1. Introduction to Connectivity: resting-state and PPI
Kimberley Whitehead & Wenhua Liu

2. Two fundamental properties of brain architecture
Functional Segregation
Functional Integration
What is the neural correlate of… ?
How do cortical areas interact … ?
Overall connectivity can refer to any analysis for which more than one signal is considered at a time. In EEG you’re typically looking at bivariate connectivity (even if you end up doing multiple bivariate analyses). Graph theory is a way of looking at multivariate connectivity.
‘Connectivity’ analysis

3. Types of Connectivity
Structural/Anatomical Connectivity: physical presence of axonal projection from one brain area to another, axon bundles detected e.g. by DTI
Functional Connectivity: covariation between fluctuations in activity from distinct regions or neural networks, e.g. temporal correlation of activity across different brain areas in resting state fMRI
Effective Connectivity: moves beyond statistical dependency to measures of directed influence and causality, e.g. PPI and DCM
r = 0.78
DTI – diffusion tensor imaging; PPI – psychophysiological interaction, it’s half-way between functional and effective connectivity; DCM – dynamic causal modelling
R = correlation coefficient. Could be coincidental.
Functional connectivity – statistical dependency in the data such that brain areas can be grouped into interactive networks. Check what statistical dependency means.
Functional connectivity measures are based on statistical interdependencies between signals (Aertsen et al., 1989). The extent to which brain regions are connected is defined by the strength or consistency of this statistical interdependency (Varela et al., 2001).
Effective Connectivity: moves beyond statistical dependency to measures of directed influence and causality within the networks constrained by further assumptions
Results of one dataset e.g. a blocked stimulus can generate hypotheses about another dataset, e.g. a resting one. If you formulate a hypothesis based on one dataset and then test it with the same one, that introduces bias. But you can use a similar separate dataset.
Studies of functional connectivity typically use standard fMRI techniques but with relatively high temporal resolution. fMRI good for connectivity work because of its spatial coverage. Coactivation is the simplest aspect – two brain areas activate at the same time e.g. activate motor cortex and cerebellum for motor tasks. But coactivation doesn’t prove that two brain areas are functionally connected or show which way the relationship is if they are, e.g. bottom up or top down. fMRI criticised for being descriptive rather than mechanistic. Simple associations are best described as systems rather than networks – the latter implies descriptions that include the causal flow of information. Can build models by having different experimental conditions and comparing coactivation.
We’re interested in unidirectional connections as well as feedback connections. Can incorporate anatomical information into your model. E.g. prefrontal cortex has heavy projections to basal ganglia but little in return.
Definitions based on Roerbroek, Seth, & Valdes-Sosa (2011)

4. Functional connectivity
“Resting-state” fMRI
Functional connectivity
Default network – a set of brain regions whose activation decreases during performance of tasks and increases when in a resting condition
Resting state networks are highly temporally positively or negatively correlated networks.

5. Resting-state networks (RSNs)
Multiple resting-state networks (RSNs) have been found
All show activity during rest and during tasks
One of the RSNs, the default mode network (DMN), shows a decrease in activity during cognitive tasks
In general, regions that are coactivated during tasks also show resting state connectivity. E.g. there’s a resting state network which involves areas such as the dorsolateral–
prefrontal cortex and superior parietal cortex, i.e., areas that have repeatedly been found to be active during memory tasks. (These networks show very little spatial
variation around the mean percentage BOLD signal change, i.e. robust to inter-subject variability). Results of one dataset e.g. a blocked stimulus can generate hypotheses about another dataset, e.g. a resting one. If you formulate a hypothesis based on one dataset and then test it with the same one, that introduces bias. But you can use a similar separate dataset.
Default mode network: cluster consisting of the prefrontal, anterior cingulate, posterior cingulate, the inferior temporal gyrus, and the superior parietal region. It represents attention and/or possibly consciousness. The appearance of the DMN is consistent across samples, but within the network the posterior parts show less variation than the anterior parts.
The fact that there are spatially independent components doesn’t exclude the idea that there are interactions between them and the brain forms a ‘small world network’
The most direct evidence of an association between some of these fluctuations and neuronal activity comes from the observed correlation between the BOLD signal and cortical electrical activity in studies employing simultaneous fMRI and electroencephalograms (19. Goldman RI, Stern JM, Engel J, Jr, Cohen MS (2002) NeuroReport 13:2487–2492; Martinez-Montes E, Valdes-Sosa PA, Miwakeichi F, Goldman RI, Cohen MS (2004) NeuroImage 22:1023–1034) and the observation of change in these networks resulting from neurological disease (22).
Frontal spatial map has been found in earlier research and is proposed to be involved in executive control and working memory function.
The percentage BOLD signal change in resting state networks can reach levels as high as 2–3%. When comparing subjects for consistency, areas with a relatively high mean percentage BOLD signal change are also the areas that are the most consistent, i.e., show the least variation around the mean.
From Mitra e-life: Infra-slow (<0.1 Hz) intrinsic (equivalently, spontaneous) activity recorded using rs-fMRI has been understood predominantly in terms of zero-lag temporal synchrony (functional connectivity) within systems known as resting state networks (RSNs). Prior rs-fMRI studies have found that RSNs are generally preserved across wake and SWS. Importantly, conventional functional connectivity analyses assume temporal synchronicity and make no provision for the possibility that intrinsic activity may propagate between regions. BOLD signals show temporal lag patterns on a scale of ~1 sec, too slow for axonal transmission.

