eprintid: 3553 rev_number: 8 eprint_status: archive userid: 69 dir: disk0/00/00/35/53 datestamp: 2016-10-04 11:13:27 lastmod: 2016-10-04 11:13:27 status_changed: 2016-10-04 11:13:27 type: article metadata_visibility: show creators_name: Bardella, Giampiero creators_name: Bifone, Angelo creators_name: Gabrielli, Andrea creators_name: Gozzi, Alessandro creators_name: Squartini, Tiziano creators_id: creators_id: creators_id: creators_id: creators_id: tiziano.squartini@imtlucca.it title: Hierarchical organization of functional connectivity in the mouse brain: a complex network approach ispublished: pub subjects: QC divisions: CSA full_text_status: public keywords: Applied physics, Complex networks abstract: This paper represents a contribution to the study of the brain functional connectivity from the perspective of complex networks theory. More specifically, we apply graph theoretical analyses to provide evidence of the modular structure of the mouse brain and to shed light on its hierarchical organization. We propose a novel percolation analysis and we apply our approach to the analysis of a resting-state functional MRI data set from 41 mice. This approach reveals a robust hierarchical structure of modules persistent across different subjects. Importantly, we test this approach against a statistical benchmark (or null model) which constrains only the distributions of empirical correlations. Our results unambiguously show that the hierarchical character of the mouse brain modular structure is not trivially encoded into this lower-order constraint. Finally, we investigate the modular structure of the mouse brain by computing the Minimal Spanning Forest, a technique that identifies subnetworks characterized by the strongest internal correlations. This approach represents a faster alternative to other community detection methods and provides a means to rank modules on the basis of the strength of their internal edges. date: 2016 date_type: published publication: Scientific Reports volume: 6 publisher: Nature Publishing Group pagerange: 32060 id_number: 10.1038/srep32060 refereed: TRUE issn: 2045-2322 official_url: http://doi.org/10.1038/srep32060 referencetext: M. P. van den Heuvel & H. E. Hulshoff Pol. Exploring the brain network: a review on resting-state fMRI functional connectivity. European Neuropsychopharmacology 20, 519–534 (2010). Z. Yao, Y. Xie, P. Moore & J. Zheng. A review of structural and functional brain networks: small world and atlas. Brain Informatics 2(9), 45–52, 10.1007/s40708-015-0009-z (2015) (Date of access: 26/04/2016). E. Bullmore & O. Sporns. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience 10, 186–198 (2010) (Date of access: 26/04/2016). O. Sporns & R. Betzel. Modular brain networks. Annual Review of Psychology 67(19), 1–28 (2016). C. Nicolini & A. Bifone. Modular structure of brain networks: breaking the resolution limit by surprise. Scientific Reports 6(19250), 10.1038/srep19250 (2016) (Date of access: 26/04/2016). P. Moretti & M. Munoz. Griffiths phases and the stretching of criticality in brain networks. Nature Communications 4(2521) (2013) (Date of access: 26/04/2016). E. Agliari et al. Retrieval Capabilities of Hierarchical Networks: From Dyson to Hopfield. Physical Review Letters 114, 028103 (2015). E. Agliari et al. Hierarchical neural networks perform both serial and parallel processing, Neural Networks 66, 22–35 (2015). E. Agliari et al. Topological properties of hierarchical networks. Physical Review E 91, 062807 (2015). C. Li, H. Wang, W. de Haan, C. J. Stam & P. Van Mieghem. The correlation of metrics in complex networks with applications in functional brain networks. Journal of Statistical Mechanics: Theory and Experiment P11018, 10.1088/1742-5468/2011/11/P11018 (2011) (Date of access: 26/04/2016). A. Liska, A. Galbusera, A. J. Schwarz & A. Gozzi. Functional connectivity hubs of mouse brain. NeuroImage 115, 281–291, 10.1016/j.neuroimage.2015.04.033 (2015). B. Biswal, F. Z. Yetkin, V. M. Haughton & J. S. Hyde. Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magnetic Resonance in Medicine 34, 537–541 (1995). C. Rosazza & L. Minati. Resting-state brain networks: literature review and clinical applications. Neurological Science 32, 773–785, 10.1007/s10072-011-0636-y (2011). D. Zhang & M. E. Raichle. Disease and the brain’s dark energy. Nature Reviews Neurology 6, 15–28 (2010). M. D. Fox & M. Grecius. Clinical applications of resting state functional connectivity. Frontiers in Systems Neuroscience 4(19) (2010) (Date of access: 26/04/2016). D. Meunier, R. Lambiotte & E. Bullmore. Modular and hierarchically modular organization of brain networks. Frontiers in Neuroscience 4(200), 10.3389/fnins.2010.00200 (2010) (Date of access: 26/04/2016). S. Achard, R. Salvador, B. Whitcher, J. Suckling & E. Bullmore. