<p>That one looks a bit familiar to me!</p>

<p><strong>Short, simple answer</strong></p>

<p><em>(extracted from the longer answer below...)</em></p>

<p>Measures of functional connectivity are <em>just correlations</em> (correlation here referring broadly to statistical relationships, not a specific statistic): they do not say anything about the causes of those correlations including whether they are direct or indirect. The "connectivity" is <em>functional</em> in that it is measured only by the <em>function</em> at the measured nodes.</p>

<p><strong>Functional connectivity</strong></p>

<p>Functional connectivity refers to temporal correlations in some measure of nervous system activity. Both positive and negative functional connectivity is possible. The canonical example is correlation in the <a href="https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging#BOLD_hemodynamic_response" rel="nofollow noreferrer">BOLD fMRI signal</a>, which is often defined as the Pearson correlation in the resting state BOLD signal time series between remote voxels, or across blocks during some task.</p>

<p>For EEG, functional connectivity measures include <a href="https://en.wikipedia.org/wiki/Coherence_(signal_processing)" rel="nofollow noreferrer">coherence</a>, amplitude correlations (such as the Pearson correlation of the signal envelope, typically band-pass filtered into named bands like delta/theta/alpha/beta/gamma), and measures of phase relationships such as the phase lag index and weighted phase lag index.</p>

<p>What these measures share in common is that they record some statistical non-independence in the activity measured in different areas of the brain. However, they differ greatly in temporal and spatial scale depending on the modality and subsequent signal processing.</p>

<p>Importantly, measures of functional connectivity are <em>just correlations</em> (correlation here referring broadly to statistical relationships, not a specific statistic): they do not say anything about the causes of those correlations including whether they are direct or indirect. The "connectivity" is <em>functional</em> in that it is measured only by the <em>function</em> at the measured nodes.</p>

<p>For example, consider a weighted directed graph of nodes A, B, and C. Even if there is no edge connecting A and B, if C drives both A and B then there will be functional connectivity between A and B.</p>

<p>You would even expect to observe functional connectivity <em>between the brains of different people</em> if they were, for example, watching the same video <em>(as an aside...I think someone actually did this experiment, leading to some bogus claims about universal consciousness or something like that...the real explanation is more like "when two people listen to the same audio track, in which sometimes there is speech and sometimes there is no speech, they both have more activity in their auditory cortex during speech" which is considerably less profound...)</em>.</p>

<p>A synaptic connection between nodes P and Q almost certainly implies there will be functional connectivity between P and Q (though it may not be measurable depending on the strength of that connection and the structure of the rest of the network), but the inverse is not true: functional connectivity is insufficient to claim a real synaptic connectivity.</p>

<p>Personally, I wish another term was used besides <em>connectivity</em> but this is the field standard terminology.</p>

<p>Functional connectivity can be distinguished from two other types of connectivity: effective and structural.</p>

<p><strong>Effective connectivity</strong></p>

<p>Effective connectivity refers to model-based measures of causal influence of some brain area on another. Examples include the use of dynamic causal modeling (see for example Friston 2009, which is also highly relevant to the rest of this answer) and multivariable autoregressive modeling (see for example Cheung et al 2010).</p>

<p><strong>Structural connectivity</strong></p>

<p>Structural connectivity refers to the physical axonal connections between brain areas. In neuroimaging, it is often measured using diffusion tensor imaging which takes advantage of the fact that water more freely diffuses along axon tracts rather than perpendicular to them. Structural connectivity can also be measured more directly using neuronal tracers (dyes).</p>

<p>The term <em>structural connectivity</em> is used both in the context of connection strengths between certain areas relative to other areas, as well as to overall white matter integrity which can be disrupted in disease.</p>

<p>Note that while structural connectivity is often expected to correlate with functional connectivity, it doesn't need to.</p>

<p><strong>Synaptic connectivity</strong></p>

<p>These other terms are mostly used in the broad areas of neuroimaging and EEG/MEG. Using these modalities, even effective and structural connectivity only loosely imply synaptic connectivity. Detecting true synaptic connectivity requires more invasive electrophysiological techniques such as paired patch clamp recordings, or via anatomical reconstructions using tracers or electron microscopy. Synaptic connectivity can also be observed in real time using live-cell imaging of dendritic spines after injection or genetic expression of a fluorescent marker.</p>

<hr>

<p>Cheung, B. L. P., Riedner, B. A., Tononi, G., &amp; Van Veen, B. D. (2010). Estimation of cortical connectivity from EEG using state-space models. IEEE Transactions on Biomedical engineering, 57(9), 2122-2134.</p>

<p>Friston, K. J. (1994). Functional and effective connectivity in neuroimaging: a synthesis. Human brain mapping, 2(1‐2), 56-78.</p>

