State 1, which is the state where there is a global coherence of BOLD phases, has the highest fractional occupancy (0.32) and the longest mean lifetime (17.8±1.8 TRs). Furthermore, all states except one had the highest transition probability to state 1.
These results indicate that the BOLDphases after spending some time misaligned with the global signal (and aligned between them), most of the time they realign with the global signal, returning to a state where all phases have the same direction.
Regarding the mean lifetime, it is important to note that all states have a mean duration greater than 10 TRs due to the temporal smoothing applied to the labels after the K-means clustering. Although it was not a strict smoothing, but a balanced smoothing which took into account the distance of each leading eigenvector to its centroid, as well as the neighbouring labels, the minimum mean lifetime could have been slightly below 10TR, however with this number of states they were all above 10TR.
Figure 3.18:Comparison between relative alpha topographies for 9 states with no delay and for different delays (from 1 to 5 seconds). The delays are introduced in the fMRI data, more specifically in the dFC labels, discarding the first to fifth samples, depending on the lag. This is done for each subject individually and in the end the labels are concatenated. As there will be some topographies in the end without any correspondence to a dFC state, these are discarded.
In order to have a measure that showed the similarity between the states of the specific frequency bands and the original band, the cosine similarity between the centroid vectors was computed. For the slow-5 band, the results are shown in table3.1.
The first state found in the slow-5 band is very similar to the first state previously found, with a similarity of 0.99, which is the state that represents the global coherence state. This state is expected to appear in all bands because it is associated to the global mode of oscillation of theBOLDsignal and all other states come from misalignment of a subset of brain regions, which align between themselves.
This state maintains a relatively high similarity with other states because some networks are formed by few regions, so the other regions are all in a global coherence state, thus being equal to the first state.
The second state has also a high similarity (r = 0.98) with state 2 previously found, which corresponds to the basal ganglia network. In this case, besides caudate nucleus, putamen and pallidum, the tallamus is also involved in this network, as well as a region from the parietal lobe.
State 3 also registered a high similarity (r = 0.97) with state 3 previously found, which corresponds to the network formed by the olfactory cortex, middle orbitofrontal gyrus and gyrus rectus. The other slow-5 state with a high similarity with another original is state 7 (r = 0.82) which is comparable to the DMN. One last note to state 4, which is composed by frontal and parietal regions, however mostly from
Figure 3.19:Dynamic functional connectivity states obtained from k-means clustering with k=9 for original, slow-5 [0.01,0.027] Hz, slow-4 [0.027,0.073] Hz, slow-3 [0.073,0.198] Hz and slow-2 [0.198,0.5[ Hz bands and the alpha power topographies associated to each state. The color scale used in the topographies is equal to the one used in the previous analysis.
Table 3.1:Cosine similarity between the dFC states obtained in the analysis with the slow-5 (0.01-0.027 Hz) band and the states obtained with the 0.01-0.1 Hz band. In bold is represented the highest similarity values above 0.8 for each state
Slow-5 states
1 2 3 4 5 6 7 8 9
dFC state 0.01- 0.1 Hz
1 0.9934 0.9176 0.8616 0.7087 0.2951 0.8545 0.4676 0.5355 0.3564 2 0.9326 0.9819 0.7935 0.8103 0.2949 0.7442 0.4558 0.4155 0.1436 3 0.9104 0.8112 0.9737 0.6198 0.0463 0.7254 0.6345 0.6005 0.3505 4 0.5091 0.4391 0.3513 0.0465 0.5429 0.7345 -0.0422 0.2499 0.6992 5 0.5160 0.4037 0.7450 0.5813 -0.4591 0.2861 0.8208 0.3620 -0.0487 6 0.6862 0.6089 0.5837 0.7842 0.2744 0.5755 0.2556 0.3644 -0.2230 7 0.6218 0.7167 0.4321 0.7753 0.1568 0.3366 0.3890 -0.0045 -0.0497 8 0.5523 0.5744 0.3570 0.2805 0.6047 0.4419 -0.2436 0.5034 0.0544 9 0.4421 0.3241 0.5496 0.0874 -0.3086 0.3682 0.7621 0.3964 0.7122
the right hemisphere.
All the other states did not reveal a high similarity with a different state from the original analysis.
The finding of differentdFCstates would be expected as theBOLDoscillations that are being analyzed are subset of those analyzed in the original analysis. Thus, the functional connectivity between brain regions is also expected to change.
Regarding the relative alpha topographies, the highest power is associated to states 3 and 7, with states 4 and 6 having also a relatively higher power than the remaining, however lower than 3 and 7.