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. The Journal of Neuroscience 26(1), 63–72 (2006) (Date of access: 26/04/2016). L. K. Gallos, H. A. Makse & M. Sigman. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Proceedings of the National Academy of Science 109(8), 2825–2830 (2012) (Date of access: 26/04/2016). A. Bifone, A. Gozzi & A. J. Schwarz. Functional connectivity in the rat brain: a complex network approach. Magnetic Resonance Imaging, 1200-9, 10.1016/j.mri.2010.07.001 (2010). H. Simon. The architecture of complexity. Proceedings of the American Philosophical Society 106(6), 467–482 (1962) (Date of access: 26/04/2016). N. Chatterjee & S. Sinha. Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans, in Progress in Brain Research 168(12), 145–153 (2008). J. G. White, E. Southgate, J. N. Thomson & S. Brenner. The structure of the nervous system of the nematode C. elegans. Philosophical Transactions of the Royal Society of London B 314, 1–340 (1986) (Date of access: 26/04/2016). R. Albert & A.-L. Barabasi. Statistical mechanics of complex networks. Reviews of Modern Physics 74, 47–97 (2002) (Date of access: 26/04/2016). S. M. Hadi Hosseini & S. R. Kesler. Influence of choice of null network on small-world parameters of structural correlation networks. PLoS ONE 8(6), e67354 (2013) (Date of access: 26/04/2016). B. Bollobas. Random Graphs. Cambridge University Press (2001). M. E. J. Newman. Finding community structure in networks using the eigenvectors of matrices. Physical Review E 69, 026113 (2004). M. E. J. Newman & M. Girvan. Finding and evaluating community structure in networks. Physical Review E 69, 026113 (2004). M. MacMahon & D. Garlaschelli. Community detection for correlation matrices. Physical Review X 5(021006) (2015) (Date of access: 26/04/2016). W. H. Thompson & P. Fransson. On stabilizing the variance of dynamic functional brain connectivity time series, arXiv:1603.00201 (Date of access: 01/07/2016). F. Murtagh & P. Contreras. Algorithms for hierarchical clustering: an overview. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 2(1), 86–97 (2012). D. Choi et al. Bed nucleus of the stria terminalis subregions differentially regulate hypothalamic-pituitary-adrenal axis activity: implications for the integration of limbic inputs. Journal of Neuroscience 27(8) (2007) (Date of access: 26/04/2016). S. D. Vann, J. P. Aggleton & E. A. Maguire. What does the retrosplenial cortex do? Nature Reviews 10, 792–803 (2009). L. R. Squire, C. E. Stark & R. E. Clark. The medial temporal lobe. Annual Review of Neuroscience 27, 279–306 (2004). M. G. Kitzbichler, M. L. Smith, S. R. Christensen & E. Bullmore. Broadband criticality of human brain network synchronization. PLoS Computational Biology 5, e1000314 (2009) (Date of access: 26/04/2016). P. A. Robinson, J. A. Henderson, E. Matar, P. Riley & R. T. Gray. Dynamical reconnection and stability constraints on cortical network architecture. Physical Review Letters 103 108104 (2009). E. Bullmore & O. Sporns. The economy of brain network organization. Nature Reviews. Neuroscience, 13(5), 336–49, 10.1038/nrn3214 (2012). A. F. Alexander-Bloch et al. Disrupted modularity and local connectivity of brain functional networks in childhood-onset schizophrenia. Frontiers in System Neuroscience 4(147), 10.3389/fnsys.2010.00147 (2010). F. Sforazzini, A. J. Schwarz, A. Galbusera, A. Bifone & A. Gozzi. Distributed BOLD and CBV-weighted resting-state networks in the mouse brain. NeuroImage 87, 403–415, 10.1016/j.neuroimage.2013.09.050 (2014). Analysis Group (FMRIB, Oxford). FMRIB Software Library v5.0 http://fsl.fmrib.ox.ac.uk/fsl/ (Date of access: 26/04/2016). M. Jenkinson, C. F. Beckmann, T. E. Behrens, M. W. Woolrich & S. M. Smith. FSL, NeuroImage 62, 782–790 (2012). AFNI/NIfTI Server (AFNI page: free software for analysis and display of fMRI data) https://afni.nimh.nih.gov/afni/ (Date of access: 26/04/2016). F. Sforazzini et al. Altered functional connectivity networks in acallosal and socially impaired BTBR mice. Brain Structure and Function 221(2), 941–954 (2014). N. J. Higham. Computing the nearest correlation matrix - a problem from finance. IMA Journal of Numerical Analysis 22, 329–343 (2002) (Date of access: 26/04/2016). projects: EU project FET-Open FOC (grant num. 255987) projects: FET Project SIMPOL (nr. 610704) projects: FET project DOLFINS (grant num. 640772) citation: Bardella, Giampiero and Bifone, Angelo and Gabrielli, Andrea and Gozzi, Alessandro and Squartini, Tiziano Hierarchical organization of functional connectivity in the mouse brain: a complex network approach. Scientific Reports, 6. p. 32060. ISSN 2045-2322 (2016) document_url: http://eprints.imtlucca.it/3553/1/srep32060.pdf