Chapter 7 - Advanced statistical analysis

What is functional connectivity?

Functional connectivity is the relationship between the functional activity of different brain regions, usually measured as a correlation between their signals over time. In the simplest case, you take the time-varying signal from one voxel or region and correlate it with another region, or even with all voxels in the brain, to identify a network of regions whose activity fluctuates together. The important point is that it is about statistical co-fluctuation, not direct proof of one region driving another.

What does it mean when two regions are functionally connected?

It means their signals rise and fall together over time. For example, if the BOLD signal in region A increases whenever the BOLD signal in region B also increases, and they tend to decrease together too, they are said to be functionally connected. This does not mean they must have a direct anatomical connection or that one necessarily causes the other’s activity. It only tells you that their activity patterns are related.

Why do the notes say functional connectivity does not mean anatomical or structural connectivity?

Because functional connectivity is based on correlation in activity, whereas anatomical connectivity refers to physical neural pathways connecting regions. Two regions can show correlated activity even when they are not directly connected by a white matter tract, because a third region may influence both of them, or the relationship may be mediated through a chain of regions. So functional connectivity can exist without a direct structural link.

What is the simplest index of functional connectivity?

The simplest index is the correlation between the activity of two regions across time. In practice, you take the time course from one region of interest and compute how strongly it correlates with another region’s time course. A stronger correlation suggests stronger functional connectivity in the statistical sense.

What does seed-based functional connectivity analysis mean?

Seed-based analysis starts with one chosen voxel or region, called the seed, and uses its time-varying signal as a reference. That seed signal is then correlated with the signal from all other voxels or regions in the brain. The result is a map of areas whose activity co-varies with the seed, effectively showing a functional network centered around that seed region.

Why is the time scale of communication important for connectivity?

Because what you can infer depends heavily on the speed of the signal you measure. Neural communication itself happens on the scale of milliseconds, with back-and-forth interactions occurring at temporal frequencies well above 1 Hz, which is why electrophysiological methods are much better suited for real-time neural timing. Hemodynamic imaging measures much slower changes, so it captures only slow co-fluctuations, not the true moment-to-moment speed of communication.

What is the time scale of neural communication according to the notes?

The notes state that the time scale of neural communication is in the milliseconds range, with back-and-forth communication occurring at temporal frequencies far above 1 Hz. This means actual neural interaction is extremely fast and is best captured by electrophysiological imaging rather than hemodynamic methods.

What time scale is measured with hemodynamic imaging?

Hemodynamic imaging captures slower signal changes rather than fast neural events. The notes mention that the hemodynamic signal is typically low-pass filtered with a cutoff around 0.1 Hz, and that frequencies above that are mostly treated as noise. So when you analyze functional connectivity in fMRI, you are looking at very slow co-fluctuations, not rapid neural exchange.

Why is functional connectivity in fMRI only an indirect window on communication?

Because fMRI does not measure neural firing directly. It measures a slow BOLD signal, which reflects hemodynamic consequences of neural activity. Therefore, when two fMRI signals correlate, you are observing a relationship between slow blood-oxygenation fluctuations, not directly measuring neural messages being passed between the regions.

Why is interpretation of correlations in brain activity difficult?

The notes say there are many possible causes for a correlation, and it is hard to differentiate among them. A correlation might reflect direct interaction, shared input from another region, global task effects, physiological noise, or even artifacts such as subject motion. That is why correlation alone is informative but limited.

Why is subject motion a serious confound in connectivity?

Because subject motion can artificially change the measured signal in many brain regions at once. If several regions show similar signal fluctuations due to movement rather than neural activity, they may appear functionally connected when they are not. The notes explicitly warn to be aware of confounding factors such as subject motion when interpreting correlations.

Why does correlation not imply directionality?

Because a correlation only tells you that two regions vary together. It does not tell you whether A influences B, B influences A, or whether both are driven by a third factor. So from functional connectivity alone you can say two areas are related, but you cannot say which one drives the other.

What is effective connectivity?

Because functional connectivity only says two regions are correlated, while effective connectivity tries to estimate directed influence. In other words, functional connectivity asks “which regions co-fluctuate?”, whereas effective connectivity asks “which region is influencing which other region, according to a model?”

Why do the notes stress that effective connectivity is not proof of real causation?

Because even though effective connectivity models direction and influence, it still relies on assumptions and a chosen model. The notes say these are model-based inferences, not definitive proof. To go beyond correlation convincingly, additional information is needed, such as hypothesis-driven predictions or evidence from other kinds of studies.

What are “middle methods” in this lecture?

The notes describe “middle methods” as more complex models than plain functional connectivity, but not yet the most advanced causal models. The two examples given are psychophysiological interactions (PPI) and structural equation modeling (SEM). These methods begin to examine interactions between regions in a more structured way.

What is PPI in simple terms?

PPI asks: does the relationship between two brain regions change depending on the task? Instead of asking whether two areas are generally correlated, it asks whether their connectivity becomes stronger or weaker under a certain psychological context. So PPI is really about context-specific connectivity

What does “psychophysiological interaction” mean exactly?