With respect to states 3 and 7, which have some similarities to small frontal network and the DMN, respectively, the high alpha power is consistent to the previous analysis. Concerning states 4 and 6, there is no clear association to any previousdFCstate, so a comparison cannot be performed. However, one should note that theBOLDfluctuations analyzed are in the very slow band 0.01-0.027 Hz, which imposed the dFC labels to have a minimum mean lifetime of, approximately, 37 s. This long mean lifetime, in fact, alters the results relatively to the ones obtained in the band 0.01-0.1 Hz.
For the comparison between the centroid vector obtained in the analysis in the slow-4 band and the original band, the cosine similarity values is shown in table3.2.
In this case, there are more high similarities between slow-4dFCstates and each one of the states reported in the original analysis. The first state is once more the global coherence state, with a similarity of 0.99; the second state has again regions from the basal ganglia, however in this state they have less connectivity and are connected with frontal regions of the right hemisphere; state 3 is very identical to state 4 previously found (r = 0.88), which corresponds to the visual network; state 4 is very similar to the DMN, thus being similar to state 5 found in the previous analysis (r = 0.91); the fifth state encompasses frontal and parietal regions mostly from the left hemisphere, which contrasts with the findings in the slow-5 band, where the right frontoparietal network was found; the last state with a high similarity is state 7 with also state 7 from the original analysis (r = 0.88). From the remaining states, only state 9 had
Table 3.2:Cosine similarity between the dFC states obtained in the analysis with the slow-4 (0.027-0.073 Hz) band and the states obtained with the 0.01-0.1 Hz band. In bold is represented the highest similarity values above 0.8 for each state
Slow-4 states
1 2 3 4 5 6 7 8 9
dFC state 0.01- 0.1 Hz
1 0.9929 0.8948 0.4755 0.5283 0.6171 0.5837 0.5420 0.4907 0.3523 2 0.9351 0.9524 0.3089 0.5019 0.5459 0.5056 0.7182 0.3196 0.4339 3 0.9430 0.8064 0.3220 0.7239 0.5243 0.6578 0.4245 0.3720 0.4123 4 0.5114 0.3610 0.8774 -0.0210 0.0290 0.7387 -0.0574 0.6367 -0.3911 5 0.5530 0.5445 -0.3658 0.9071 0.3880 0.2731 0.2091 0.0603 0.8018 6 0.6677 0.6703 -0.0170 0.3188 0.8766 0.0678 0.3344 0.5893 0.6352 7 0.5921 0.7873 -0.0042 0.4002 0.2573 0.2078 0.8816 -0.1814 0.5221 8 0.5479 0.3638 0.5979 -0.2035 0.6643 0.0290 0.5215 0.3554 -0.1953 9 0.4599 0.3851 0.2497 0.7000 -0.0653 0.6187 -0.0837 0.0411 0.1461
a relatively high similarity with state 5 (r = 0.8) that corresponds to theDMN, however in this state all the frontal brain regions have high functional connectivity. States 6 and 8 both have connection between occipital regions, with state 6 also connecting with frontal regions and state 8 with parietal regions. As none of these states was found in the original analysis, both had small similarity values.
Concerning the state topographies, there is clearly one topography that stands out, belonging to state 5, the left frontoparietal network. In the original analysis, the frontoparietal network also exhibited a high alpha topography, so this is consistent with that result. States 4 and 9 also show an relatively high alpha topography. These states, as mentioned before, encompass regions from theDMN, just like the original state 5, which also displayed high alpha, so the results are consistent. The only different topography belongs to state 6, which has connections between occipital and frontal regions, and is associated to a relatively high alpha topography, similar to states 4 and 9.
These more identical results of this band with the original band are, to a certain extent, expected as the band analyzed (0.027-0.073 Hz) encompasses most of theBOLDfrequencies from the original band (0.01-0.1 Hz).
Following the same procedure as the previous bands, the cosine similarity values between the cen- troid vectors of slow-3 band and original band are shown in table3.3.