<p>Friston, K. (2009). Causal modelling and brain connectivity in functional magnetic resonance imaging. PLoS biology, 7(2), e1000033.</p>

<p>Jones, D. K., Simmons, A., Williams, S. C., &amp; Horsfield, M. A. (1999). Non‐invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 42(1), 37-41.</p>

<p>Nägerl, U. V., Willig, K. I., Hein, B., Hell, S. W., &amp; Bonhoeffer, T. (2008). Live-cell imaging of dendritic spines by STED microscopy. Proceedings of the National Academy of Sciences, 105(48), 18982-18987.</p>

<p>Vinck, M., Oostenveld, R., Van Wingerden, M., Battaglia, F., &amp; Pennartz, C. M. (2011). An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. Neuroimage, 55(4), 1548-1565.</p>

CC BY-SA 4.0
2020-01-07T17:33:50.800Z
Thanks a very lot!
Hans-Peter Stricker
CC BY-SA 4.0
2020-01-07T17:37:40.853Z
@Hans-PeterStricker No problem. Not sure if you noticed but the paper you link is one of mine... :) (well, a pre-print)
Bryan Krause
CC BY-SA 4.0
2020-01-17T13:27:12.217Z
Please allow me to point you to a question I've asked at Philosophy SE, in which I reference this post: [Models of the brain as a graph and another neural correlate of consciousness](https://philosophy.stackexchange.com/questions/69689/models-of-the-brain-as-a-graph-and-another-neural-correlate-of-consciousness)
Hans-Peter Stricker
CC BY-SA 4.0
2020-01-07T17:23:31.027Z
2020-01-07T17:34:58.853Z
2020-01-07T17:34:58.853Z
Bryan Krause
<p>I used to believe that connectivity is nothing but synaptic connectivity and thus a long-term concept: synapses grow and synaptic strengths change on rather large time scales. But recently I found that connectivity sometimes is used as a short-term concept, e.g. in statements like this:</p>

<blockquote>
  <p><em><a href="https://www.researchgate.net/publication/336920763_Cortical_functional_connectivity_indexes_arousal_state_during_sleep_and_anesthesia" rel="nofollow noreferrer">»[C]ortical connectivity will reflect clear changes when transitioning
  into states of reduced consciousness.«</a></em></p>
</blockquote>

<p>Assuming that transitioning into a state of reduced consciousness takes place in some seconds or minutes, also connectivity would have to change on this time scale. But what kind of connectivity would this be?</p>

<p>The authors of the paper cited above call it "functional connectivity" and measure it by the so-called "weighted phase lag index".</p>

<p>How is functional connectivity defined or explained (understandable to a non-specialist) and how does it relate to synaptic connectivity (which can easily be understood by non-specialists)?</p>

<neuroscience><neurophysiology><connectionism>
Functional vs. synaptic connectivity
Hans-Peter Stricker
# Functional vs. synaptic connectivity

(Asked by: username_0 on 2020-01-07)

I used to believe that connectivity is nothing but synaptic connectivity and thus a long-term concept: synapses grow and synaptic strengths change on rather large time scales. But recently I found that connectivity sometimes is used as a short-term concept, e.g. in statements like this:

> *[»[C]ortical connectivity will reflect clear changes when transitioning
> into states of reduced consciousness.«](https://www.researchgate.net/publication/336920763_Cortical_functional_connectivity_indexes_arousal_state_during_sleep_and_anesthesia)*

Assuming that transitioning into a state of reduced consciousness takes place in some seconds or minutes, also connectivity would have to change on this time scale. But what kind of connectivity would this be?

The authors of the paper cited above call it "functional connectivity" and measure it by the so-called "weighted phase lag index".

How is functional connectivity defined or explained (understandable to a non-specialist) and how does it relate to synaptic connectivity (which can easily be understood by non-specialists)?

**Tags:** neuroscience, neurophysiology, connectionism


---

## 1 answers

### Answer by username_1 on 2020-01-07. Score: 2 | Accepted answer

That one looks a bit familiar to me!

**Short, simple answer**

*(extracted from the longer answer below...)*

Measures of functional connectivity are *just correlations* (correlation here referring broadly to statistical relationships, not a specific statistic): they do not say anything about the causes of those correlations including whether they are direct or indirect. The "connectivity" is *functional* in that it is measured only by the *function* at the measured nodes.

**Functional connectivity**

Functional connectivity refers to temporal correlations in some measure of nervous system activity. Both positive and negative functional connectivity is possible. The canonical example is correlation in the [BOLD fMRI signal](https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging#BOLD_hemodynamic_response), which is often defined as the Pearson correlation in the resting state BOLD signal time series between remote voxels, or across blocks during some task.