It refers to an interaction between a psychological factor and a physiological signal. The psychological factor is the context, such as the task condition, and the physiological factor is the time course from a chosen region of interest. The method identifies brain regions whose activity depends on the interaction between those two factors.

What is the goal of PPI?

The goal of PPI is to identify regions whose activity changes as a function of the interaction between task context and the signal from a region of interest. In other words, it tests whether the influence or relationship of one region with the rest of the brain depends on what the participant is doing

What is a PPI effect?

A PPI effect is a context-specific change in the relationship between brain regions. So if connectivity between two regions is stronger during condition A than condition B, that difference is the PPI effect. It does not just reflect the main effect of task or the main effect of the region’s activity, but their interaction.

What example of PPI is given in the notes?

The notes mention Friston et al. (1997), described as attentional modulation of V1 to V5. The point of the example is that the relationship between visual regions changed depending on attentional context. The notes also say that it may not be mathematically possible to fully distinguish two interpretations, although one may be neurologically more plausible.

What is the limitation of PPI shown by the Friston example?

The limitation is that PPI may show that a relationship changes with context, but it may still be hard to distinguish between competing interpretations mathematically. So even when a PPI effect is found, interpreting exactly how one region influences another may remain ambiguous.

What is structural equation modeling (SEM)?

SEM is a statistical method used to estimate directed influence between multiple brain regions using a predefined anatomical model. You start from a hypothesized network of connections based on known anatomy, and the method estimates how strongly those regions influence each other within that model.

Why is SEM hypothesis-driven?

Because SEM does not discover the network from scratch. It begins with an a priori anatomical model, meaning the researcher already specifies which regions and pathways are supposed to be connected. The analysis then estimates the strengths of those connections rather than inventing the network structure on its own.

What does SEM estimate?

SEM estimates the causal influence of multiple areas on each other, using prior anatomical knowledge as a constraint. The result is a set of pathway strengths showing which routes in the hypothesized model best account for the observed data.

What example of SEM is given in the notes?

The notes cite Santens et al. (2010), which studied numerical representations. The model included primary visual cortex (VIS), a number-sensitive area (SENS), and a number-selective area (SEL), and it compared direct versus indirect input routes from visual representations to number-selective representations.

What was the main idea of the Santens SEM example?

The study modeled two possible routes through which visual information could reach number-processing regions. SEM then estimated the relative strength of those pathways and showed that their relative importance could be modulated by format, such as symbolic versus non-symbolic numbers.

Why does the Santens example not prove directionality?

Because, as the notes explicitly say, there is no proof of directionality. SEM estimates directional influences within a chosen model, but it remains a model-based inference. The estimated path strengths are informative, but they do not constitute absolute proof that the brain truly uses that route in that exact way.

What is the difference between functional and anatomical connectivity?

Functional connectivity refers to correlations in activity between regions, while anatomical connectivity refers to the physical neural pathways connecting them. Anatomical connectivity is about wiring; functional connectivity is about coordinated activity. One is structural, the other statistical.

Can functional connectivity occur without a direct anatomical connection?

Yes. The notes say functional connectivity can occur without a direct anatomical connection because correlations may arise through intermediate regions. So two regions can look functionally linked even when they are not directly wired together.

How do functional and anatomical connectivity differ during an experiment?

Functional connectivity can change during the experiment, because the pattern of correlated activity can vary with context, task, or mental state. Anatomical connectivity is static during the experiment, because the physical wiring of the brain does not change from one trial to the next.

When would direct influence from A to B require anatomical connectivity?

If functional connectivity actually reflects a direct influence of A on B, then there should be an anatomical connection present. However, if the effect is mediated through intermediate regions, then A and B can show functional connectivity without a direct structural pathway between them.

What is resting-state fMRI?

Resting-state fMRI measures brain activity when participants are instructed to rest and think of nothing in particular. It is used to study intrinsic connectivity patterns in the brain without imposing an explicit task. The notes say it is very feasible because it often requires only one or two scans of about eight minutes each

Why is resting-state fMRI especially feasible in challenging patient groups?

Because it is relatively simple to perform: participants do not need to carry out a difficult task, and the scanning session can be short, often just one or two 8-minute scans. That makes it suitable even in populations where task compliance is difficult.

What is PCA in the context of resting connectivity?

Principal component analysis (PCA) identifies components that explain most of the variance in the data. In connectivity, it can summarize a subset of regions with high correlations in activity into a smaller number of components, making the large dataset easier to interpret.

What does it mean that a subset of regions is summarized by one PCA component?

It means those regions share enough correlated variance that their joint activity can be represented by a single underlying pattern or component. Instead of describing each region separately, PCA captures their common fluctuation in a more compact form.

What is ICA in resting-state fMRI?

ICA is a data-driven blind source separation method. It assumes that the fMRI data are a linear mixture of statistically independent sources and tries to separate those sources from the mixed signal. In resting-state analysis, this is used to recover independent resting-state networks.

