The authors have declared that no competing interests exist.
Conceived and designed the experiments: AI CS. Performed the experiments: AI. Analyzed the data: AI. Contributed reagents/materials/analysis tools: AI CS. Wrote the paper: AI CS. Designed the software used in the analysis: AI.
Functional connectivity has become an increasingly important area of research in recent years. At a typical spatial resolution, approximately 300 million connections link each voxel in the brain with every other. This pattern of connectivity is known as the functional connectome. Connectivity is often compared between experimental groups and conditions. Standard methods used to control the type 1 error rate are likely to be insensitive when comparisons are carried out across the whole connectome, due to the huge number of statistical tests involved. To address this problem, two new cluster based methods – the cluster size statistic (CSS) and cluster mass statistic (CMS) – are introduced to control the family wise error rate across all connectivity values. These methods operate within a statistical framework similar to the cluster based methods used in conventional task based fMRI. Both methods are data driven, permutation based and require minimal statistical assumptions. Here, the performance of each procedure is evaluated in a receiver operator characteristic (ROC) analysis, utilising a simulated dataset. The relative sensitivity of each method is also tested on real data: BOLD (blood oxygen level dependent) fMRI scans were carried out on twelve subjects under normal conditions and during the hypercapnic state (induced through the inhalation of 6% CO2 in 21% O2 and 73%N2). Both CSS and CMS detected significant changes in connectivity between normal and hypercapnic states. A family wise error correction carried out at the individual connection level exhibited no significant changes in connectivity.
Functional connectivity MRI has become a widely used method for investigating human brain networks in health and disease; its potential in cognitive neuroscience and clinical research has been demonstrated in a large number of neuroimaging studies
Investigating the functional connectivity between all grey matter voxels makes full use of the connectional information available in the data. However, this approach results in a very large number of connectivity values, as illustrated by the following example: The total grey matter volume of the brain is approximately 675 ml
A simple solution to address the multiple comparison problem is to reduce the number of tests that are carried out. This can be achieved by parcellating the cortex into anatomical regions of interest (ROI)
In most functional connectivity studies, the multiple comparison problem is tackled by comparing univariate ‘connectivity maps’ consisting of N voxels, rather than connectivity matrices consisting of N×N elements. This approach is formally equivalent to the comparison of univariate parametric maps in task-based fMRI. Consequently, standard methods used to control the false positive rate (e.g., FDR or FWER) can be applied
Univariate connectivity maps can be produced in a number of different ways. Seed-based connectivity mapping is one of the most widely used methods
Independent component analysis (ICA)
In recent years, graph theoretical measures of functional connectivity have become increasingly popular
Recently proposed methods, such as the network based statistic (NBS)
Typical patterns of connectivity change that the different clustering methods are sensitive to. Here, squares represent voxels and lines represent thresholded connectivity changes. (a) NBS cluster size is defined by the number of thresholded connectivity changes forming continuously connected components. The NBS cluster above has an extent of eight. (b) SPC cluster size is defined by the number of thresholded connectivity changes forming pairwise spatial clusters. The SPC cluster above has an extent of eight. (c) CMS size is defined by the total number of connectivity changes between a spatially distinct cluster, and the rest of the brain. The CMS cluster above has an extent of eight. CSS size is defined by the spatial extent of a cluster, where each voxel in the cluster exhibits at least one connectivity change with another voxel in the brain. The CSS cluster above has an extent of five.
A limitation of NBS is that connectivity changes are not localisable to a particular region of the brain. Only the network as a whole, rather than its individual components, can be considered significant. Furthermore, the application of NBS on a voxel-by-voxel level is suboptimal; NBS does not explicitly model the spatial smoothness that is intrinsic to BOLD fMRI data. SPC does utilise this smoothness. However, SPC requires a cluster search over an enormous N(N-1)/2×N(N-1)/2 matrix
In the present investigation, we introduce two new cluster based statistics to control for comparisons made over all connectivity values. These statistics are termed the Cluster Size Statistic (CSS) and the Cluster Mass Statistic (CMS). CSS is defined as the voxel-wise extent of a spatially continuous cluster, where each voxel in the cluster possesses at least one cluster-link with other voxels in the brain. CMS is defined as the total number of cluster-links between a spatially continuous cluster, and the rest of the brain (see
CSS and CMS measures have the advantage over NBS in that connectivity changes can be localised to a particular region of the brain. They also make full use of the spatial correlation that is intrinsic to fMRI data. They have the advantage over SPC that a cluster search over an N(N-1)/2×N(N-1)/2 matrix is not required. However, these analyses also provide information on connectivity change that is fundamentally different from what is offered by SPC or NBS. CSS and CMS statistics are designed to identify areas of the brain that show significant global connectivity change between groups or conditions. Clusters that are identified by CSS/CMS will not be detected by SPC or NBS, and vice versa.