Regarding the similarity between the original analysis, the global coherence state is once again present (state 1) with a similarity of 0.99; state 2 resembles the basal ganglia network, thus having high similarity with state 2 from the original analysis (r= 0.97); state 3 is practically identical to state 3 from the original analysis, with a network composed by the olfactory cortex, middle orbitofrontal gyrus and gyrus rectus (r = 0.97); state 4 is mostly composed by the visual network, with a connection with right gyrus rectus, thus being very similar to the original state 4 (r = 0.83); theDMN network shows again in state 6, with a high similarity (r = 0.91) with the original state 5; finally, state 7 has a relatively high similarity with the original state 8 which was correlated with the SMnetwork. Interestingly, this is the
Table 3.3:Cosine similarity between the dFC states obtained in the analysis with the slow-3 (0.073-0.198 Hz) band and the states obtained with the 0.01-0.1 Hz band. In bold is represented the highest similarity value above 0.8 for each state
Slow-3 states
1 2 3 4 5 6 7 8 9
dFC state 0.01- 0.1 Hz
1 0.9905 0.9592 0.8672 0.6750 0.7700 0.4621 0.8290 0.3953 0.5570 2 0.8972 0.9710 0.8285 0.5629 0.8995 0.4733 0.8198 0.3037 0.4775 3 0.9269 0.9141 0.9655 0.6325 0.6838 0.6095 0.7213 0.1833 0.5999 4 0.5349 0.4685 0.2959 0.8261 0.1555 -0.2113 0.3878 0.7563 -0.0781 5 0.5325 0.5243 0.7818 0.1953 0.5280 0.9153 0.2305 -0.5001 0.5606 6 0.7012 0.6337 0.6141 0.1995 0.6762 0.4744 0.5053 0.1001 0.7160 7 0.5257 0.6462 0.5254 0.2234 0.8153 0.4491 0.5726 0.0159 0.1734 8 0.5619 0.5405 0.3192 0.1159 0.3304 -0.2493 0.8221 0.7205 0.5235 9 0.4461 0.4176 0.5189 0.6527 0.2448 0.5453 0.1534 -0.1226 -0.0159
first band where thisdFCstate appears, suggesting that the connectivity of this network appears on the fasterBOLDfluctuations of the 0.01-0.1 Hz band.
From Figure 3.19 it is possible to observe that most dFC states have a lot more non correlated brain regions, shown in the dFC matrix by the green lines and in the cortical representation by the presence of yellow and light blue dots (these colors mean little strength, which in the matrix is translated to non correlated regions). At these frequencies (0.073-0.198) there is a greater influence of non- neuronal fluctuations of theBOLDsignal, which may lead to the appearance of more non correlations.
Furthermore, Yaesoubi and colleagues [40], which made a dFCanalysis for different frequency bands convolving with a complex Morlet Wavelet centered at different frequencies, also found that in relatively higher frequencies ( 0.15 Hz and higher), which in this study comprises the slow-3 and slow-2 bands, the there was less connectivity structure, i.e, the brain regions were less correlated between them, which is also found here for somedFCstates.
Regarding the alpha topographies there are some differences in relation to the original analysis.
Although state 3 also has a high alpha topography compared to the other ones, state 6 (the similar to theDMN) does not show a topography with high alpha power and state 1, surprisingly, shows this type of topography. One possible explanation is that, at high frequencies (>0.1 Hz) theBOLDsignal may be contaminated by noise (non-neuronal fluctuations) that influence the computed dynamic functional connectivity. With rather differentdFCmatrices, the assignment of adFCmatrix to each cluster can be also different, thus the time-course of the state 1 obtained in the analysis in the slow-3 band is different from the one acquired in the original analysis, despite the same state being present in both analysis, most likely due to the neuronal fluctuations. Therefore, as the alpha topographies are computed based on these labels of the k-means algorithm, they will be carrying ”noisy” information, as the one observed on state 1.
Finally, the cosine similarity between the centroid vectors obtained on slow-2 band (0.198-0.5 Hz)
and original analysis is shown in table3.4.
Table 3.4:Cosine similarity between the dFC states obtained in the analysis with the slow-2 (0.198-0.5 Hz) band and the states obtained with the 0.01-0.1 Hz band. In bold is represented the highest similarity value above 0.8 for each state
Slow-2 states
1 2 3 4 5 6 7 8 9
dFC state 0.01- 0.1 Hz
1 0.9811 0.9025 0.8553 0.9016 0.4810 0.5473 0.6185 0.5789 0.6525 2 0.9195 0.9706 0.8144 0.8130 0.5816 0.5360 0.4667 0.5534 0.5686 3 0.9474 0.8526 0.9436 0.8765 0.4681 0.4394 0.4470 0.6588 0.7329 4 0.5133 0.3333 0.2551 0.5133 -0.3623 0.1069 0.9077 0.3468 0.6286 5 0.5504 0.5101 0.7779 0.4612 0.6587 0.1027 -0.1310 0.5152 0.3355 6 0.6389 0.6054 0.5550 0.6642 0.7318 0.5497 0.2438 0.0481 0.2546 7 0.5577 0.7538 0.5434 0.3562 0.5740 0.3148 0.0954 0.4915 0.1739 8 0.5472 0.5282 0.3273 0.6408 0.2562 0.8550 0.3850 -0.1195 0.2763 9 0.4781 0.3253 0.5503 0.3377 -0.0067 -0.2382 0.4106 0.8206 0.4148 The results show that the non correlations seem to increase in thedFCstates, however some net- works can still be observed. State 1 continues to appear as the global coherence state and besides that state 4 is also very similar to the global coherence state, however with a lot more non correlations between some brain regions; the basal ganglia network is also found in state 2; state 3 presents high similarity with state 3 from the original analysis, however the regions belonging to the network have less strength and for that reason they are not shown connected in the cortical representation of this state; state 6 appears once again showing high similarity with original state 8, which had significative correlation with the somatomotor network; finally, the visual network is also present in state 7.