6. Default mode network
There was also significant evidence of thalamo-cortical connectivity for RSNs 1, 3, 4, and 5 (SI Fig. 7), showing the participation of the thalamus in the modulation of resting cerebral fluctuations (8, 38). Furthermore, the detection of hippocampal activity in RSN 1 (SI Table 3) further supported the involvement of the defaultmode system in memory processes (39).
In this study, the fMRI total variance explained by all of the RSNs was 44.6%.
EEG-fMRI maps contain regions with a positive (warm colors, yellow-orange) or a negative (cool colors, azure-blue) correlation of the BOLD signal with the power fluctuations in the various EEG bands (Figs. 1 and 2). It is assumed that a positive correlation of electrical rhythmic activity with BOLD signals underlies neuronal oscillatory synchronization whereas a negative correlation underlies neuronal desynchronization. Correlation levels were not high, up to BOLD signal was associated with different frequency bands and in different directions. (The same correlations were found in two separate chunks of data (in the same experiment), suggesting data was reproducible.) The profile of correlation was different across the different RSNs.
Mantini et al. Electrophysiological signatures of resting state networks in the human brain

7. Default mode network This is a ‘rendered’ brain.
Default mode network association with EEG activity from various frequency bands from Mantini et al with orange representing positive correlations. They used a 1-50Hz frequency range (why not lower?)
Dorsal attention and visual network can be separated on the basis of BOLD signal fluctuations and EEG power fluctuations, with the dorsal network more weighted toward alpha and beta rhythms, and the visual cortex more weighted toward delta and theta rhythms. This separation breaks down during visual processing when these areas show common task variability (48).
Only default mode network and self-referential network (often combined as all default mode) show positive correlations with EEG.
Recent work has isolated ultra-slow (1 Hz) fluctuations of theEEGsignal in the same range as the BOLD signal fluctuations, which are positively correlated with faster EEG oscillations, but are unlikely to mediate neuronal communication (49). Another possibility is that slow BOLD signal fluctuations are related to the so-called up–down neuronal states, slow (1 Hz) intrinsic fluctuations of the membrane potential identified in anesthetized animals, and recently shown to fluctuate synchronously between two connected areas (50).
49. Vanhatalo S, Palva JM, Holmes MD, Miller JW, Voipio J, Kaila K (2004) Proc Natl Acad
Sci USA 101:5053–5057.
50. Hahn TT, Sakmann B, Mehta MR (2006) Nat Neurosci 9:1359–1361.

8. Resting-state fMRI: acquisition
resting-state paradigm
no task; participant asked to lie still
time course of spontaneous BOLD signal measured
Commonly, subjects are asked to close the eyes and not to fall asleep but you can’t control where their thoughts will wander. Longer duration study increases stability of resting state networks but more likely subjects will become drowsy.
Fox & Raichle, 2007