Following a description of the principles underlying these tests, we demonstrate the performance of these methods in a simulation. The relative sensitivity of CSS and CMS methods is then tested on a real dataset by comparing BOLD fMRI scans carried out under normocapnic and hypercapnic conditions. The hypercapnic state is known to alter BOLD based measures of functional connectivity
Cluster size thresholding was introduced to fMRI by Poline et al
In a task-based fMRI study, the test proceeds in the following manner: For each permutation of the experimental labels, an image of voxel-wise test statistics (e.g., t-statistics) quantifying group activation is generated. This image is thresholded at a user-defined, cluster-forming threshold. The size of the largest cluster of voxels above this threshold is recorded. Voxels are considered to be a part of the same cluster if they are connected by a ‘face’ or an ‘edge’ (this is known as 18-connectivity). This procedure is repeated for many permutations of the experimental labelling. In this way, a maximal cluster size distribution is constructed from the data
In this section, two novel cluster based statistics are described. These methods can be regarded as an extension of conventional cluster size testing. The following description is made with reference to a comparison between experimental conditions (repeated measures design); this is the experimental design used in the present investigation. However, this theoretical framework can also be applied to a comparison between two or more groups (cross-sectional design).
The first stage of both CSS and CMS methods is to map the functional connectivity between all voxel pairs in the brains' grey matter. Connectivity is mapped for all subjects, under both conditions. T-statistics are calculated between connectivity values taken under different experimental conditions. However, instead of using the Student t-distribution to assess the significance of connectivity changes, a cluster-forming threshold is applied across all test statistics. This is similar to the way in which a cluster-forming threshold is applied in conventional activation studies. T-values exceeding the initial threshold are termed ‘cluster links’, CSS and CMS statistics are defined from these cluster links. CSS is defined as the size of a spatially distinct cluster, where each voxel in the cluster possesses at least one cluster-link with other grey matter voxels. CMS is defined as the total number of cluster-links between voxels in a distinct cluster, and the rest of the brain (see
The workflow these procedures follow is illustrated in
Illustration of data processing workflow for CSS and CMS measures. Note: The matrices are limited in size and only contain positive values for ease of exposition.
A general problem with cluster size testing (this includes NBS and SPC) is the arbitrary nature of the cluster-forming threshold
Here, we take two extreme cases to illustrate how the sensitivity and specificity of a cluster-based procedure can be affected by initial threshold choice. In permutation-based cluster tests, an initial threshold is set, and the permutation distribution is used to obtain a critical cluster size that defines significance in the experimental labelling. If the cluster-forming threshold is set very low, the critical cluster size could encompass most of the brain; this will severely limit the spatial specificity of the method. Conversely, setting the initial threshold very high could result in a critical cluster size smaller than the smoothing in the data. In the most severe case, the critical cluster size could be the size of one voxel/connection. In this situation, the ‘borrowing power’ of neighbouring voxels is not utilised. This is likely to limit the statistical power of the method: statistically, this would be very similar to a single voxel/connection test. Neither of the cases described in the text above is desirable.
Carrying out multiple tests to decide on an initial threshold post hoc is not viable as it is associated with an increased risk of false positives. Here, we describe a simple procedure to help guide the initial threshold choice. Using this method, we obtain the critical cluster size (CSS extent) associated with a particular cluster-forming threshold, without ‘looking’ to determine whether there are any significant clusters in the experimental labelling. Critical cluster size is then plotted against cluster forming threshold in an isocontour significance plot (this is similar to Friston et al
Multiple permutation distributions are calculated from the data for a range of initial threshold values. Each of these distributions produces a critical cluster size. The critical cluster size is the p<0.05 FWE corrected significance level associated with a particular cluster-forming threshold. Clusters in the data that are larger than this critical size can be declared significant at a probability corrected for family wise errors. In order to reduce computational complexity, a smaller subset of the permutation distribution can be used in place of the full set
Each critical cluster size is then plotted against the cluster-forming threshold associated with it; an example based on the data from the present study is shown in
This plot provides information on the cluster threshold and extent combinations that are required for statistical significance in the experimental labelling.
