Skip to main content
SpringerLink
Log in

Statistical Analysis of fMRI Data

  • Protocol
  • First Online:
fMRI Techniques and Protocols

Part of the book series: Neuromethods ((NM,volume 119))

Abstract

fMRI is a powerful tool used in the study of brain function. It can noninvasively detect signal changes in areas of the brain where neuronal activity is varying. This chapter is a comprehensive description of the various steps in the statistical analysis of fMRI data. This will cover topics such as the general linear model (including orthogonality, hemodynamic variability, noise modeling, and the use of contrasts), multisubject statistics, and statistical thresholding (including random field theory and permutation methods).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For the remainder of this chapter, reference to “stimulation” should be taken to include also the carrying out of physical or cognitive activity.

  2. 2.

    The particular HRF in Fig. 5 has parameter values μ 1 = 6 s, σ 1 = 2.45 s, μ 2 = 16 s, σ 2 = 4 s, and ρ = 6.

  3. 3.

    Note that this common usage is slightly different from the definition sometimes used in the statistics literature, where effect size means β divided by the noise level.

References

  1. Friston K, Worsley K, Frackowiak R, Mazziotta J, Evans A (1994) Assessing the significance of focal activations using their spatial extent. Hum Brain Mapp 1:214–220

    Google Scholar 

  2. Hykin J, Bowtell R, Glover P, Coxon R, Blumhardt L, Mansfield P (1995) Investigation of the linearity of functional activation signal changes in the brain using echo planar imaging (EPI) at 3.0 T. In: Proc of the SMR and ESMRB Joint Meeting. p 795

    Google Scholar 

  3. Cohen M (1997) Parametric analysis of fMRI data using linear systems methods. NeuroImage 6:93–103

    Article  CAS  PubMed  Google Scholar 

  4. Dale A, Buckner R (1997) Selective averaging of rapidly presented individual trials using fMRI. Hum Brain Mapp 5:329–340

    Article  CAS  PubMed  Google Scholar 

  5. Burock MA, Buckner RL, Woldorff MG, Rosen BR, Dale AM (1998) Randomized event-related experimental designs allow for extremely rapid presentation rates using functional MRI. NeuroReport 9:3735–3739

    Article  CAS  PubMed  Google Scholar 

  6. Bullmore E, Brammer M, Williams S et al (1996) Statistical methods of estimation and inference for functional MR image analysis. Magn Reson Med 35:261–277

    Article  CAS  PubMed  Google Scholar 

  7. Friston K, Josephs O, Zarahn E, Holmes A, Rouquette S, Poline J-B (2000) To smooth or not to smooth? NeuroImage 12:196–208

    Article  CAS  PubMed  Google Scholar 

  8. Woolrich M, Ripley B, Brady J, Smith S (2001) Temporal autocorrelation in univariate linear modelling of FMRI data. NeuroImage 14:1370–1386

    Article  CAS  PubMed  Google Scholar 

  9. Locascio J, Jennings P, Moore C, Corkin S (1997) Time series analysis in the time domain and resampling methods for studies of functional magnetic resonance brain imaging. Hum Brain Mapp 5:168–193

    Article  CAS  PubMed  Google Scholar 

  10. Purdon P, Weisskoff R (1998) Effect of temporal autocorrelation due to physiological noise and stimulus paradigm on voxel-level false-positive rates in fMRI. Hum Brain Mapp 6:239–249

    Article  CAS  PubMed  Google Scholar 

  11. Marchini J, Ripley B (2000) A new statistical approach to detecting significant activation in functional MRI. NeuroImage 12:366–380

    Article  CAS  PubMed  Google Scholar 

  12. Worsley K, Liao C, Aston J et al (2002) A general statistical analysis for fMRI data. NeuroImage 15:1–15

    Article  CAS  PubMed  Google Scholar 

  13. Gautama T, Van Hulle MM (2004) Optimal spatial regularisation of autocorrelation estimates in fMRI analysis. Neuroimage 23:1203–1216

    Article  PubMed  Google Scholar 

  14. Penny W, Kiebel S, Friston K (2003) Variational Bayesian inference for fMRI time series. NeuroImage 19:1477–1491

    Article  PubMed  Google Scholar 

  15. Woolrich M, Behrens T, Smith S (2004) Constrained linear basis sets for HRF modelling using Variational Bayes. NeuroImage 21:1748–1761

    Article  PubMed  Google Scholar 

  16. Smith S, Jenkinson M, Beckmann C, Miller K, Woolrich M (2007) Meaningful design and contrast estimability in fMRI. NeuroImage 34:127–136

    Article  PubMed  Google Scholar 

  17. Dale A, Greve D, Burock M (1999) Optimal stimulus sequences for event-related fMRI. NeuroImage 9:S33

    Article  Google Scholar 

  18. Wager T, Nichols T (2003) Optimization of experimental design in fMRI: a general framework using a genetic algorithm. Neuroimage 18:293–309

