2.8. Within-network static functional connectivity and dynamic functional connectivity
The individualized network parcellation39 outputs network rather than node-level labels. Thus, to calculate within-network connectivity measures for each subject, each network was first split into constrained anatomical nodes. This was performed by binarizing each network label in Freesurfer for each individual, followed by the mri_surfcluster command. Consequently, the number of nodes for each network could differ between patients. To calculate within-network sFC, average resting-state time series were extracted from nodes of each network across both hemispheres. For each of the 18 networks in each patient, pairwise Pearson correlations were performed between time series of every pair of nodes within the network, followed by Fisher r-to-z transformation of these correlation values. These measures were then averaged for each network and for each subject. Thus, each subject had 18 within-network sFC values corresponding to each of their 18 individualized networks. For within-network dFC, the dynamic conditional correlation method was applied between time series of every pair of nodes within each network. The SD of each dynamic conditional correlation was then taken as a measure of dFC as per done previously6 and shown to be test–retest reliable.8 These dFC values were then averaged within each network. Thus, each subject had 18 within-network dFC values corresponding to each of their 18 individualized networks.
2.9. Cross-network static functional connectivity and dynamic functional connectivity
The average time series for each of the 18 individualized resting-state networks across the brain was extracted for each subject. To calculate cross-network sFC in each subject, Pearson correlations were performed between averaged time series of every pair of networks, followed by Fisher r-to-z transformation of these correlation values. Thus, 153 unique internetwork sFC measures were generated for each subject. To calculate internetwork dFC in each subject, the dynamic conditional correlation method was applied between averaged time series of every pair of networks. The SD of each dynamic conditional correlation was then taken as a measure of dFC. Thus, 153 unique internetwork dynamic connectivity measures were generated for each subject.
2.10. Machine learning: elastic-net regularized cross-validated regression
Multiple linear regression is a useful technique for analyzing the association between many independent variables and a continuous dependent variable. However, given the presence of many independent variables (dFC and sFC in this study), overfitting and problems with multicollinearity can arise.19 One solution is to include only the relevant independent variables in the model by penalizing greater model complexity—a technique called regularization.42 Thus, we used elastic-net regression45—a type of regularized multiple linear regression—to look at the association between brain connectivity (dFC and sFC) and pain (state and trait) (Fig. 3 for methods schematic). To perform the necessary parameter tuning involved with elastic-net regression, and to test the generalizability of the outputted multivariate brain model for pain, we implemented elastic-net regression within a nested cross-validation framework. In a nested cross-validation, the whole data set is split into a training set and a testing set for each outer fold. The training set in the outer fold is then further split into a training set and a testing set for each inner fold (Fig. 3). During inner fold cross-validation, optimization of parameters for elastic-net (alpha and lambda) is performed, and the multivariate model of brain connectivity for pain is created. The value of lambda determines the amount of regularization that is performed, and a range of 50 values to cross-validate across from ∼0.01 to 1 was supplied. Alpha determines whether the model is lasso-regularized (alpha = 1; regression coefficients can be set to 0), ridge-regularized (alpha = 0; regression coefficients are minimized but not equal to 0), or in-between (elastic-net). The 3 values of alpha cross-validated across were 0.1, 0.5, and 1. A value 0.1 rather than 0 was chosen as a lower limit of alpha, as we did not expect every independent variable to be associated with the outcome variable, and thus wanted at least a minimal level of feature selection. Thus, a total possible 150 parameter combinations were tested within the inner loop. The combination of alpha and lambda that led to the lowest average mean squared error across folds was determined within the inner loop, and then the entire training set of the outer loop was trained using this parameter combination to derive the multivariate brain model of pain. To determine the goodness of this model, or the ability to generalize to new data, this model was tested on the testing data within the outer fold. Here, the brain connectivity features of the testing subjects were provided, but their self-reported pain ratings were not. If the multivariate model developed within the inner fold captured generalizable associations between brain connectivity features and pain, the model estimates of pain based on the testing subjects' brain connectivity would be positively correlated with their self-reported pain ratings. Within both the inner and the outer folds, K-fold rather than leave-one-out cross-validation was used, as leave-one-out cross-validation suffers from higher variance and thus does not yield stable estimates of predictive accuracy.38 For analyses that used all subjects, 20-fold cross-validation was used within the outer loop, and 10-fold cross-validation was used within the inner loop. With analyses that looked separately at patients with non-NP and NP, 10-fold cross-validation was used within the outer loop because of a fewer number of subjects, and 10-fold cross-validation was used within the inner loop.