Plot of initial t-threshold (p<0.05 FWE corrected) against critical cluster extent. A cubic spline curve was fitted to the calculated data points.
The curve in
The choice of exactly what cluster-forming threshold to use is still somewhat arbitrary. However, we argue that this procedure allows the experimenter to make a more informed choice regarding initial threshold selection. Using this procedure provides the experimenter with information on what
This method utilises the spatial correlation that is intrinsic to the data to guide the selection of the cluster-forming threshold. It is therefore reasonable to use this threshold selection procedure for both the CSS and CMS methods. However, it should be noted that this cluster selection procedure is not an integral feature of CSS or CMS and any initial threshold can be used with these methods.
Receiver operator characteristic (ROC) plots were constructed from simulated data to test the efficacy of CSS and CMS methods. The performance of these procedures was evaluated in the detection of a known ‘ground truth’ contrast, corrupted by noise. ROC curves are constructed by plotting the true positive rate (TPR) against the false positive rate (FPR) of contrast detection, across a range of discrimination thresholds. The discrimination threshold determines whether a test is classified as ‘true’ or ‘false’. In the present investigation, the discrimination threshold is defined by CSS/CMS cluster size.
Standard ROC methodology is designed to deal with single inferences (e.g. is a contrast present at a single voxel? yes/no). In this framework, TPR and FPR both have straightforward definitions: TPR is the proportion of true positives identified from all actual positives; FPR is the proportion of false positives out of all actual negatives. When multiple tests are carried out simultaneously, a number of different TPR and FPR definitions exist: free response receiver operator characteristic (FROC)
The true positive rate was calculated by comparing a pure noise dataset with a dataset containing a known contrast. Calculating the false positive rate from this comparison is problematic when the test has a spatial aspect
The simulation presented here was carried out using a single brain slice. A 2-D slice was used in place of the whole brain to account for the computational demands posed by CSS and CMS statistics: Using the full 3-D dataset, each individual simulation run took over an hour on an Linux machine with 48 GB of memory and eight cores, each with 2.56 GHz of processing power, this time was decreased dramatically by reducing the simulation to two dimensions (∼2 minutes per run). A necessarily restricted 8-connectivity scheme was used to define spatially distinct clusters. All other aspects of the analysis remain the same using two in place of three dimensions. As in Zalesky et al 2010
The pre-processing carried out on the simulated data was the same as that used on the experimental data.
The process used to construct ROC curves is described in detail below:
1. Two groups filled with Gaussian random noise were constructed. Each group consisted of twelve ‘scans’. For each subject, timecourses of Gaussian random noise were generated for voxels in a single slice of the study grey matter mask; timecourses were equal in length to the experimental normocapnia/hypercapnia scans. These two groups are subsequently referred to as groups A and B.
2. A contrast + noise group was also created. Here, a time-varying sine curve was added to the timecourses of a subset of ‘contrast’ voxels in group A (see
ROC curves were calculated as the contrast parameters illustrated above were varied. The performance of methods was assessed as four parameters were varied:
3. A temporal autocorrelation structure matching that of the real data was added to voxel timecourses across subjects and groups. Data was then spatially smoothed using an 8×8 mm Gaussian kernel and low-pass filtered at a frequency of 0.1 Hz.
4. Both methods were used to calculate the true positive rate of primary cluster detection between groups A and B. TPR was calculated as |C ∩ ĥ|/|C| where C is the set of voxels associated with the primary cluster, and ĥ is the set of voxels which form clusters above the discrimination threshold. The true positive rate was calculated as a function of the discrimination threshold.
5. The FPR was calculated between groups B and C. FPR = 1 if |ĥ|≥1, FPR = 0 if | ĥ| = 0, where V denotes all voxels under analysis. The false positive rate was calculated as a function of the discrimination threshold.
6. Steps 1-5 were repeated a thousand times for each condition. The mean TPR and FPR were calculated across trials for each discrimination threshold. They were then plotted against one another.
The performance of the CSS and CMS methods was evaluated under different conditions by changing methodological parameters and contrast properties. The efficacy of CSS and CMS were tested as three contrast properties were varied:
ROC curves illustrating the performance of CSS and CMS methods as contrast and methodological properties were varied. 5a) shows how varying the initial threshold can effect performance 5b)shows the effect of contrast to noise on method performance 5c) shows how varying the number of contrast voxels changes performance 5d) illustrates how altering the primary cluster radius can effect performance. Green curves: CMS, Blue curves: CSS.