Although this frequency band is not usually analyzed, mostly due to the presence of physiological noise, this analysis showed that there are some networks that are very similar to states obtained using the usualfMRIband (0.01-0.1 Hz), namely the basal ganglia, the visual and the somatomotor networks.
The state of global synchronization (state 1) is also found in this band, however, as seen before this state is related to the global mode of oscillation of the brain, being the state where almost all states transition to, so it was expected that it present even in a high frequency analysis of the functional connectivity.
Concerning the alpha topographies, they are all very similar, not existing one that shows much more power than the others. For the same reason described earlier, these topographies may also be affected by ”noisy” results from thefMRIdata processing, more concretely thedFC labels time-course, so the association between each topography and thedFCstate is contaminated.
4
Conclusion
Contents
4.1 Conclusions . . . 63 4.2 Limitations and Future Work . . . 64
4.1 Conclusions
The main goal of the present dissertation was to studyEEGspectral correlates ofdFCstates in order to understand the electrophysiological underpinnings of these states. Furthermore, it was also investigated if theseEEGcorrelates could be used to solve an old problem ofdFCclustering, which is the choice of the number of states. In a first analysis a bandpass filter in the frequency range 0.01-0.1 Hz was applied to the BOLD signal, since this is the band less affected by physiological noise and where neuronal fluctuations are usually found [13]. The results showed associations between three dFC states and topographies with high alpha power. From thedFCstates found, one was similar to the frontoparietal network, the other to theDMNand a third one not similar to anyRSN, as the network was composed by the olfactory cortex, orbitofrontal gyrus and gyrus rectus. These results provide further support to the electrophysiological underpinnings offMRI dFCstates, and in particular indicate a relationship withEEG alpha power. Regarding the choice of number of states, theEEGrevealed to be the decisive factor to this choice. As seen in the results, the number ofdFCstates associated to distinct alpha power topographies was consistent throughout the majority of the range k = 3 to 15 states. However, if the number of states was, for example, 5 there was onedFCstate associated to a high alpha power topography that would be missed. Nonetheless, the criteria to choose the ”optimal” number of states still needs to be investigated.
The second analysis consisted in studying the BOLDsignal in four different bands: slow-5 (0.01- 0.027 Hz), slow-4 (0.027-0.073 Hz), slow-3 (0.073-0.198 Hz) and slow-2 (0.198-0.5 Hz). As the division in these bands is not usually done, mostly due to the physiological noise that is present in slow-3 and slow-2, the purpose was to compare with the first analysis and examine any differences that could be found in the topographies associated to thedFCstates, as well as in the states itself.
The main conclusions taken this comparison are that there is not a single band where the association between alpha topographies anddFCstates is the same as in the original analysis. They are mainly di- vided by the two slowest bands (slow-5 [0.01,0.027] Hz and slow-4 [0.027,0.073] Hz), which is expected as these two bands encompass almost all frequencies of the original band (0.01-0.1 Hz). Despite not finding the bilateral frontoparietal network in neither of these two bands, the left and right frontoparietal networks were found in separate bands and exhibit a topography with high alpha power. Regarding the olfactory cortex-middle orbitofrontal gyrus-gyrus rectus network, it was found in the slowest band (0.01- 0.027 Hz) as well as in the slow-3 band (0.073-0.198 Hz). Although this band involves fast frequencies (>0.1 Hz), it also contains frequencies from original band, thus being possible to find the samedFC states in both bands.
Secondly, the dFC states found when analysing the BOLD signal in the original band can almost all be found in the two slowest bands, with some minor changes in the connectivity of a few states.
However, the state similar to the SM network is only found in the slow-3 band, suggesting that there are differences in the frequency that theBOLDsignal fluctuates and even within a relatively small band
(0.01 - 0.1 Hz) if we segment into smaller bands, different states can be found.
Finally, the analysis of the functional connectivity between brain regions oscillating at fast frequencies (0.198 - 0.5 Hz) demonstrates a lot more non correlated regions than the previous analysis, indicating that this band is catching more physiological noise and consequently less neuronal fluctuations.
Although the analysis with multiple frequency bands was more comparative to the results obtained in the original analysis, there were some promising results regarding thedFCstates found with the partition in small frequency bands.