nach oben

Journal of Computational Neuroscience

01.02.2011

Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity

verfasst von: Joseph T. Lizier, Jakob Heinzle, Annette Horstmann, John-Dylan Haynes, Mikhail Prokopenko

Erschienen in: Journal of Computational Neuroscience | Ausgabe 1/2011

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The human brain undertakes highly sophisticated information processing facilitated by the interaction between its sub-regions. We present a novel method for interregional connectivity analysis, using multivariate extensions to the mutual information and transfer entropy. The method allows us to identify the underlying directed information structure between brain regions, and how that structure changes according to behavioral conditions. This method is distinguished in using asymmetric, multivariate, information-theoretical analysis, which captures not only directional and non-linear relationships, but also collective interactions. Importantly, the method is able to estimate multivariate information measures with only relatively little data. We demonstrate the method to analyze functional magnetic resonance imaging time series to establish the directed information structure between brain regions involved in a visuo-motor tracking task. Importantly, this results in a tiered structure, with known movement planning regions driving visual and motor control regions. Also, we examine the changes in this structure as the difficulty of the tracking task is increased. We find that task difficulty modulates the coupling strength between regions of a cortical network involved in movement planning and between motor cortex and the cerebellum which is involved in the fine-tuning of motor control. It is likely these methods will find utility in identifying interregional structure (and experimentally induced changes in this structure) in other cognitive tasks and data modalities.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

The TE can be formed as T _k,l(Y →X), where l past states of Y are considered as the information source \(y_n^{(l)}=\{ y_n, y_{n-1}, \ldots ,y_{n-l+1} \}\).

Note that the TE is equivalent to the directed transinformation (DTI) measure under certain parameter settings for the DTI (specifically M = 1 and N = 0) as per Hinrichs et al. (2006). Also, note that the TE is equivalent to the specific formulation of the DTI used in Saito and Harashima (1981) if the TE parameter l (discussed in footnote 1) is set equal to k.

Note the TE could be computed in the style of Kraskov et al. (2004) and Kraskov (2004) but with a direct conditional MI calculation as per Frenzel and Pompe (2007).

For example, fMRI regions contain potentially hundreds of voxels.

The following explanation assumes that only one previous state y _n of the source is used in the computation of T _k(Y →X); i.e. the parameter l = 1 (see Schreiber 2000).

We use z-tests in our experiments in Section 4 because we are comparing to very low α values after making Bonferroni corrections (see Section 2.2.2), which would render direct counting quite sensitive to statistical fluctuations.

We analyze the MI with separate matrices.

Note that testing against a binomial distribution is a conservative choice here, because it is less likely to get 6 significant results (5 with positive mean and 1 with negative mean) than to get 4 positive ones only. However, when tested over the group we consider the threshold according to the latter, which is truly binomial.

See Chapter 5 of the PhD thesis which can be downloaded from the German National Library: http://d-nb.info/992989221.

We explain in Appendix B how the number of joint voxels v = 3 was selected to balance the ability to capture multivariate interactions with the limitations of the number of available observations. Also in that appendix, we explore the effect of altering v (including conducting univariate analysis with v = 1). Furthermore, the appendix explores the effect of altering the number of subset pairs S and surrogate measurements P.

As described in Appendix A.3, this simple test does not mean that the right SC → right Cerebellum link is a false positive; it simply does not add evidence against the false positive.

Our use of 140 time steps for each C and χ combination matches the length of fMRI time series analyzed in Section 4.

The minimum strengths required for detection here may seem large at first glance, however one must bear in mind the specific difficulties built into this data set: the non-linear coupling, the small number of samples, and relatively low influence of the Y on X (low χ/ϵ _x). Also our correction for a large number of comparisons is a factor here. This being said, correcting for multiple comparisons provides important protection against false positives so must be maintained when investigating all values of C here.

High memory in the source Z is required for the values z _n (considered by the interregional TE) to contain some information about the previous values z _n − 1 which had an indirect effect on x _n + 1 via y _n.

We expected that high memory in the destinations Y and X and in the common source Z would help preserve information in Y about the source Z which would be helpful to predicting X.

Note that the combination of undersampling and memory in our variables provides a smoothing-type effect on the data. As such, these results imply some level of robustness for the technique against temporal smoothing in the underlying data.

Similarly, only two interregional links were inferred at the group level by the interregional TE with univariate analysis (v = 1) and S = 3,000, P = 300.