These results illustrate that the performance of CMS is generally higher than that of CSS across the range of methodological and contrast properties used.
The study was approved by the local ethics committee (College Ethics Review Board, University of Aberdeen), ethical approval was confirmed online. Written informed consent was obtained from all participants.
Measurements were carried out on a Philips 3T Achieva scanner (Philips Healhcare, Best, The Netherlands) using a 32-channel phased-array receiver coil. Gradient-echo EPI was used for the functional connectivity MRI (fcMRI). Imaging parameters were TE = 30 ms, TR = 2 s, flip angle = 78°, matrix size = 96×96, field of view = 240×240 mm2, number of slices = 32, slice thickness = 3.5 mm, parallel imaging method = SENSE, acceleration factor = 2, number of dynamic scans = 540, number of dummy scans = 4. In addition, a high-resolution T1-weighted structural scan was obtained using fast 3D gradient echo imaging. Scan parameters were TR = 8.2 s, TE = 3.8 ms, flip angle = 8°, matrix size = 240×240×125, field of view = 240×240×160 mm3, voxel size = 1.0×1.0×1.0 mm3, total acquisition time = 5 min 35 s.
Twelve healthy volunteers (seven male; mean age and SD = 24±4 years) with no medical history of migraine, anxiety or any illnesses of the heart, brain, circulatory or respiratory systems were recruited. Participants who had a family history of subarachnoid aneurysm, subarachnoid haemorrhage, intracranial aneurysm or arteriovenous malformation were excluded.
Transient hypercapnia was induced by breathing a specialised gas mixture consisting of 6% CO2, 21% O2 and 73% N2 (BOC Healthcare, Manchester, UK). Subjects were positioned supine on the patient table and wore an anaesthetic facemask (QuadraLite, Intersurgical, Wokingham, UK). A specially designed unidirectional breathing circuit (Intersurgical, Wokingham, UK; product code: 2013014) was used to deliver either room air or the 6% CO2 mixture (this circuit is illustrated in
Each scan started with two minutes where the participant was instructed to lie still and ‘think of nothing in particular'. This was followed by six minutes where visual and motor tasks were carried out. This task section was followed by two minutes where the screen went blank and the subject was again asked to do ‘nothing in particular'. The six minute task section was then repeated. Task sections were carried out under normocapnia and hypercapnia, the ordering of these sections was randomised across subjects to avoid any effects introduced by subject habituation to the scan environment. Functional connectivity was compared between the two, six-minute task sections carried out under normocapnic and hypercapnic conditions. These simple visual/motor tasks were used to keep the participants' attention focused during the scan. Tasks requiring only low cognitive demand have been argued to provide a more stable baseline in functional connectivity analyses, compared to a pure resting state condition
Standard fMRI pre-processing was carried out using the Statistical Parametric Mapping software package SPM8 (
In order to further reduce computational complexity, a study specific, binary grey matter mask was created and applied to the data. This was achieved by averaging the individual, probabilistic grey matter maps produced during segmentation, and applying a probability threshold of 0.8 for inclusion within the mask. The resulting binary mask consisted of 9,083 grey matter voxels. All further analysis of the data was restricted to the grey matter voxels defined by the binary mask. Voxel timecourses were low-pass filtered (cut-off frequency = 0.1 Hz) and baseline corrected using a 2nd order cosine basis set to remove low-frequency signal drifts. Realignment parameters were used as covariates of no interest in a voxel-wise linear regression on each timecourse and the resulting residual signal timecourses were used in all further analyses.
Connectivity matrices – also known as similarity matrices – were calculated using Pearson's correlation coefficient for each participant and condition (hypercapnia, normocapnia) from the preprocessed timecourse data.
Comparisons were made between normocapnic and hypercapnic connectivity matrices using a non-parametric paired t-test, for all 4096 permutations of the experimental labelling. As explained in the
Permutation distribution of maximum and minimum t-statistics across all matrix elements in a comparison between normocapnic and hypercapnic states. The solid lines represent p<0.05 FWE corrected significance thresholds. The dashed lines represent the maximum and minimum t-statistics in the experimental labelling.
Both maximum and minimum element-wise t-values were recorded for each permutation, to produce distributions of maximum/minimum t-statistics. Element-wise t-values in the actual, experimental labelling were then compared to these distributions. T-values in the top or bottom 2.5 percentiles of the distribution can be declared significant at the 0.05 FWE corrected level. Statistics in the top or bottom 2.5 percentile, rather than the top or bottom 5 are considered significant as the test carried out was two-sided.
