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Small-world indices via network efficiency for brain networks from diffusion MRI

  • Lan Lin
  • Zhenrong Fu
  • Cong Jin
  • Miao Tian
  • Shuicai Wu
Research Article
  • 34 Downloads

Abstract

The small-world architecture has gained considerable attention in anatomical brain connectivity studies. However, how to adequately quantify small-worldness in diffusion networks has remained a problem. We addressed the limits of small-world measures and defined new metric indices: the small-world efficiency (SWE) and the small-world angle (SWA), both based on the tradeoff between high global and local efficiency. To confirm the validity of the new indices, we examined the behavior of SWE and SWA of networks based on the Watts–Strogatz model as well as the diffusion tensor imaging (DTI) data from 75 healthy old subjects (aged 50–70). We found that SWE could classify the subjects into different age groups, and was correlated with individual performance on the WAIS-IV test. Moreover, to evaluate the sensitivity of the proposed measures to network, two network attack strategies were applied. Our results indicate that the new indices outperform their predecessors in the analysis of DTI data.

Keywords

Small world Connectome DTI Brain network 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful suggestions and appreciate professor Zalesky from the University of Melbourne and Melbourne Health for sharing the uniform parcellation algorithm. This work was supported by Grants from the Scientific Research General Project of Beijing Municipal Education Committee (KM201810005033), the Natural Science Foundation of Beijing (7143171) and the National Key Technology Support Program of China (2015BAI02B03).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Akil H, Martone ME, Van Essen DC (2011) Challenges and opportunities in mining neuroscience data. Science 331(6018):708CrossRefPubMedPubMedCentralGoogle Scholar
  2. Andrews-Hanna JR, Snyder AZ, Vincent JL, Lustig C, Head D, Raichle ME, Buckner RL (2007) Disruption of large-scale brain systems in advanced aging. Neuron 56(5):924–935CrossRefPubMedPubMedCentralGoogle Scholar
  3. Ashburner J (2009) Computational anatomy with the SPM software. Magn Reson Imaging 27(8):1163–1174CrossRefPubMedGoogle Scholar
  4. Ashburner J, Friston KJ (2005) Unified segmentation. Neuroimage 26(3):839–851CrossRefPubMedGoogle Scholar
  5. Bai F, Shu N, Yuan Y, Shi Y, Yu H, Wu D et al (2012) Topologically convergent and divergent structural connectivity patterns between patients with remitted geriatric depression and amnestic mild cognitive impairment. J Neurosci 32(12):4307–4318CrossRefPubMedGoogle Scholar
  6. Bartzokis G, Sultzer D, Lu PH, Nuechterlein KH, Mintz J, Cummings JL (2004) Heterogeneous age-related breakdown of white matter structural integrity: implications for cortical “disconnection” in aging and Alzheimer’s disease. Neurobiol Aging 25(7):843–851CrossRefPubMedGoogle Scholar
  7. Bassett DS, Bullmore ED (2006) Small-world brain networks. Neurosci 12(6):512–523Google Scholar
  8. Bellec P, Benhajali Y, Carbonell F, Dansereau C, Albouy G, Pelland M, Orban P (2015) Impact of the resolution of brain parcels on connectome-wide association studies in fMRI. Neuroimage 123:212–228CrossRefPubMedGoogle Scholar
  9. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: Structure and dynamics. Phys Rep 424(4):175–308CrossRefGoogle Scholar
  10. Bortoletto M, Veniero D, Thut G, Miniussi C (2015) The contribution of TMS–EEG coregistration in the exploration of the human cortical connectome. Neurosci Biobehav Rev 49:114–124CrossRefPubMedGoogle Scholar