9. Resting-state fMRI: pre-processing
…exactly the same as other fMRI data!

10. Spontaneous BOLD activity
The brain is always active, even in the absence of explicit input or output
task-related changes in neuronal metabolism are only about 5% of brain’s total energy consumption
What is the “noise” in standard activation studies?
faster frequencies related to respiratory and cardiac activities
spontaneous, neuronal oscillations between 0.01 – 0.1 Hz
< 0.10 Hz
In fMRI you filter out the very low and very high. Can pick up the rise and fall of stomach and HR – that would be the best way to regress them out. You can also measure white noise and CSF and model non-neuronal noise. BR is >0.1Hz.
Point out that this is different to task-related fMRI.
HbO2 = oxyhaemoglobin
Vasomotion is the spontaneous oscillation in tone of blood vessels, independent of heart beat, innervation or respiration.
Need to sample at a high rate to identify cardiac artefacts and slower respiration without aliasing artefacts
The estimated power spectra do not show isolated peak frequencies for any of these effects, but instead all show distribution of strong power at low frequency across a
range of frequencies, consistent with the majority of resting fMRI studies. The estimated power spectra did not show isolated frequencies, and the separation of signal into
different components, therefore, is largely driven by the difference in the spatial characteristics.
Low-frequency fluctuations observed in the BOLD signal have been found to display spatial structure comparable to task-related activation
ICA can separate resting fluctuations from other structured noise-related signal variations, such as those induced by head motion or cardiac and respiratory pulsations.
Do these fluctuations predominantly reflect changes of the underlying brain physiology independent of neuronal function, or instead reflect the neuronal baseline activity? The latter is supported by the fact they’re within cortical gray matter areas of known functional relevance.

11. Methods of Analysis
Seed voxel based analysis – region of interest crosscorrelation approach (SPM compatible)
Independent component analysis – model-free analysis which allows decomposition into individual maps to extract a variety of resting networks (cannot be done in SPM)
Two main types of analysis
* Region-of-interest crosscorrelation analysis approach (9–13), where the spatial characteristics of these resting fluctuations are estimated by using correlation analysis against a reference time course derived from secondary recordings (19) or the resting data itself (seed-voxelbased correlation analysis) (9).
* Model-free analysis by using independent component analysis (ICA) (14, 15, 20) instead of time-course regression. Such decompositions are of particular importance because they allow for a simultaneous separation into individual maps. These decompositions can simultaneously extract a variety of different coherent resting networks and separate such effects from other signal modulations such as those induced by head motion or physiological confounds, such as the cardiac pulsation or the respiratory cycle (13, 15). ICA approach does not require predefined regions of interest or the identification of a seed voxel location.
Seed voxel – voxel chosen as a starting point for a connectivity analysis
Complex network analysis, a branch of graph theory, reduces the brain into a collection of ‘nodes’ and ‘edges’ and allows quantitative characterization of these networks. In a weighted network, the strength of this interaction is taken into account, whereas in an unweighted network only the existence or absence of an interaction is taken into account.
An optimal network organization is characterized by a short average shortest path length and a high average clustering coefficient, also called a ‘small-world’ configuration (Watts and Strogatz, 1998).

12. Resting-state fMRI: Analysis
Hypothesis-driven: seed method
a priori or hypothesis-driven from previous literature
Data from: Single subject, taken from the FC1000 open access database. Subject code: sub07210
The first SPM results are the correlation on a glass brain which is beneficial because it’s not a slice so you can see all activations. Red is the seed region – it will always show correlation with the parts of the brain closest to it. The time series is extracted from the seed region. This network is the motor network which is very stable.
On the table/chart, the first column is the positive correlation. Preprocessing also gives you 6 movement parameters which are the later columns and they’re adjusted for. You could also have a column allowing you to adjust for age or sex. This is a group-level analysis. The 20 down to 160 is your time series.

13. Reviewing correlations
Van Dijk et al., 2010

14. Resting-state fMRI: Analysis
Hypothesis-free: independent component analysis (ICA)
“The aim of ICA is to decompose a multi-channel or imaging time-series into a set of linearly separable ‘spatial modes’ and their associated time course or dynamics” (Friston, 1998)

15. Pros & Cons of Resting state fMRI
easy to acquire
one data set allows to study different functional networks in the brain
good for exploratory analyses
(potentially) helpful as a clinical diagnostic tool
source of the 0.1 Hz oscillations in BOLD signal debatable
experimental paradigm eyes open/closed
establishes correlational, not causal, relationships
 Effective connectivity
Potentially helpful as a clinical diagnostic tool (e.g. epilepsy, Alzheimer’s disease)

16. Functional connectivity
“Resting-state” EEG
Functional connectivity
Default network – a set of brain regions whose activation decreases during performance of tasks and increases when in a resting condition