The procedure described in the
Inhalation of 6% CO2 increased the across subject mean end-tidal-CO2 from 42.9±1.8 mm Hg to 52±1.7 mm Hg. These values were calculated by computing the mean Et-CO2 value across normocapnia/hypercapnia sections, then across subjects. All subjects tolerated this well; no side effects were reported by any of the participants.
In contrast to the element-wise comparison, the methods introduced in this paper (CSS, CMS) identified both significant increases and decreases (p<0.05, FWE corrected) in functional connectivity associated with the hypercapnic state. The results are shown in
Significant decreases (p<0.05 FWE corrected) in functional connectivity between normocapnia and hypercapnia, identified by the CSS and CMS statistics.
Significant (p<0.05 FWE corrected) increases in functional connectivity between normocapnia and hypercapnia identified by the CSS and CMS statistics.
Method | Cluster number | Statistic size | FWE corrected significance | Brodmann area | MNI co-ordinates |
CSS | CSS1 | 26 | 0.039 | 23 | −2 −58 27 |
CSS2 | 24 | 0.041 | 17 | −11 −92 −2 | |
CMS | CMS1 | 46 | 0.042 | 23 | −2 −58 27 |
MNI coordinates, statistic size and significance of all p<0.05 FWE corrected decreases in global connectivity between normocapnia and hypercapnia, identified by the CSS and CMS statistics.
Method | Cluster number | Statistic size | FWE corrected significance | Brodmann area | MNI co-ordinates |
CSS | CSS7 | 22 | 0.049 | 40 | 40 −35 47 |
MNI coordinates, statistic size and significance of all p<0.05 FWE corrected increases in global connectivity between normocapnia and hypercapnia, identified by the CSS and CMS statistics.
Each of the clusters of altered connectivity identified by CMS and CSS is associated with pseudo thresholded changes across the cortex. These changes can be displayed in image space.
Altered functional connectivity identified by the CSS and CMS statistics (red) with the pseudo thresholded changes that contribute to these clusters (blue). It should be noted here that only whole clusters, rather than individual connections, can be deemed to be significant.
Running both of the whole brain comparison tests introduced in this paper (CSS, CMS) required less than 22 hours of computation time on an Linux machine with 48 GB of memory and eight cores, each with 2.56 GHz of processing power. Most of this time was spent in calculating the matrix of t-statistics for each permutation of the experimental labels. Once this matrix was determined, calculating each of the cluster based statistics from the matrix required a negligible amount of computation time. For this reason, running one of the two tests separately would have required approximately the same amount of time as running them both together.
Both CSS and CMS detected changes in global connectivity between experimental conditions, while the element-wise comparison of connectivity matrices identified no significant changes when corrected for multiple comparisons (p<0.05 FWE corrected). Similar to conventional clustering methods in fMRI, CSS and CMS make use of the spatial smoothness in the data to provide an increase in statistical power. Spatial smoothness arises from intrinsic factors such as the spatial extent of the BOLD signal
Overall, CSS detected three clusters of significant connectivity change, whilst CMS detected one. Significance in CSS is determined by spatial extent, this method is therefore sensitive to spatially extended clusters. CSS detected two clusters of altered connectivity that CMS was unable to recognize. These clusters were large by volume but of low intensity, leading to lower CMS significance values relative to CSS. CMS has the potential to detect clusters that are smaller by volume but more focal in intensity than the clusters identified by CSS. As can be seen from the simulation results, CMS is generally more sensitive than CSS. However, in the present investigation, CMS did not detect any changes that CSS was unable to identify. Note that in this context, ‘intensity’ refers to the number of connectivity changes between a voxel, and all other voxels in the brain (see
CSS and CMS are capable of identifying clusters of significantly altered global connectivity. These clusters are associated with pseudo thresholded connectivity changes across the brain (cluster-links). Changes between a primary cluster and the rest of the brain may be widely distributed across the cortex, or localised to just a few areas. These different patterns of connectivity change can be seen in
In seed based connectivity mapping, connectivity is calculated between a single cortical region, and the rest of the brain. When connectivity maps are compared between groups or conditions, it is possible to identify cortical regions where connectivity is significantly altered with the seed used, with strong control over connection-wise changes. CSS and CMS methods are closely related to analyses involving the comparison of seed based connectivity maps. In CSS and CMS, connectivity matrices are compared between groups or conditions. Each column of the connectivity matrix is equivalent to a seed based map, associated with a distinct voxel ‘seed’. This initial comparison can be thought of as a test between all possible connectivity maps in the brain. CSS and CMS are defined from connectivity changes exceeding the initial threshold in spatially contiguous voxels.