Bassett, D. S., & Bullmore, E. T. (2009). Human brain networks in health and disease. Current Opinion in Neurology, 22(4), 340–347.CrossRefPubMed

Bettencourt, L. M. A., Stephens, G. J., Ham, M. I., & Gross, G. W. (2007). Functional structure of cortical neuronal networks grown in vitro. Physical Review E, 75(2), 021915.CrossRef

Bode, S., & Haynes, J. D. (2009). Decoding sequential stages of task preparation in the human brain. NeuroImage, 45(2), 606–613.CrossRefPubMed

Bressler, S. L., Tang, W., Sylvester, C. M., Shulman, G. L., & Corbetta, M. (2008). Top-down control of human visual cortex by frontal and parietal cortex in anticipatory visual spatial attention. Journal of Neuroscience, 28(40), 10056–10061.CrossRefPubMed

Büchel, C., & Friston, K. J. (1997). Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cerebral Cortex, 7(8), 768–778.CrossRefPubMed

Bullier, J. (2001). Integrated model of visual processing. Brain Research Reviews, 36, 96–107.CrossRefPubMed

Chai, B., Walther, D. B., Beck, D. M., & Fei-Fei, L. (2009). Exploring functional connectivity of the human brain using multivariate information analysis. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, & A. Culotta (Eds.), Advances in neural information processing systems (Vol. 22, pp. 270–278). NIPS Foundation.

Chávez, M., Martinerie, J., & Le Van Quyen, M. (2003). Statistical assessment of nonlinear causality: Application to epileptic EEG signals. Journal of Neuroscience Methods, 124(2), 113–128.CrossRefPubMed

Frenzel, S., & Pompe, B. (2007). Partial mutual information for coupling analysis of multivariate time series. Physical Review Letters, 99(20), 204101.CrossRefPubMed

Friston, K. (2002). Beyond phrenology: What can neuroimaging tell us about distributed circuitry? Annual Review of Neuroscience, 25, 221–250.CrossRefPubMed

Friston, K., Ashburner, J., Kiebel, S., Nichols, T., & Penny, W. (2006). Statistical parametric mapping: The analysis of functional brain images. Elsevier, London.

Friston, K. J. (1994). Functional and effective connectivity in neuroimaging: A synthesis. Human Brain Mapping, 2, 56–78.CrossRef

Friston, K. J., & Büchel, C. (2000). Attentional modulation of effective connectivity from V2 to V5/MT in humans. Proceedings of the National Academy of Sciences of the USA, 97(13), 7591–7596.CrossRefPubMed

Friston, K. J., Harrison, L., & Penny, W. (2003). Dynamic causal modelling. Neuroimage, 19(4), 1273–1302.CrossRefPubMed

Gong, P., & van Leeuwen, C. (2009). Distributed dynamical computation in neural circuits with propagating coherent activity patterns. PLoS Computational Biology, 5(12), e1000611.CrossRef

Grosse-Wentrup, M. (2008). Understanding brain connectivity patterns during motor imagery for brain-computer interfacing. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems (Vol. 21, pp. 561–568). Curran Associates, Inc.

Handwerker, D. A., Ollinger, J. M., & D’Esposito, M. (2004). Variation of bold hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage, 21(4), 1639–1651.CrossRefPubMed

Haynes, J. D., & Rees, G. (2006). Decoding mental states from brain activity in humans. Nature Reviews Neuroscience, 7(7), 523–534.CrossRefPubMed

Haynes, J. D., Tregellas, J., & Rees, G. (2005). Attentional integration between anatomically distinct stimulus representations in early visual cortex. Proceedings of the National Academy of Sciences of the USA, 102(41), 14925–14930.CrossRefPubMed

Hinrichs, H., Heinze, H. J., & Schoenfeld, M. A. (2006). Causal visual interactions as revealed by an information theoretic measure and fMRI. NeuroImage, 31(3), 1051–1060.CrossRefPubMed

Honey, C. J., Kotter, R., Breakspear, M., & Sporns, O. (2007). Network structure of cerebral cortex shapes functional connectivity on multiple time scales. Proceedings of the National Academy of Sciences, 104(24), 10240–10245.CrossRef

Horstmann, A. (2008). Sensorimotor integration in human eye-hand coordination: Neuronal correlates and characteristics of the system. Ph.D. thesis, Ruhr-Universität Bochum.

Johansen-Berg, H., Behrens, T. E., Robson, M. D., Drobnjak, I., Rushworth, M. F., Brady, J. M., et al. (2004). Changes in connectivity profiles define functionally distinct regions in human medial frontal cortex. Proceedings of the National Academy of Sciences of the USA, 101(36), 13335–13340.CrossRefPubMed

Kantz, H., & Schreiber, T. (1997). Nonlinear time series analysis. Cambridge: Cambridge University Press.