As a measure of performance, a Spearman correlation was run between model estimates of the outcome variable across all folds of the outer loop, with actual values of the outcome variable itself. Statistical significance testing of the models was performed using permutation-based testing, with significance set at P < 0.05. Permutation-based significance testing was only performed in models where a positive correlation was observed between model estimates and actual ratings. If a negative correlation was observed between model estimates and actual ratings, then these models were not statistically significant (P > 0.05). For permutation-based significance testing, the dependent variable (self-reported pain) was shuffled from the independent variables (dFC and sFC) across subjects through random permutation, and the entire machine learning procedure was repeated. This was iterated 2500 times. The P value was calculated by finding the proportion of iterations in which the shuffled model had a larger correlation value between model estimates and actual ratings, in comparison with the correlation value derived from the unpermuted model.
We derived 12 multivariate brain connectivity models for pain in total. Two examined the relationship between cross-network brain measures with state and trait pain, and 2 examined the relationship between within-network brain measures with state and trait pain. Each analysis was then repeated for patients with NP and non-NP separately to see whether the model differed according to these groups.
2.11. Feature extraction and correlation with forward model
The magnitude of the multivariate weight for each feature can represent the importance of the feature for the model. Here, we extracted the multivariate weights to determine the features that drove the significant brain models of AS-related pain. To do this, the median regression coefficient for each feature was taken across all the outer-fold models. This was done because with each elastic-net regression run, the number of models generated was equivalent to the number of outer folds. However, it has also been shown that the magnitude of a multivariate weight may not be related to the amount of “signal” (relationship with state pain here) for each feature.14 Rather, a forward modeling approach, such as examining the covariance between each feature (dFC and sFC) and the dependent variable (pain), may be more appropriate.12,14 Thus, we also compared the multivariate weights with the covariance pattern before we interpreted the magnitude of the multivariate weights as a proxy of feature importance. To do so, we compared the median multivariate weight for each feature with the covariance of that feature with pain to determine whether their sign (positive/negative) was in the same direction. We also ran a Spearman correlation between the multivariate weight pattern with the covariance pattern to determine whether they were similar or different.
2.12. Comparison of brain features between patients with neuropathic pain and healthy controls
As the cross-network brain models for state and trait NP were statistically significant (see Results), we investigated whether the magnitude of NP resulted in more prominent abnormalities across the top-10 features of these models compared with healthy controls. To do so, we compared patterns of brain connectivity across these top features between patients with NP and their age-/sex-matched healthy controls. For the top-10 features selected in a cross-network brain model for pain, the appropriate dFC and sFC values were extracted for each patient with NP and their age-/sex-matched healthy control. Separately for each patient and their matched healthy control, a Spearman correlation was then run between these extracted features. This yielded a correlation value for each patient, representing the similarity across these features to their matched healthy control. A Spearman correlation was then used between this similarity measure and patients' pain (state or trait depending on the model assessed) across all patients with NP. This analysis was repeated for both the cross-network brain model for state and trait pain.
3.1. Dissociation between pain intensity and pain pathophysiology
Across all patients, state pain ranged from 1 to 9, with a mean ± SD of 3.3 ± 2.2. Trait pain ratings were slightly higher on average across subjects, ranging from 1 to 8, with a mean ± SD of 4.0 ± 2.2. State and trait pain ratings were significantly positively correlated across all patients (Spearman rho = 0.74, P = 6.36 × 10−11). Large interindividual differences were observed in painDETECT ratings, ranging from 0 to 24, with a mean ± SD of 9.4 ± 5.5. The NP and non-NP groups were not statistically different in terms of state pain (meanNP ± SDNP = 4.1 ± 2.4, n = 19; meannon-NP ± SDnon-NP = 2.9 ± 2.0, n = 39; t = 1.9, P = 0.074) or trait pain (meanNP ± SDNP = 4.6 ± 2.0, n = 20; meannon-NP ± SDnon-NP = 3.8 ± 2.3, n = 43; t = 1.4, P = 0.18). The patients with NP who provided state pain ratings included 14 men and 5 women with a mean ± SD age of 38.9 ± 9.8, whereas the patients with NP who provided trait pain ratings included the previous subjects with an additional woman and a mean ± SD age of 39.0 ± 9.5. The patients with non-NP who provided state pain ratings included 29 men and 10 women with a mean ± SD age of 33.1 ± 11.3, whereas the patients with non-NP who provided trait pain ratings included 30 men and 13 women with a mean ± SD age of 32.1 ± 11.2.