The Network based statistic (NBS) is sensitive to connectivity changes that form altered network components. The main problem with NBS is that connectivity changes cannot be localised to a single area of the brain. Furthermore, NBS does not model the intrinsic spatial smoothness of BOLD fMRI data, which makes it less suitable for applications on a voxel-by-voxel level. The methods introduced here are less complex and require less computational time than spatial pairwise clustering (SPC). SPC demands the initialisation of a very large (N2-N)/2×(N2-N)/2 matrix
A challenge CSS and CMS share with other cluster-based methods such as SPC and NBS, is the need to specify a cluster-forming threshold. While this is not a problem from a statistical point of view, the initial threshold choice will affect the sensitivity and spatial specificity of the method. In this investigation, a procedure was outlined that helps guide the initial threshold choice. However, it is important to note that this procedure does not circumvent all the problems associated with the initial threshold choice. The somewhat arbitrary nature of this choice remains an issue, as it does for all cluster-based methods.
Meskaldji et al have proposed an alternative framework for the comparison of connectivity matrices; this procedure is termed subnetwork based analysis (SNBA)
In this investigation, maximum CSS and CMS statistics were calculated for positive and negative cluster forming thresholds, at each of the 4096 possible experimental permutations. Similarly, maximum and minimum t-values were calculated across all connectivity values for each permutation of the experimental labels. As noted in the
CSS and CMS were applied to compare functional connectivity between different experimental conditions (i.e., hypercapnia and normocapnia). Both methods can easily be adapted to allow for a comparison between multiple experimental conditions or between different groups of subjects by replacing the paired t-statistic (see
The connectivity analysis described here was based on BOLD fMRI data. However, CSS and CMS methods could equally well be applied to other modalities which are capable of producing connectivity data, for example: electroencephalography or diffusion tensor imaging.
The primary objective of using hypercapnia in this study was to induce transient changes in functional connectivity in order to test the sensitivity of the CSS and CMS methods, rather than to investigate any specific effects of hypercapnia on functional connectivity or to study the mechanisms underlying BOLD fMRI. However, the findings presented here may have implications for the experimental design of calibrated fMRI studies, and are therefore discussed in more detail in this section.
The BOLD effect relies on the variation of magnetic susceptibility in brain tissue caused by changes in blood oxygenation. Because the BOLD effect is not a direct measure of neuronal activity, the signal measured is subject to non-neuronal, physiological confounds. Calibration methods utilising the hypercapnic state are theoretically able to remove many of these confounding effects
The neural response to the hypercapnic challenge is difficult to characterise using BOLD fMRI. CO2 is a potent vasodilator and therefore has an effect on the BOLD signal that is at least partly independent of any metabolic demands
In this study, both increases and decreases in functional connectivity were observed during hypercapnia (see
Generally, a decrease in functional connectivity under hypercapnic conditions can be explained by a decrease in the relative vascular response to metabolic demands as originally proposed by Biswal et al. (1997). However, this mechanism cannot explain the observed increases in functional connectivity during hypercapnia (exhibited by cluster CSS3), unless the increase in functional connectivity is driven by a reduction in anticorrelation. Further analysis provided no evidence for decreases in anticorrelation, and showed that the observed changes were genuine, absolute increases in connectivity.
While the observed increases in functional connectivity may suggest changes in neuronal activity, this hypothesis cannot be proven on the basis of current data as this inference is indirect. In this study, the hypercapnic state was induced through the inhalation of a fixed concentration of CO2 gas. Wise et al have shown that this method of inducing hypercapnia is associated with a change in arterial O2; this leads to fluctuations in the BOLD signal that are not accounted for
To help account for these problems, an interesting prospective area of study would be a simultaneous EEG-fMRI resting state investigation, taken under normal and hypercapnic conditions. A study of this type would be able to take advantage of the superior spatial resolution of fMRI whilst utilising EEG as a more direct measure of neuronal activity. As the level of neuronal activity is closely linked to the cerebral metabolic rate of oxygen (CMRO2), a confirmation of altered neuronal activity during hypercapnia would have direct implications for the experimental design of calibrated fMRI studies
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