For EEG, functional connectivity measures include [coherence](https://en.wikipedia.org/wiki/Coherence_(signal_processing)), amplitude correlations (such as the Pearson correlation of the signal envelope, typically band-pass filtered into named bands like delta/theta/alpha/beta/gamma), and measures of phase relationships such as the phase lag index and weighted phase lag index.

What these measures share in common is that they record some statistical non-independence in the activity measured in different areas of the brain. However, they differ greatly in temporal and spatial scale depending on the modality and subsequent signal processing.

Importantly, measures of functional connectivity are *just correlations* (correlation here referring broadly to statistical relationships, not a specific statistic): they do not say anything about the causes of those correlations including whether they are direct or indirect. The "connectivity" is *functional* in that it is measured only by the *function* at the measured nodes.

For example, consider a weighted directed graph of nodes A, B, and C. Even if there is no edge connecting A and B, if C drives both A and B then there will be functional connectivity between A and B.

You would even expect to observe functional connectivity *between the brains of different people* if they were, for example, watching the same video *(as an aside...I think someone actually did this experiment, leading to some bogus claims about universal consciousness or something like that...the real explanation is more like "when two people listen to the same audio track, in which sometimes there is speech and sometimes there is no speech, they both have more activity in their auditory cortex during speech" which is considerably less profound...)*.

A synaptic connection between nodes P and Q almost certainly implies there will be functional connectivity between P and Q (though it may not be measurable depending on the strength of that connection and the structure of the rest of the network), but the inverse is not true: functional connectivity is insufficient to claim a real synaptic connectivity.

Personally, I wish another term was used besides *connectivity* but this is the field standard terminology.

Functional connectivity can be distinguished from two other types of connectivity: effective and structural.

**Effective connectivity**

Effective connectivity refers to model-based measures of causal influence of some brain area on another. Examples include the use of dynamic causal modeling (see for example Friston 2009, which is also highly relevant to the rest of this answer) and multivariable autoregressive modeling (see for example Cheung et al 2010).

**Structural connectivity**

Structural connectivity refers to the physical axonal connections between brain areas. In neuroimaging, it is often measured using diffusion tensor imaging which takes advantage of the fact that water more freely diffuses along axon tracts rather than perpendicular to them. Structural connectivity can also be measured more directly using neuronal tracers (dyes).

The term *structural connectivity* is used both in the context of connection strengths between certain areas relative to other areas, as well as to overall white matter integrity which can be disrupted in disease.

Note that while structural connectivity is often expected to correlate with functional connectivity, it doesn't need to.

**Synaptic connectivity**

These other terms are mostly used in the broad areas of neuroimaging and EEG/MEG. Using these modalities, even effective and structural connectivity only loosely imply synaptic connectivity. Detecting true synaptic connectivity requires more invasive electrophysiological techniques such as paired patch clamp recordings, or via anatomical reconstructions using tracers or electron microscopy. Synaptic connectivity can also be observed in real time using live-cell imaging of dendritic spines after injection or genetic expression of a fluorescent marker.

---

Cheung, B. L. P., Riedner, B. A., Tononi, G., & Van Veen, B. D. (2010). Estimation of cortical connectivity from EEG using state-space models. IEEE Transactions on Biomedical engineering, 57(9), 2122-2134.

Friston, K. J. (1994). Functional and effective connectivity in neuroimaging: a synthesis. Human brain mapping, 2(1‐2), 56-78.

Friston, K. (2009). Causal modelling and brain connectivity in functional magnetic resonance imaging. PLoS biology, 7(2), e1000033.

Jones, D. K., Simmons, A., Williams, S. C., & Horsfield, M. A. (1999). Non‐invasive assessment of axonal fiber connectivity in the human brain via diffusion tensor MRI. Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine, 42(1), 37-41.

Nägerl, U. V., Willig, K. I., Hein, B., Hell, S. W., & Bonhoeffer, T. (2008). Live-cell imaging of dendritic spines by STED microscopy. Proceedings of the National Academy of Sciences, 105(48), 18982-18987.

Vinck, M., Oostenveld, R., Van Wingerden, M., Battaglia, F., & Pennartz, C. M. (2011). An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. Neuroimage, 55(4), 1548-1565.

> **Comments:**
> **username_0**: Thanks a very lot!  
> **username_1**: @Hans-PeterStricker No problem. Not sure if you noticed but the paper you link is one of mine... :) (well, a pre-print)  
> **username_0**: Please allow me to point you to a question I've asked at Philosophy SE, in which I reference this post: [Models of the brain as a graph and another neural correlate of consciousness](https://philosophy.stackexchange.com/questions/69689/models-of-the-brain-as-a-graph-and-another-neural-correlate-of-consciousness)  

---