Furthermore, there were no sex differences in state pain (meanfemales ± SDfemales = 4.2 ± 2.6, n = 15; meanmales ± SDmales = 3.1 ± 2.0, n = 43; t = 1.5, P = 0.14), trait pain (meanfemales ± SDfemales = 4.3 ± 2.4, n = 19; meanmales ± SDmales = 3.9 ± 2.2, n = 44; t = −0.62, P = 0.54), or painDETECT scores (meanfemales ± SDfemales = 9.9 ± 4.8, n = 20; meanmales ± SDmales = 9.1 ± 5.8, n = 50; t = −0.57, P = 0.58).
3.2. State pain can be modeled by multivariate cross-network but not within-network functional connectivity
We found a profound difference in the generalizability of models of state pain based on within-network connectivity vs cross-network connectivity. The multivariate brain model for state pain derived using within-network sFC and dFC failed to generalize to unseen (left-out) subjects (Spearman rho = 0.21, P = 0.17). By contrast, the multivariate brain model for state pain derived using cross-network sFC and dFC generalized to unseen subjects, with model-estimated state pain being significantly correlated with self-reported state pain (model 1 in Fig. 4; Spearman rho = 0.41, P = 0.01). In Figure 4, we further show how the model estimate of pain differs from the self-report of pain for each individual. The deviation of the regression line from a perfect model (ie, the dotted line where y = x) indicates model overestimates and underestimates of pain. For state pain, these 2 lines cross at a level of approximately 3/10 pain and the y-intercept is approximately 2.5. Thus, for subjects who reported a state pain ∼ <3, the model tended to overestimate their pain, whereas the model tended to underestimate pain for subjects who reported a state pain >3 (model 1 in Fig. 4).
To determine whether the generalizability of the cross-network model of state pain was driven by a particular type of pain, we constructed separate cross-network models for the patients with NP (model 2) and non-NP (model 3) (Fig. 4). These specific pain type models indicate that model 1 was likely driven by the patients with NP. Specifically, there was a stronger relationship between model-estimated state pain and self-reported state pain within NP patients alone (model 2 in Fig. 4; Spearman rho = 0.55, P = 0.03) than within non-NP patients alone (model 3 in Fig. 4; Spearman rho = −0.09, P > 0.05), and all subjects combined (model 1: Spearman rho = 0.41). By contrast, the ability of model 1 to generalize to unseen subjects was not driven by sex (women: Spearman rho = −0.27, P > 0.05; men: Spearman rho = 0.05, P = 0.16) or treatment effects (no biologics: Spearman rho = 0.27, P = 0.12; biologics: Spearman rho = −0.06, P > 0.05).
In examining the pain estimates in model 2, it was similar to model 1 in which it overestimated low levels of self-reported pain and underestimated higher levels of self-reported pain. For completion, we also constructed within-network models of state pain in NP and non-NP patients alone, but these models did not generalize to unseen subjects (Spearman rho = −0.11, P > 0.05; Spearman rho = −0.18, P > 0.05, respectively).
3.3. Features of cross-network functional connectivity that drive the multivariate model of state neuropathic pain
We found that the multivariate weight for each feature selected always had the same sign (positive/negative) as the covariance of that feature with state pain. Furthermore, the multivariate weights were highly correlated with the covariances across the selected features (Spearman rho = 0.74, P = 2.23 × 10−7, n = 41). In comparing the cross-network dFC and sFC features (Fig. 5), cross-network dFC features generally had larger magnitude weights than the sFC features selected (absolute meandFC ± SDdFC = 0.85 ± 0.87, n = 21, absolute meansFC ± SDsFC = 0.34 ± 0.35, n = 20, t = 2.5, P = 0.019). Examining these weight patterns, greater cross-network dFC was also typically associated with less pain (negative regression weights), whereas greater sFC was typically associated with more pain (positive regression weights). For each feature selected, we also plotted the dFC and sFC for a single patient with NP, and for comparison, the dFC and sFC for these features in an age-/sex-matched healthy control (Fig. 5).