    Article  PubMed  Google Scholar 

  19. Josephs O, Turner R, Friston K (1997) Event-related fMRI. Hum Brain Mapp 5:1–7

    Article  Google Scholar 

  20. Lange N, Zeger S (1997) Non-linear Fourier time series analysis for human brain mapping by functional magnetic resonance imaging. Appl Stat 46:1–29

    Google Scholar 

  21. Genovese C (2000) A Bayesian time-course model for functional magnetic resonance imaging data (with discussion). J Am Stat Assoc 95:691–703

    Article  Google Scholar 

  22. Friston KJ (2002) Bayesian estimation of dynamical systems: an application to fMRI. NeuroImage 16:513–530

    Article  CAS  PubMed  Google Scholar 

  23. Marrelec G, Benali H, Ciuciu P, Pélégrini-Issac M, Poline J-B (2003) Robust Bayesian estimation of the hemodynamic response function in event-related BOLD MRI using basic physiological information. Hum Brain Mapp 19:1–17

    Article  PubMed  Google Scholar 

  24. Woolrich M, Jenkinson M, Brady J, Smith S (2004) Fully Bayesian spatio-temporal modelling of FMRI data. IEEE Trans Med Imaging 23:213–231

    Article  PubMed  Google Scholar 

  25. Buxton R, Uludag K, Dubowitz D, Liu T (2004) Modeling the hemodynamic response to brain activation. NeuroImage 23(S1):220–233

    Article  Google Scholar 

  26. Boynton G, Engel S, Glover G, Heeger D (1996) Linear systems analysis of functional magnetic resonance imaging in human V1. J Neurosci 16:4207–4221

    CAS  PubMed  Google Scholar 

  27. Glover G (1999) Deconvolution of impulse response in event-related BOLD fMRI. NeuroImage 9:416–429

    Article  CAS  PubMed  Google Scholar 

  28. Friston K, Josephs O, Rees G, Turner R (1998) Nonlinear event-related responses in fMRI. Magn Reson Med 39:41–52

    Article  CAS  PubMed  Google Scholar 

  29. Beckmann C, Smith S (2004) Probabilistic independent component analysis for functional magnetic resonance imaging. IEEE Trans Med Imaging 23:137–152

    Article  PubMed  Google Scholar 

  30. Glover G, Li T, Ress D (2000) Image-based method for retrospective correction of physiological motion effects in fMRI: Retroicor. Magn Reson Med 44:162–167

    Article  CAS  PubMed  Google Scholar 

  31. Holmes A, Friston K (1998) Generalisability, random effects & population inference. Fourth Int Conf on Functional Mapping of the Human Brain. NeuroImage 7:S754

    Google Scholar 

  32. Talairach J, Tournoux P (1988) Co-planar stereotaxic atlas of the human brain. Thieme, New York

    Google Scholar 

  33. Collins D, Neelin P, Peters T, Evans A (1994) Automatic 3D intersubject registration of MR volumetric data in standardized Talairach space. J Comput Assist Tomo 18:192–205

    Article  CAS  Google Scholar 

  34. Friston KJ, Penny W, Phillips C, Kiebel S, Hinton G, Ashburner J (2002) Classical and Bayesian inference in neuroimaging: theory. NeuroImage 16:465–483

    Article  CAS  PubMed  Google Scholar 

  35. Beckmann C, Jenkinson M, Smith S (2003) General multi-level linear modelling for group analysis in FMRI. NeuroImage 20:1052–1063

    Article  PubMed  Google Scholar 

  36. Woolrich M, Behrens T, Beckmann C, Jenkinson M, Smith S (2004) Multi-level linear modelling for FMRI group analysis using Bayesian inference. NeuroImage 21:1732–1747

    Article  PubMed  Google Scholar 

  37. Kherif F, Poline J-B, Meriaux S, Benali H, Flandin G, Brett M (2003) Group analysis in functional neuroimaging: selecting subjects using similarity measures. Neuroimage 20:2197–2208

    Article  PubMed  Google Scholar 

  38. Luo W-L, Nichols TE (2003) Diagnosis and exploration of massively univariate neuroimaging models. Neuroimage 19:1014–1032

    Article  PubMed  Google Scholar 

  39. Seghier M, Friston K, Price C (2007) Detecting subject-specific activations using fuzzy clustering. Neuroimage 36:594–605

    Article  PubMed  PubMed Central  Google Scholar 

  40. Wager T, Keller M, Lacey S, Jonides J (2005) Increased sensitivity in neuroimaging analyses using robust regression. NeuroImage 26:99–113

    Article  PubMed  Google Scholar 

  41. Woolrich M (2008) Robust group analysis using outlier inference. NeuroImage 41:286–301

    Article  PubMed  Google Scholar 

  42. Meriaux S, Roche A, Dehaene-Lambertz G, Thirion B, Poline J (2006) Combined permutation test and mixed-effect model for group average analysis in fMRI. Hum Brain Mapp 27:402–410

    Article  PubMed  Google Scholar 

  43. Roche A, Meriaux S, Keller M, Thirion B (2007) Mixed-effect statistics for group analysis in fMRI: a nonpara-metric maximum likelihood approach. Neuroimage 38:501–510

