 10240–10245 (2007)
Hu, X., Li, F., Samaras, D., Chen, C.: Topology-preserving deep image segmentation. In: Advances in Neural Information Processing Systems (2019)
Kang, H., Ombao, H., Fonnesbeck, C., Ding, Z., Morgan, V.L.: A Bayesian double fusion model for resting-state brain connectivity using joint functional and structural data. Brain Connectivity 7(4), 219–227 (2017)
Lee, H., Kang, H., Chung, M.K., Kim, B.N., Lee, D.S.: Persistent brain network homology from the perspective of dendrogram. IEEE Trans. Med. Imag. 31(12), 2267–2277 (2012)
Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: International Conference on Computer Vision, pp. 1482–1489. IEEE (2005)
Leordeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: Advances in Neural Information Processing Systems, pp. 1114–1122 (2009)
Marchese, A., Maroulas, V.: Signal classification with a point process distance on the space of persistence diagrams. Adv. Data Anal. Classification 12(3), 657–682 (2017). https://doi.org/10.1007/s11634-017-0294-x
McKay, D., et al.: Influence of age, sex and genetic factors on the human brain. Brain Imag. Behav. 8(2), 143–152 (2013). https://doi.org/10.1007/s11682-013-9277-5
Munkres, J.R.: Elements of Algebraic Topology. CRC Press, Boca Raton (2018)
Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein barycenter and its application to texture mixing. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 435–446. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-24785-9_37
Smit, D., Stam, C., Posthuma, D., Boomsma, D., De Geus, E.: Heritability of small-world networks in the brain: a graph theoretical analysis of resting-state EEG functional connectivity. Hum. Brain Map. 29, 1368–1378 (2008)
Songdechakraiwut, T., Chung, M.K.: Dynamic topological data analysis for functional brain signals. In: 17th International Symposium on Biomedical Imaging Workshops, pp. 1–4. IEEE (2020)
Surampudi, S.G., Naik, S., Surampudi, R.B., Jirsa, V.K., Sharma, A., Roy, D.: Multiple kernel learning model for relating structural and functional connectivity in the brain. Sci. Rep. 8(1), 1–14 (2018)
Tzourio-Mazoyer, N., et al.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15, 273–289 (2002)
Van Essen, D.C., et al.: The human connectome project: a data acquisition perspective. NeuroImage 62(4), 2222–2231 (2012)
Xia, K., Wei, G.W.: Persistent homology analysis of protein structure, flexibility, and folding. Int. J. Numerical Methods Biomed. Eng. 30(8), 814–844 (2014)
Xue, W., Bowman, F.D., Pileggi, A.V., Mayer, A.R.: A multimodal approach for determining brain networks by jointly modeling functional and structural connectivity. Front. Comput. Neurosci. 9, 22 (2015)
Acknowledgments
We thank Shih-Gu Huang (National University of Singapore) and Gregory Kirk (University of Wisconsin–Madison) for assistance in preprocessing fMRI data. This study is funded by NIH R01 EB022856, EB02875, EB022574 and NSF MDS-2010778.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Songdechakraiwut, T., Shen, L., Chung, M. (2021). Topological Learning and Its Application to Multimodal Brain Network Integration. In: de Bruijne, M., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2021. MICCAI 2021. Lecture Notes in Computer Science(), vol 12902. Springer, Cham. https://doi.org/10.1007/978-3-030-87196-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-87196-3_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87195-6
Online ISBN: 978-3-030-87196-3
eBook Packages: Computer ScienceComputer Science (R0)