Kraskov, A. (2004). Synchronization and interdependence measures and their applications to the electroencephalogram of epilepsy patients and clustering of data. In Publication series of the John von Neumann Institute for computing (Vol. 24). Ph.D. thesis, John von Neumann Institute for Computing, Jülich, Germany.

Kraskov, A., Stögbauer, H., & Grassberger, P. (2004). Estimating mutual information. Physical Review E, 69(6), 066138.CrossRef

Liang, H., Ding, M., & Bressler, S. L. (2001). Temporal dynamics of information flow in the cerebral cortex. Neurocomputing, 38–40, 1429–1435.CrossRef

Lizier, J. T., & Prokopenko, M. (2010). Differentiating information transfer and causal effect. European Physical Journal B, 73(4), 605–615.CrossRef

Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (2008). Local information transfer as a spatiotemporal filter for complex systems. Physical Review E, 77(2), 026110.CrossRef

Logothetis, N., Pauls, J., Augath, M., Trinath, T., & Oeltermann, A. (2001). Neurophysiological investigation of the basis of the fMRI signal. Nature, 412, 150–157.CrossRefPubMed

Lunenburger, L., Kleiser, R., Stuphorn, V., Miller, L. E., & Hoffmann, K. P. (2001). A possible role of the superior colliculus in eye-hand coordination. Progress in Brain Research, 134, 109–125. 0079-6123 (Print) 0079-6123 (Linking) Journal Article Research Support, Non-U.S. Gov’t Review.

Lungarella, M., Pegors, T., Bulwinkle, D., & Sporns, O. (2005). Methods for quantifying the informational structure of sensory and motor data. Neuroinformatics, 3(3), 243–262.CrossRefPubMed

MacKay, D. J. (2003). Information theory, inference, and learning algorithms. Cambridge: Cambridge University Press.

Norman, K. A., Polyn, S. M., Detre, G. J., & Haxby, J. V. (2006). Beyond mind-reading: Multi-voxel pattern analysis of fMRI data. Trends in Cognitive Sciences, 10(9), 424–430.CrossRefPubMed

Penhune, V. B., & Doyon, J. (2005). Cerebellum and m1 interaction during early learning of timed motor sequences. Neuroimage, 26(3), 801–812.CrossRefPubMed

Ramsey, J., Hanson, S., Hanson, C., Halchenko, Y., Poldrack, R., & Glymour, C. (2010). Six problems for causal inference from fMRI. NeuroImage, 49(2), 1545–1558.CrossRefPubMed

Rubinov, M., Knock, S. A., Stam, C. J., Micheloyannis, S., Harris, A. W. F., Williams, L. M., et al. (2009). Small-world properties of nonlinear brain activity in schizophrenia. Human Brain Mapping, 30, 403–416.CrossRefPubMed

Saito, Y., & Harashima, H. (1981). Tracking of information within multichannel EEG record - causal analysis in EEG. In N. Yamaguchi & K. Fujisawa (Eds.), Recent advances in EEG and EMG data processing (pp. 133–146). Amsterdam: Elsevier/North Holland Biomedical Press.

Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85(2), 461–464.CrossRefPubMed

Soon, C. S., Brass, M., Heinze, H. J., & Haynes, J. D. (2008). Unconscious determinants of free decisions in the human brain. Nature Neuroscience, 11(5), 543–545.CrossRefPubMed

Tanaka, Y., Fujimura, N., Tsuji, T., Maruishi, M., Muranaka, H., & Kasai, T. (2009). Functional interactions between the cerebellum and the premotor cortex for error correction during the slow rate force production task: An fmri study. Experimental Brain Research, 193(1), 143–150.CrossRef

Tung, T. Q., Ryu, T., Lee, K. H., & Lee, D. (2007). Inferring gene regulatory networks from microarray time series data using transfer entropy. In P. Kokol, V. Podgorelec, D. Mičetič-Turk, M. Zorman, & M. Verlič (Eds.), Proceedings of the twentieth IEEE international symposium on computer-based medical systems (CBMS ’07), Maribor, Slovenia (pp. 383–388). Los Alamitos: IEEE.CrossRef

Verdes, P. F. (2005). Assessing causality from multivariate time series. Physical Review E, 72(2), 026222–026229.CrossRef

Titel: Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity
verfasst von: Joseph T. Lizier
Jakob Heinzle
Annette Horstmann
John-Dylan Haynes
Mikhail Prokopenko
Publikationsdatum: 01.02.2011
Verlag: Springer US
Erschienen in: Journal of Computational Neuroscience / Ausgabe 1/2011
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-010-0271-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"