17. Two key types: power-based and phase-based Potential draw-backs
EEG and connectivity
Oscillatory synchronisation: neural populations transmit information and form larger networks
Two key types: power-based and phase-based
Potential draw-backs
Time lags
Volume conduction
Project back from ‘signal space’ to ‘source space’ (inverse problem)
Connectivity is complicated by lag. E.g. may appear there’s a phase lag connectivity between A and B but it’s really because each has a lagged connection with a completely separate region C. Or, if two regions are out of phase, how can you tell which one leads the other?
Another problem is volume conduction – two regions may seem connected but they’re picking up activity from the same generator
Phase likely reflecting the timing of activity within a neural population – useful for connectivity that occurs at the same time. Typically they ignore zero lag connectivity. (Some types are insensitive to lag). When neural populations are functionally coupled, the timing of their oscillatory processes become synchronised. Phase-based good for taking account of non-linearity.
Power likely reflecting the number of neurons or spatial extent of the neuron population. More robust for temporal jitters. More similar to fMRI connectivity measures because the correlated fluctuations in activity are relatively slower compared to phase-based measures.
Nonzero phase lag cannot be due to volume conduction (unless it’s pi if the electrodes are on opposite sides of the same dipole). Zero phase lag connectivity could be an artefact of volume conduction but it can also be a true brain process. Very strong connectivity at neighbouring electrodes suggests volume conduction.
Granger prediction looks for causality, for each pair it tests whether A influences B or B influences A
Also, the amplitude of the EEG recording changes as a result of different body postures due to shifts in cerebrospinal fluid layer thickness (Rice et al., 2013). Eyes closed condition is more stable over sessions and useful to have the alpha as a marker.
Correlation measures such as coherence, however, are increasingly abandoned in connectivity studies, as they fail to include information on the intrinsic nonlinearity of brain activity.
Many resting state EEG and MEG studies use the activity at the electrode level to infer how brain regions are (functionally) interconnected. This analysis is performed in so-called ‘signal space’ as neural activity is directly inferred from signals measured at the EEG electrode. Studies project the activity measured at the electrode or sensor (signal space) back to the underlying sources, the so-called ‘source space’. You get a mixture of signals arising from spatially separated sources at a single electrode which is problematic.
A noiseless recording condition may also allow source localization with a standard 10–20 system (Laarne et al., 2000).

18. EEG default mode network
At each of the EC or EO state, the dominant regional EEG field powers are shown to be a distinct set of spectral activities distributed in the head space. The main study findings indicate that the resting EEG in eyes-closed state devoid of stimulation or task is composed of a defined set of regional spectral activities in the classic 7 broad bands, termed EEG default mode network (EEG DMN). After completing the current work, an important off-press publication indicated that bold fMRI can be correlated with EEG powers in six widely distributed resting state networks, characterized by EEG features involved in combination with different brain rhythms (Mantini et al., 2007). The spectral topographic distributions showing little changes attest the stability of the underlying structures associated with the EEG field powers. Instead, the major changes largely in reduction of the field power, except the increase of prefrontal delta, are the main manifestation of the EC to EO state. 
Fig. 8. Constellation of spectral field powers measured in a 3-min period depicts the regional distribution of the respective seven frequency band powers on the brain topography, at EC vs. EO state, viewed from superior-anterior (s. a.) and superior-posterior ...
Andrew C.N. Chen, Weijia Feng, Huixuan Zhao, Yanling Yin, Peipei Wang
EEG default mode network in the human brain: Spectral regional field powers
NeuroImage, Volume 41, Issue 2, 2008, 561–574

19. Psychophysiological Interactions
Lorenzo 19

20. Introduction
PPI overview
Steps for PPI
How PPI results is interpreted

21. PPI overview PPI Other approaches: connectivity analysis
Task-dependent functional connectivity (Friston et al., 1997)
How psychological variables or external manipulations change the coupling between regions
Other approaches: connectivity analysis
e.g., Dynamic Causal Modelling (DCM, Friston et al.,2003); Granger causality (Granger, 1969)
analysisConcerns task-specific increases in the relationship between different brain areas’ activity (Friston et al., 1997)
Concerns task-specific increases in the relationship between different brain areas’ activity (Friston et al., 1997)

22. Psychophysiological Interaction
The purpose of PPI analysis
Determine which voxels in the brain increase their relationship with a seed region of interest in a given context, such as during a particular behavioural task, but not at resting condition or control condition
Identify regions whose activity depends on an interaction between psychological factors (the task) and physiological factors (the time course of a region of interest)
Or to identify regions whose activity depends on an interaction between psychological factors (the task) and physiological factors (the time courses of a region of interest)

23. What is PPI for? A example
Attention condition vs. No attention condition
V2 and V5 were active in attention V5 V2
attention
attention
attention
attention V2 V2 V2 V5 V1