Why is ICA called “data-driven”?

Because ICA does not require you to define the networks in advance. Instead, it analyzes the data itself and extracts components that are statistically independent. So unlike SEM, it is not strongly constrained by an a priori anatomical model.

What assumption does ICA make in resting-state fMRI?

CA assumes that the observed fMRI data are a linear mixture of statistically independent sources. The goal is then to separate those underlying sources from the recorded mixed signals.

What are the resting-state networks listed in the notes?

The notes list the following resting-state networks: default mode network, somatomotor network, visual network, language network, dorsal attention network, ventral attention network, and frontoparietal control network. These are recurring large-scale systems identified from resting activity patterns.

Why are resting-state networks important?

They show that the brain is organized into large-scale functional systems even when no explicit task is being performed. This means the brain is not inactive at rest; instead, it maintains structured patterns of spontaneous activity.

What example of resting-state network abnormality is mentioned?

The notes mention Wang et al. (2017), where internet addiction was associated with imbalanced interactions between the default mode network (DMN) and salience network (SN). This illustrates how altered resting-state connectivity can be related to clinical or behavioral conditions.

What is graph analysis in this lecture?

Graph analysis uses parameters that summarize network properties. Instead of focusing only on pairwise connectivity, it treats the brain as a network of nodes and edges and computes summary measures describing how information may be organized or distributed in that network.

What example of graph analysis is given?

Da Baene et al. (2019), where better cognitive flexibility and complex attention were related to better spread of information over the network, specifically involving mutually interconnected contralesional hubs. So graph analysis is used to connect overall network organization to behavior.

What is multi-voxel pattern analysis (MVPA)?

MVPA is an analysis approach that focuses on patterns of activation across multiple voxels, rather than testing each voxel individually. It is multivariate rather than univariate, and it asks whether the spatial pattern across voxels differs between conditions, even when the overall average activation may be the same.

How does MVPA differ from standard voxel-wise analysis?

In standard univariate analysis, nearby voxels are often treated individually and may even be expected to show similar signals after smoothing. In MVPA, the interest is specifically in differences between voxels within the pattern, because the information may lie in the configuration of activity across voxels rather than in overall signal magnitude.

Why can two conditions have the same overall activation but still be distinguishable by MVPA?

Because the pattern across voxels can differ even if the mean activation is identical. For example, nine voxels might have the same total activity in two conditions, but with a different arrangement of which voxels are more or less active. MVPA is sensitive to that difference in pattern, whereas a standard average-based analysis might miss it.

What is correlational MVPA, also called representational similarity analysis (RSA)?

RSA tests whether within-condition correlations between datasets are higher than between-condition correlations. If activity patterns are more similar within the same condition than across different conditions, that suggests the region distinguishes those conditions at the representational level

What does RSA tell you conceptually?

t tells you whether a brain region represents two conditions as similar or dissimilar patterns. So instead of asking “is activation higher?”, RSA asks “does this region contain a consistent representational pattern that differentiates the conditions?

What is decoding MVPA?

In decoding MVPA, the pattern of activity across voxels in one dataset is used to train a classifier. The classifier learns a decision boundary in multidimensional space and is then tested on an independent dataset through cross-validation. If it performs above chance, the voxel pattern carries information that can distinguish the conditions.

Why is cross-validation essential in decoding MVPA?

Because the classifier must be tested on independent data, not the same data it learned from. Otherwise, it might only memorize noise or idiosyncrasies of the training set. Cross-validation checks whether the learned pattern generalizes to new data.

What example of decoding MVPA is in the notes?

Bogner et al. (2024), showing that automatic recognition of visited rooms could be decoded without requiring explicit judgments about those rooms. This illustrates that MVPA can detect represented information even when participants are not overtly reporting it.

What is the major strength of MVPA compared with standard activation analysis?

Its major strength is that it can detect distributed information patterns that do not necessarily produce a strong average activation difference. So MVPA is often more sensitive to representational content than simple univariate contrasts.

What is the relation between ROI and whole-brain MVPA?

MVPA can be performed within a predefined region of interest (ROI) or across the whole brain. ROI-based MVPA focuses on a selected area, often based on prior hypotheses, while whole-brain MVPA searches more broadly for informative patterns.

Final integration: how do functional connectivity, effective connectivity, and MVPA differ

Functional connectivity asks whether regions’ signals are correlated over time. Effective connectivity asks whether one region may influence another within a model. MVPA is different from both: it is not primarily about inter-region relationships, but about whether patterns of activity contain information that distinguishes conditions. So FC is about co-fluctuation, EC is about modeled direction, and MVPA is about representation.

Most advanced models:

Dynamic causal modelling

Repetition suppression/adaptation:

neural response diecreases if stimulus repeats = adaptation

basic measure fmri adaptation: difference between repeat stimulus and different stimulus

assumption: areas with diminished response for repeat are sensitive to siimulus features