IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1005325.html
   My bibliography  Save this article

Structure-Function Network Mapping and Its Assessment via Persistent Homology

Author

Listed:
  • Hualou Liang
  • Hongbin Wang

Abstract

Understanding the relationship between brain structure and function is a fundamental problem in network neuroscience. This work deals with the general method of structure-function mapping at the whole-brain level. We formulate the problem as a topological mapping of structure-function connectivity via matrix function, and find a stable solution by exploiting a regularization procedure to cope with large matrices. We introduce a novel measure of network similarity based on persistent homology for assessing the quality of the network mapping, which enables a detailed comparison of network topological changes across all possible thresholds, rather than just at a single, arbitrary threshold that may not be optimal. We demonstrate that our approach can uncover the direct and indirect structural paths for predicting functional connectivity, and our network similarity measure outperforms other currently available methods. We systematically validate our approach with (1) a comparison of regularized vs. non-regularized procedures, (2) a null model of the degree-preserving random rewired structural matrix, (3) different network types (binary vs. weighted matrices), and (4) different brain parcellation schemes (low vs. high resolutions). Finally, we evaluate the scalability of our method with relatively large matrices (2514x2514) of structural and functional connectivity obtained from 12 healthy human subjects measured non-invasively while at rest. Our results reveal a nonlinear structure-function relationship, suggesting that the resting-state functional connectivity depends on direct structural connections, as well as relatively parsimonious indirect connections via polysynaptic pathways.Author Summary: One of the major challenges in neuroscience is to understand how brain structure is related to function. In this work, we present a whole-brain method to quantify the structure-function relationship. Our data-driven approach allows the inferred functional connectivity matrix to be represented as a weighted sum of the powers of the structural matrix, containing both direct and indirect pathways. We further introduce a novel measure of network similarity based on persistent homology for assessing the goodness of fit for the mapping; such a measure enables the complete comparison of network topological changes across all possible thresholds, and thus effectively circumvents the problem of selecting the arbitrary threshold for the resulting functional networks. Our results show that our approach is able to uncover both direct and indirect structural paths for predicting functional connectivity in all three connectivity datasets, suggesting that the resting-state functional connectivity is at least in part mediated by indirect pathways, in addition to direct structural connections. The finding of a nonlinear relationship between brain structure and function is conceptually new, thus advances our understanding of how structural networks shape functional networks. This work demonstrates the potential utility of our approach in a rapidly growing field of network neuroscience.

Suggested Citation

  • Hualou Liang & Hongbin Wang, 2017. "Structure-Function Network Mapping and Its Assessment via Persistent Homology," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-19, January.
  • Handle: RePEc:plo:pcbi00:1005325
    DOI: 10.1371/journal.pcbi.1005325
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005325
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005325&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1005325?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Volker Pernice & Benjamin Staude & Stefano Cardanobile & Stefan Rotter, 2011. "How Structure Determines Correlations in Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-14, May.
    2. Roberto F Galán, 2008. "On How Network Architecture Determines the Dominant Patterns of Spontaneous Neural Activity," PLOS ONE, Public Library of Science, vol. 3(5), pages 1-10, May.
    3. Peng, Jie & Wang, Pei & Zhou, Nengfeng & Zhu, Ji, 2009. "Partial Correlation Estimation by Joint Sparse Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 735-746.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    2. Thibault Jaisson & Mathieu Rosenbaum, 2015. "Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes," Papers 1504.03100, arXiv.org.
    3. Luo, Shan & Chen, Zehua, 2014. "Edge detection in sparse Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 138-152.
    4. Natalia Bailey & Sean Holly & M. Hashem Pesaran, 2016. "A Two‐Stage Approach to Spatio‐Temporal Analysis with Strong and Weak Cross‐Sectional Dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 249-280, January.
    5. Claudia Angelini & Daniela De Canditiis & Anna Plaksienko, 2021. "Jewel : A Novel Method for Joint Estimation of Gaussian Graphical Models," Mathematics, MDPI, vol. 9(17), pages 1-24, August.
    6. Matteo Barigozzi & Marc Hallin, 2017. "A network analysis of the volatility of high dimensional financial series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 581-605, April.
    7. Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    8. Sacha Jennifer van Albada & Moritz Helias & Markus Diesmann, 2015. "Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-37, September.
    9. Brownlees, Christian & Mesters, Geert, 2021. "Detecting granular time series in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 544-561.
    10. Gabriel Koch Ocker & Ashok Litwin-Kumar & Brent Doiron, 2015. "Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-40, August.
    11. Matteo Barigozzi & Christian Brownlees, 2019. "NETS: Network estimation for time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 347-364, April.
    12. Mingyang Ren & Sanguo Zhang & Qingzhao Zhang & Shuangge Ma, 2022. "Gaussian graphical model‐based heterogeneity analysis via penalized fusion," Biometrics, The International Biometric Society, vol. 78(2), pages 524-535, June.
    13. Chi, Eric C. & Lange, Kenneth, 2014. "Stable estimation of a covariance matrix guided by nuclear norm penalties," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 117-128.
    14. Huihang Liu & Xinyu Zhang, 2023. "Frequentist model averaging for undirected Gaussian graphical models," Biometrics, The International Biometric Society, vol. 79(3), pages 2050-2062, September.
    15. Tan, Kean Ming & Witten, Daniela & Shojaie, Ali, 2015. "The cluster graphical lasso for improved estimation of Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 23-36.
    16. Jonathan Schiefer & Alexander Niederbühl & Volker Pernice & Carolin Lennartz & Jürgen Hennig & Pierre LeVan & Stefan Rotter, 2018. "From correlation to causation: Estimating effective connectivity from zero-lag covariances of brain signals," PLOS Computational Biology, Public Library of Science, vol. 14(3), pages 1-18, March.
    17. Jie Cheng & Elizaveta Levina & Pei Wang & Ji Zhu, 2014. "A sparse ising model with covariates," Biometrics, The International Biometric Society, vol. 70(4), pages 943-953, December.
    18. Hirose, Kei & Fujisawa, Hironori & Sese, Jun, 2017. "Robust sparse Gaussian graphical modeling," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 172-190.
    19. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    20. Fan, Xinyan & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2021. "Conditional score matching for high-dimensional partial graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1005325. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.