24. V1 V2 V5
attention
Your interpretations?
e.g.,the V2 and V5 both independently active in the attention condition
or, the V2 and V5 work together interactively in attention condition 1. No
attention
If two active areas interact during attention, their activities will be more strongly related during attention than no-attention
two areas increases and decreases ‘in synch’ V2 V5 V1 24

25. Observed BOLD response
PPI: how it works?
Observed BOLD response
Y = β β β3 + error
PPI is an interaction term between a task regressor and a time series from an ROI(β3=β1*β2); test of slopes β1
Physiological Variable:
V1/V2 Activity
Psychological Variable:
Attention – No attention
Interaction: the effect of attention vs no attention on V1/V2 activity β2
Attention Β3
=β1* β2
No attention 25

26. Steps for PPI Plan your design First Level SPM Model of Task Activity
Identify and create a seed region
Run PPI ( a GLM analysis including a time course of seed region as a regressor), will do
Model estimation
Create PPI regressors
Create and Run PPI-GLM
Instructions are described briefly in this presentation, but detailed in the tutorial.
Run PPI ( a GLM analysis including a time course of seed region as a regressor), will do
Model estimation
Create PPI regressors:
A regressor representing the main effect of task
A time course of ROI
Interaction regressor: a PPI regressor as an product of the task and seed ROI 26

27. PPIs in SPM
Plan your experiment carefully! (you need 2 experimental factors, with one factor preferably being a psychological manipulation)
Stimuli:
SM = Radially moving dots
SS = Stationary dots
Task:
TA = Attention: attend to speed of the moving dots
TN = No attention: passive viewing of
moving dots
Buechel and Friston, Cereb Cortex 1997 27

28. PPIs in SPM
2. Perform Standard GLM Analysis to determine regions of interest and other brain activities 28

29. How to define your ‘seed’ region of interest, e.g.,
Select the voxels with the strongest task effect in a group analysis;
The common approach
Define ROI (regions of interest) anatomically;
Need a strong hypothesis
Define the region of interest individually for each participant
May be the most sensitive approach
O'Reilly,et al., Soc Cogn Affect Neurosci,2012

30. PPIs in SPM
3. Define source region and extract a representative time course of activity from the region (e.g. V2)
Use Eigenvariates (a button in SPM) to create a summary value of the activation across the region over time.
How to define a mask at your ‘seed’ region of interest, e.g.,
Select the voxels with the strongest task effect in a group analysis;
------The common approach
Define mask anatomically;
Need a strong hypothesis
Define the region of interest individually for each participant
------May be the most sensitive approach 30

31. PPIs in SPM
4. Enter this time course as a regressor into a GLM analysis
3. Enter this time course as a regressor into a GLM analysis
The voxels that show a significant effect for the seed ROI time course are the ones that vary their activity ‘in synch’ with the ROI.
If the activity in two areas increases and decreases ‘in synch’ this suggests that activity in on area may be driven by activity in the other (although the direction of causality is unknown) 31

32. PPIs in SPM Select PPI in SPM
• Select the parameters of interest from the original GLM
• Physiological condition: Activity in V2
• Psychological condition: Attention vs. No attention
This step will produce the Interaction term (source signal x experimental manipulation) 32

33. PPI regressores
Interaction regressor is an product of task time course and the seed ROI time course
The PPI regressores
The interaction term (Psychophysiological interaction)
Psychological time courses (co-variates of no interest)
Physiological time courses (co-variates of no interest)
If we only include the interaction term in analysis, regions in which there is an effect of task, or which are correlated with the seed ROI regardless of task, may also show up as being related to the interaction term

34. PPIs in SPM
5. Create PPI-GLM using the Interaction term – seen before!
Y = V1 β1 + (Att-NoAtt) β2 + (Att-NoAtt) * V1 β3 + βiXi + e
H0: β3 = 0
V1/V2 Att-NoAtt V1 * Att/NoAtt Constant
6. Determine significance!
Based on a change in the PPI Interaction 34

35. PPI results 35

36. PPI plot 36

37. PPI: How should we interpret our results?
Two possible interpretations:
The contribution of the source area to the target area response depends on experimental context
e.g. V2 input to V5 is modulated by attention
Target area response (e.g. V5) to experimental variable (attention) depends on activity of source area (e.g. V2)
e.g. The effect of attention on V5 is modulated by V2 input V1 V2 V5
attention 1. V1 V5
attention V2 2.
Mathematically, both are equivalent!
But… one may be more neurobiologically plausible 37

38. Need DCM to elaborate a mechanistic model!
Pros & Cons of PPIs
Pros:
Given a single source region, PPIs can test for regions exhibiting context-dependent connectivity across the entire brain
“Simple” to perform
Based on regressions and assume a dependent and independent variables (i.e., they assume causality in the statistical sense).
Cons:
Very simplistic model: only allows modelling contributions from a single area
Ignores time-series properties of data
Need DCM to elaborate a mechanistic model!
Adapted from D. Gitelman, 2011 38

39. Many thanks to Sarah Gregory!
The End
Many thanks to Sarah Gregory!
& to Katharina Ohrnberger & Lorenzo Caciagli for previous years’ slides!
THANKS FOR YOUR ATTENTION!

40. References previous years’ slides, and…
O'Reilly, J.X., Woolrich, M.W., Behrens, T.E., Smith, S.M., Johansen-Berg, H., Tools of the trade: psychophysiological interactions and functional connectivity. Soc Cogn Affect Neurosci 7,
Buckner, R. L., Andrews-Hanna, J. R., & Schacter, D. L. (2008). The brain’s default network: anatomy, function, and relevance to disease. Annals of the New York Academy of Sciences, 1124, 1–38. doi: /annals
Damoiseaux, J. S., Rombouts, S. A. R. B., Barkhof, F., Scheltens, P., Stam, C. J., Smith, S. M., & Beckmann, C. F. (2006). Consistent resting-state networks, (2).
De Luca, M., Beckmann, C. F., De Stefano, N., Matthews, P. M., & Smith, S. M. (2006). fMRI resting state networks define distinct modes of long-distance interactions in the human brain. NeuroImage, 29(4), 1359–67. doi: /j.neuroimage
Elwell, C. E., Springett, R., Hillman, E., & Delpy, D. T. (1999). Oscillations in Cerebral Haemodynamics. Advances in Experimental Medicine and Biology, 471, 57–65.
Fox, M. D., & Raichle, M. E. (2007). Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nature reviews. Neuroscience, 8(9), 700–11. doi: /nrn2201
Fox, M. D., Snyder, A. Z., Vincent, J. L., Corbetta, M., Van Essen, D. C., & Raichle, M. E. (2005). The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proceedings of the National Academy of Sciences of the United States of America, 102(27), 9673–8. doi: /pnas
Friston, K. J. (2011). Functional and effective connectivity: a review. Brain connectivity, 1(1), 13–36. doi: /brain
Greicius, M. D., Krasnow, B., Reiss, A. L., & Menon, V. (2003). Functional connectivity in the resting brain: a network analysis of the default mode hypothesis. Proceedings of the National Academy of Sciences of the United States of America, 100(1), 253–8. doi: /pnas
Greicius, M. D., Supekar, K., Menon, V., & Dougherty, R. F. (2009). Resting-state functional connectivity reflects structural connectivity in the default mode network. Cerebral cortex (New York, N.Y. : 1991), 19(1), 72–8. doi: /cercor/bhn059
Marreiros, A. (2012). SPM for fMRI slides.
Smith, S. M., Miller, K. L., Moeller, S., Xu, J., Auerbach, E. J., Woolrich, M. W., Beckmann, C. F., et al. (2012). Temporally-independent functional modes of spontaneous brain activity. Proceedings of the National Academy of Sciences of the United States of America, 109(8), 3131–6. doi: /pnas
Friston, K. (1998). Modes or models: a critique on independent component analysis for fMRI, TICS, Lee, M.H., Smyser, C.D., & Shominy, J.S. (2013). Resting-state fMRI: A review of methods and clinical applications. American Journal of Neuroradiology,
Roerbroek, A., Seth, A., & Valdes-Sosa, P. (2011). Causal Time Series Analysis of functional Magnetic Resonance Imaging Data. JMLR: Workshop and Conference Proceedings 12 (2011) 65–94 .
Friston KJ, Buechel C, Fink GR et al. Psychophysiological and Modulatory Interactions in Neuroimaging. Neuroimage (1997) 6,
Büchel C, Friston KJ, Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. Cereb Cortex (1997) 7,
Dolan RJ, Fink GR, Rolls E, et al., How the brain learns to see objects and faces in an impoverished context, Nature (1997) 389,
Gitelman DR, Penny WD, Ashburner J et al. Modeling regional and neuropsychologic interactions in fMRI: The importance of hemodynamic deconvolution. Neuroimage (2003) 19;
Graphic of the brain is taken from Quattrocki Knight et al., submitted.
Several slides were adapted from D. Gitelman’s presentation for the October 2011 SPM course at MGH