  11. Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10(3):186CrossRefPubMedGoogle Scholar
  12. Chen VCH, Shen CY, Liang SHY, Li ZH, Tyan YS, Liao YT et al (2016) Assessment of abnormal brain structures and networks in major depressive disorder using morphometric and connectome analyses. J Affect Disord 205:103–111CrossRefPubMedGoogle Scholar
  13. Chhabra A, Thakkar RS, Andreisek G, Chalian M, Belzberg AJ, Blakeley J et al (2013) Anatomic MR imaging and functional diffusion tensor imaging of peripheral nerve tumors and tumor like conditions. Am J Neuroradiol 34(4):802–807CrossRefPubMedGoogle Scholar
  14. Cui Z, Zhong S, Xu P, He Y, Gong G (2013) Panda: a pipeline toolbox for analyzing brain diffusion images. Front Hum Neurosci 7(42):42PubMedPubMedCentralGoogle Scholar
  15. de Reus MA, Van den Heuvel MP (2013) The parcellation-based connectome: limitations and extensions. Neuroimage 80:397–404CrossRefPubMedGoogle Scholar
  16. Delbeuck X, Van der Linden M, Collette F (2003) Alzheimer’disease as a disconnection syndrome? Neuropsychol Rev 13(2):79–92CrossRefPubMedGoogle Scholar
  17. Gigandet X, Griffa A, Kober T, Daducci A, Gilbert G, Connelly A et al (2013) A connectome-based comparison of diffusion MRI schemes. PloS one 8(9):e75061CrossRefPubMedPubMedCentralGoogle Scholar
  18. Hagmann P, Kurant M, Gigandet X, Thiran P, Wedeen VJ, Meuli R, Thiran JP (2007) Mapping human whole-brain structural networks with diffusion MRI. PloS one 2(7):e597CrossRefPubMedPubMedCentralGoogle Scholar
  19. Hagmann P, Sporns O, Madan N, Cammoun L, Pienaar R, Wedeen VJ,et al (2010) White matter maturation reshapes structural connectivity in the late developing human brain. Proc Natl Acad Sci 107(44):19067–19072CrossRefPubMedGoogle Scholar
  20. Humphries MD, Gurney K, Prescott TJ (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc R Soc Lond B Biol Sci 273(1585):503–511CrossRefGoogle Scholar
  21. Jenkinson M, Beckmann CF, Behrens TE, Woolrich MW, Smith SM (2012) FSL. Neuroimage 62(2):782–790CrossRefPubMedGoogle Scholar
  22. Johansenberg H, Rushworth MF (2009) Using diffusion imaging to study human connectional anatomy. Annu Rev Neurosci 32(1):75CrossRefGoogle Scholar
  23. Jones DK (2010) Challenges and limitations of quantifying brain connectivity in vivo with diffusion MRI. Imaging Med 2(3):341CrossRefGoogle Scholar
  24. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87(19):198701CrossRefPubMedGoogle Scholar
  25. Lin L, Jin C, Fu Z, Zhang B, Bin G, Wu S (2016) Predicting healthy older adult’s brain age based on structural connectivity networks using artificial neural networks. Comput Methods Progr Biomed 125:8–17CrossRefGoogle Scholar
  26. Liu Y, Duan Y, He Y, Wang J, Xia M, Yu C et al (2012) Altered topological organization of white matter structural networks in patients with neuromyelitis optica. PloS one 7(11):e48846CrossRefPubMedPubMedCentralGoogle Scholar
  27. Lo CY, Wang PN, Chou KH, Wang J, He Y, Lin CP (2010) Diffusion tensor tractography reveals abnormal topological organization in structural cortical networks in Alzheimer’s disease. J Neurosci 30(50):16876–16885CrossRefPubMedGoogle Scholar
  28. Long Z, Duan X, Wang Y, Liu F, Zeng L, Zhao JP, Chen H (2015) Disrupted structural connectivity network in treatment-naive depression. Prog Neuropsychopharmacol Biol Psychiatry 56:18–26CrossRefPubMedGoogle Scholar
  29. Mori S, van Zijl P (2002) Fiber tracking: principles and strategies—a technical review. NMR Biomed 15(7–8):468–480CrossRefPubMedGoogle Scholar
  30. O’Sullivan M, Jones DK, Summers PE, Morris RG, Williams SCR, Markus HS (2001) Evidence for cortical “disconnection” as a mechanism of age-related cognitive decline. Neurology 57(4):632–638CrossRefPubMedGoogle Scholar
  31. Odish OF, Caeyenberghs K, Hosseini H, Van Den Bogaard SJ, Roos RA, Leemans A (2015) Dynamics of the connectome in Huntington’s disease: a longitudinal diffusion MRI study. NeuroImage Clinl 9:32–43CrossRefGoogle Scholar
  32. Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3):1059–1069CrossRefPubMedGoogle Scholar
  33. Shu N, Liu Y, Li J, Li Y, Yu C, Jiang T (2009) Altered anatomical network in early blindness revealed by diffusion tensor tractography. PloS one, 4(9):e7228CrossRefPubMedPubMedCentralGoogle Scholar
  34. Simard D, Nadeau L, Kröger H (2004) Fastest learning in small-world neural networks. Phys Lett A 336(1):8–15CrossRefGoogle Scholar
  35. Sporns O (2012) From simple graphs to the connectome: networks in neuroimaging. Neuroimage 62(2):881–886CrossRefPubMedGoogle Scholar
  36. Sporns O, Tononi G, Kötter R (2005) The human connectome: a structural description of the human brain. PLoS Comput Biol 1(4):e42CrossRefPubMedPubMedCentralGoogle Scholar
  37. Strogatz SH (2001) Exploring complex networks. Nature 410(6825):268CrossRefPubMedGoogle Scholar
  38. Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ (2011) The ubiquity of small-world networks. Brain Connect 1(5):367CrossRefPubMedPubMedCentralGoogle Scholar
  39. Teng X, Yong H (2012) Mapping the Alzheimer’s brain with connectomics. Front Psychiatry 2:77Google Scholar
  40. Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N et al (2002) Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage 15(1):273–289CrossRefPubMedGoogle Scholar
  41. Vaessen MJ, Hofman PAM, Tijssen HN, Aldenkamp AP, Jansen JF, Backes WH (2010) The effect and reproducibility of different clinical DTI gradient sets on small world brain connectivity measures. Neuroimage 51(3):1106–1116CrossRefPubMedGoogle Scholar
  42. van den Heuvel MP, Mandl RC, Stam CJ, Kahn RS, Pol HEH (2010) Aberrant frontal and temporal complex network structure in schizophrenia: a graph theoretical analysis. J Neurosci 30(47):15915–15926CrossRefPubMedGoogle Scholar
  43. Wang B, Fan Y, Lu M, Li S, Song Z, Peng X et al (2013) Brain anatomical networks in world class gymnasts: a DTI tractography study. NeuroImage 65:476–487CrossRefPubMedGoogle Scholar
  44. Wang T, Shi F, Jin Y, Yap PT, Wee CY, Zhang J et al (2016) Multilevel deficiency of white matter connectivity networks in alzheimer’s disease: a diffusion mri study with dti and hardi models. Neural Plast 2016(2):2947136PubMedPubMedCentralGoogle Scholar
  45. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393(6684):440CrossRefPubMedGoogle Scholar
  46. Weiss LG, Saklofske DH, Coalson DL, Raiford SE (2010) WAIS-IV clinical use and interpretation. Academic Press, San DiegoGoogle Scholar
  47. Zalesky A, Fornito A, Harding IH, Cocchi L, Yücel M, Pantelis C, Bullmore ET (2010) Whole-brain anatomical networks: does the choice of nodes matter? Neuroimage 50(3):970–983CrossRefPubMedGoogle Scholar
  48. Zhao T, Cao M, Niu H, Zuo XN, Evans A, He Y et al (2015) Age-related changes in the topological organization of the white matter structural connectome across the human lifespan. Hum Brain Mapp 36(10):3777–3792CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lan Lin
    • 1
  • Zhenrong Fu
    • 1
  • Cong Jin
    • 2
  • Miao Tian
    • 1
  • Shuicai Wu
    • 1
  1. 1.Biomedical Research Center, College of Life Science and BioengineeringBeijing University of TechnologyBeijingChina
  2. 2.Medical Engineering Department, Beijing Friendship HospitalCapital Medical UniversityBeijingChina

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