    Article  PubMed  Google Scholar 

  44. Thirion B, Pinel P, Mriaux S, Roche A, Dehaene S, Poline J (2007) Analysis of a large fMRI cohort: statistical and methodological issues for group analyses. Neuroimage 35:105–120

    Article  PubMed  Google Scholar 

  45. Hartvig NV, Jensen JL (2000) Spatial mixture modeling of fMRI data. Hum Brain Mapp 11:233–248

    Article  CAS  PubMed  Google Scholar 

  46. Hayasaka S, Nichols TE (2003) Validating cluster size inference: random field and permutation methods. NeuroImage 20:2343–2356

    Article  PubMed  Google Scholar 

  47. Friston KJ, Holmes A, Poline J-B, Price CJ, Frith CD (1996) Detecting activations in PET and fMRI: levels of inference and power. NeuroImage 4:223–235

    Article  CAS  PubMed  Google Scholar 

  48. Nichols TE, Hayasaka S (2003) Controlling the familywise error rate in functional neuroimaging: a comparative review. Stat Methods Med Res 12:419–446

    Article  PubMed  Google Scholar 

  49. Cao J, Worsley KJ (2001) Applications of random fields in human brain mapping. In: Moore M, (ed) Spatial statistics: methodological aspects and applications, vol 159, Springer lecture notes in statistics. Springer. pp 169–182

    Google Scholar 

  50. Worsley KJ, Evans AC, Marrett S, Neelin P (1992) Three-dimensional statistical analysis for cbf activation studies in human brain. J Cerebr Blood F Met 12:900–918

    Article  CAS  Google Scholar 

  51. Worsley KJ, Marrett S, Neelin P, Vandal AC, Friston KJ, Evans AC (1996) A unified statistical approach for determining significant signals in images of cerebral activation. Hum Brain Mapp 4:58–73

    Article  CAS  PubMed  Google Scholar 

  52. Hayasaka S, Luan Phan K, Liberzon I, Worsley KJ, Nichols TE (2004) Nonstationary cluster-size inference with random field and permutation methods. NeuroImage 22:676–687

    Article  PubMed  Google Scholar 

  53. Nichols T, Holmes A (2001) Nonparametric permutation tests for functional neuroimaging: a primer with examples. Hum Brain Mapp 15:1–25

    Article  Google Scholar 

  54. Bullmore E, Long C, Suckling J et al (2001) Colored noise and computational inference in neurophysiological (fMRI) time series analysis: resampling methods in time and wavelet domains. Hum Brain Mapp 12:61–78

    Article  CAS  PubMed  Google Scholar 

  55. Benjamini Y, Hochberg Y (1995) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B Methodol 57:289–300

    Google Scholar 

  56. Genovese C, Lazar N, Nichols T (2002) Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage 15:870–878

    Article  PubMed  Google Scholar 

  57. Benjamini Y, Yekutieli D (2001) The control of the false discovery rate in multiple testing under dependency. Ann Stat 29:1165–1188

    Article  Google Scholar 

  58. Everitt B, Bullmore E (1999) Mixture model mapping of brain activation in functional magnetic resonance images. Hum Brain Mapp 7:1–14

    Article  CAS  PubMed  Google Scholar 

  59. Hartvig N (2000) A stochastic geometry model for fMRI data. Technical Report 410. Department of Theoretical Statistics, University of Aarhus

    Google Scholar 

  60. Woolrich M, Behrens T (2006) Variational Bayes inference of spatial mixture models for segmentation. IEEE Trans Med Imaging 25:1380–1391

    Article  PubMed  Google Scholar 

  61. Bartsch A, Homola G, Biller A, Solymosi L, Bendszus M (2006) Diagnostic functional MRI: illustrated clinical applications and decision-making. J Magn Reson Imaging 23:921–932

    Article  PubMed  Google Scholar 

  62. Van De Ville D, Blu T, Unser M (2006) Surfing the brain – an overview of wavelet-based techniques for fMRI data analysis. IEEE Eng Med Biol 25:65–78

    Article  Google Scholar 

  63. Smith SM, Nichols TE (2008) Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference. NeuroImage. doi:10.1016/j.neuroimage.2008.03.061, In press; Epub ahead of print April 11, 2008

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Oxford University Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB), John Radcliffe Hospital, Oxford, OX3 9DU, UK

    Mark W. Woolrich, Christian F. Beckmann, Thomas E. Nichols & Stephen M. Smith

Authors
  1. Mark W. Woolrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian F. Beckmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas E. Nichols
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Stephen M. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark W. Woolrich .

Editor information

Editors and Affiliations

  1. Neuroimaging Research Unit, INSPE, Division of Neuroscience, San Raffaele Scientific Institute and Vita-Salute San Raffaele University, Milan, Italy

    Massimo Filippi

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this protocol

Cite this protocol

Woolrich, M.W., Beckmann, C.F., Nichols, T.E., Smith, S.M. (2016). Statistical Analysis of fMRI Data. In: Filippi, M. (eds) fMRI Techniques and Protocols. Neuromethods, vol 119. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-5611-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-5611-1_7

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-5609-8

  • Online ISBN: 978-1-4939-5611-1

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation