Brain Network Analysis: Separating Cost from Topology Using Cost-Integration

Abstract

A statistically principled way of conducting brain network analysis is still lacking. Comparison of different populations of brain networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using cost-integrated topological metrics. Our focus is on comparing populations of weighted undirected graphs that differ in mean association weight, using global efficiency. Our key result shows that integrating over cost is equivalent to controlling for any monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any unweighted topological measure, and for any choice of distribution over cost levels. Cost-integration is therefore helpful in disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of a topological metric is generally not a valid approach to this problem. Indeed, we prove that, under weak conditions, the use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the reporting of (i) differences in weighted costs and (ii) differences in cost-integrated topological measures with respect to different distributions over the cost domain. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. We also provide a Monte Carlo method for approximating cost-integrated topological measures. Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero, when multiplicities exist in the ranks of the weights, and when one expects subtle cost-dependent topological differences, which could be masked by cost-integration.

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References 42

1. 1.

   Watts DJ, Strogatz SH. Collective dynamics of ‘small-world’ networks. Nature. 1998;393:440-442.

   Not in our library10.1038/30918

2. 2.

   Barabasi AL, Albert R. Emergence of scaling in random networks. Science. 1999;286:509-512.

   Not in our library10.1126/science.286.5439.509

3. 3.

   Sporns O, Tononi G, Edelman G. Theoretical neuroanatomy: Relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex. 2000;10:127-141.

   Not in our library10.1093/cercor/10.2.127

4. 4.

   Sporns O, Chialvo DR, Kaiser M, Hilgetag CC. Organization, development and function of complex brain networks. Trends in Cognitive Sciences. 2004;8:418-425.

   Not in our library10.1016/j.tics.2004.07.008

5. 5.

   Eguiluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV. Scale-free brain functional networks. Phys Rev Lett. 2005;94:18102-18106.

   Not in our library10.1103/physrevlett.94.018102

6. 6.

   Achard S, Salvador R, Whitcher B, Suckling J, Bullmore E. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci. 2006;26:63-72.

   Not in our library10.1523/jneurosci.3874-05.2006

7. 7.
   Efficiency and Cost of Economical Brain Functional Networks · 2007

   No notice
8. 8.

   He Y, Chen ZJ, Evans AC. Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cereb Cortex. 2007;17:2407-2419.

   Not in our library10.1093/cercor/bhl149

9. 9.

   Bassett DS, Bullmore E, Verchinski BA, Mattay VS, Weinberger DR, et al. Hierarchical organization of human cortical networks in health and schizophrenia. J Neurosci. 2008;28:9239-9248.

   Not in our library10.1523/jneurosci.1929-08.2008

10. 10.

    van den Heuvel MP, Stam CJ, Kahn RS, Hulshoff Pol HE. Efficiency of functional brain networks and intellectual performance. J Neurosci. 2009;29:7619-7624.

    Not in our library10.1523/jneurosci.1443-09.2009

11. 11.

    De Vico Fallani F, Astolfi L, Cincotti F, Mattia D, Marciani M, et al. Cortical network dynamics during foot movements. Neuroinformatics. 2008;6:23-34.

    Not in our library10.1007/s12021-007-9006-6

12. 12.

    Cecchi G, Rao A, Centeno M, Baliki M, Apkarian A, et al. Identifying directed links in large scale functional networks: application to brain fMRI. BMC Cell Biology. 2007;8:1-10.

    Not in our library10.1186/1471-2121-8-s1-s5

13. 13.

    Astolfi L, Cincotti F, Mattia D, De Vico Fallani F, Salinari S, et al. Study of the time-varying cortical connectivity changes during the attempt of foot movements by spinal cord injured and healthy subjects. Conf Proc IEEE Eng Med Biol Soc. 2009;2208-11.

    Not in our library10.1109/iembs.2009.5334878

14. 14.

    Bassett DS, Meyer-Lindenberg A, Achard S, Duke T, Bullmore E. Adaptive reconfiguration of fractal small-world human brain functional networks. Proceedings of the National Academy of Sciences of the United States of America. 2006;103:19518-19523.

    Not in our library10.1073/pnas.0606005103

15. 15.

    Pachou E, Vourkas M, Simos P, Smit D, Stam C, et al. Working memory in schizophrenia: An EEG study using power spectrum and coherence analysis to estimate cortical activation and network behavior. Brain Topography. 2008;21:128-137.

    Not in our library10.1007/s10548-008-0062-5

16. 16.

    Salvador R, Martinez A, Pomarol-Clotet E, Gomar J, Vila F, et al. A simple view of the brain through a frequency-specific functional connectivity measure. Neuro Image. 2008;39:279-289.

    Not in our library10.1016/j.neuroimage.2007.08.018

17. 17.
    Mapping the Structural Core of Human Cerebral Cortex · 2008

    No notice
18. 18.

    Gong G, He Y, Concha L, Lebel C, Gross DW, et al. Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. Cereb Cortex. 2009;19:524-536.

    Not in our library10.1093/cercor/bhn102

19. 19.

    Latora V, Marchiori M. Efficient behavior of small-world networks. Phys Rev Lett. 2001;87:198701-198705.

    Not in our library10.1103/physrevlett.87.198701

20. 20.

    Rubinov M, Sporns O. Complex network measures of brain connectivity: Uses and interpretations. Neuroimage. 2010;52:1059-1069.

    Not in our library10.1016/j.neuroimage.2009.10.003

21. 21.
    Uncovering Intrinsic Modular Organization of Spontaneous Brain Activity in Humans · 2009

    No notice
22. 22.
    Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory · 2010

    No notice
23. 23.

    Kolaczyk E. Statistical Analysis of Network Data: Methods and Models. 2009.

    Not in our library

24. 24.

    Newman M. Networks: An Introduction. 2010.

    Not in our library

25. 25.

    Kaiser M. Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. New Journal of Physics. 2008;10:083042.

    Not in our library

26. 26.

    Latora V, Marchiori M. Economic small-world behavior in weighted networks. The European Physical Journal B - Condensed Matter and Complex Systems. 2003;32:249-263.

    Not in our library

27. 27.

    He Y, Dagher A, Chen Z, Charil A, Zijdenbos A, et al. Impaired small-world efficiency in structural cortical networks in multiple sclerosis associated with white matter lesion load. Brain. 2009;132:3366-3379.

    Not in our library10.1093/brain/awp089

28. 28.

    Billingsley P. Probability and Measure. Wiley Series in Probability and Mathematical Statistics. 1995.

    Not in our library

29. 29.

    Bernardo J, Smith A. Bayesian theory. 1994.

    Not in our library

30. 30.
    Development of Large-Scale Functional Brain Networks in Children · 2009

    No notice
31. 31.

    Ginestet CE, Simmons A. Statistical parametric network analysis of functional connectivity dynamics during a working memory task. Neuro Image. 2011;5(2):688-704.

    Not in our library10.1016/j.neuroimage.2010.11.030

32. 32.

    Simmons A, Moore E, Williams SC. Quality control for functional magnetic resonance imaging using automated data analysis and shewhart charting. Magn Reson Med. 1999;41:1274-1278.

    Not in our library10.1002/(sici)1522-2594(199906)41:6<1274::aid-mrm27>3.0.co;2-1

33. 33.

    Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, et al. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuro Image. 2002;15:273-289.

    Not in our library10.1006/nimg.2001.0978

34. 34.

    Benjamini Y, Hochberg Y. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B (Methodological). 1995;57:289-300.

    Not in our library

35. 35.

    Nichols T, Hayasaka S. Controlling the familywise error rate in functional neuroimaging: a comparative review. Statistical Methods in Medical Research. 2003;419-446.

    Not in our library10.1191/0962280203sm341ra

36. 36.

    Minka T. A family of algorithms for approximate Bayesian inference. 2001.

    Not in our library

37. 37.

    Laird N, Ware J. Random-effects models for longitudinal data. Biometrics. 1982;38:963-974.

    Not in our library

38. 38.

    Pinheiro J, Bates D. Mixed-effects mode in S and S-Plus. 2000.

    Not in our library

39. 39.

    Bollobas B, Riordan O, Bornholdt S, Schuster H. Mathematical results on scale-free random graphs. Handbook of Graphs and Networks: From the Genome to the Internet. 2003;1-32.

    Not in our library

40. 40.

    Gilks W, Richardson S, Spiegelhalter D. Introducing Markov chain Monte Carlo. 1996.

    Not in our library

41. 41.

    Robert C, Casella G. Monte Carlo Statistical Methods (2nd Ed.). 2004.

    Not in our library

42. 42.

    Lin R, Louis T, Paddock S, Ridgeway G. Loss function based ranking in two-stage hierarchical models. Bayesian analysis. 2006;1(4):915-946.

    Not in our library10.1214/06-ba130

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