3.4. Multivariate cross-network functional connectivity models trait pain in patients with neuropathic pain but not non–neuropathic pain
When we investigated whether cross- or within-network brain connectivity was associated with patients' trait pain, we found that the multivariate cross-network (model 4 in Fig. 4) and within-network brain models for trait pain derived across all subjects did not generalize to unseen subjects (Spearman rho = −0.22, P > 0.05; Spearman rho = −0.28, P > 0.05, respectively). However, the multivariate cross-network brain model for trait pain derived in patients with NP (model 5 in Fig. 4) but not non-NP (model 6 in Fig. 4) was able to generalize to unseen subjects (Spearman rho = 0.72, P = 0.004; Spearman rho = −0.08, P > 0.05, respectively). In examining the pain estimates in model 5, it was similar to model 2 in which it overestimated low levels of self-reported pain and underestimated higher levels of self-reported pain.
We next examined the features selected in the cross-network brain model for trait pain derived in patients with NP (model 5). The multivariate weight for each feature always had the same sign as the covariance of that feature with trait pain. The multivariate weights were also strongly correlated with the covariances across the selected features (Spearman rho = 0.48, P = 1.25 × 10−6, n = 93). Similar to model 2, cross-network dFC features generally had larger magnitude weights than the sFC features selected (absolute meandFC ± SDdFC = 0.80 ± 0.75, n = 43, absolute meansFC ± SDsFC = 0.14 ± 0.17, n = 50, t = 5.64, P = 1.0 × 10−6) (Fig. 6). However, different from model 2 was that more features were selected in the trait pain compared with the state pain model (n = 93 vs 41; Fig. 6 vs Fig. 5, respectively), reflected by a more ridge-like regularization penalty selected in the model (median alpha = 0.1 vs 0.5, respectively).
For completion, we also generated multivariate within-network brain models for trait pain in patients with NP and patients with non-NP, but these models were unable to generalize to unseen subjects in their respective groups (Spearman rho = −0.40, P > 0.05; Spearman rho = −0.13, P > 0.05, respectively).
3.5. Cross-network brain models for state and trait neuropathic pain are not driven by head motion
As head motion may cause spurious correlations in FC,31 we also repeated the model building of models 2 and 5 but with mean relative head displacement for each subject included as an additional independent variable. Mean relative head displacement was not selected as a feature in either of these models. In addition, similar correlations were observed between model estimates and self-report for the state and trait NP models when mean relative head displacement was accounted for (Spearman rho = 0.52, P = 0.035 and Spearman rho = 0.78, P = 0.0016, respectively), compared with when it was not (Spearman rho = 0.55, P = 0.03 and Spearman rho = 0.72, P = 0.004, respectively).
3.6. Top features in the multivariate cross-network brain models for neuropathic pain are dynamic functional connectivity features
To visualize the top-10 most important features in the cross-network brain models for state and trait NP (models 2 and 5, respectively), we created circle plots (Fig. 7; Figs. 1 and 2 for corresponding network visualization). For the cross-network brain model of state pain, 8/10 top features were cross-network dFC and 2 were cross-network sFC (Table 2 and Fig. 7). Of these top-10 dFC features, cross-network dFC with executive control networks (ECN with visual, somatomotor, limbic networks as well as the DMN, and dpINS) was negatively related to state pain, whereas cross-network dFC with limbic networks (limbic with attention and SN/ECN) was positively related to state pain. Of the sFC features (DMN with the attention and somatomotor networks) within the top-10, cross-network sFC was positively related to state pain.
For the cross-network brain model of trait pain, all the features with the top-10 greatest multivariate weights were dFC features (Table 2 and Fig. 7). Similar to findings with state pain, cross-network dFC with ECNs (ECN with visual, somatomotor, attention networks as well as the dpINS) was negatively related to trait pain, and cross-network dFC with limbic networks (limbic with attention and SN/ECN) was positively related to trait pain. Unique to trait pain, however, was that cross-network dFC with DMNs (DMN with somatomotor and SN/ECN as well as the dpINS) was additionally positively related to trait pain.
3.7. Greater magnitude of trait pain in patients with neuropathic pain is associated with greater brain abnormalities
We also investigated whether the magnitude of NP resulted in more prominent abnormalities across the top-10 features of the significant brain models for state and trait pain compared with age-/sex-matched healthy controls. There were no statistically significant differences in age between patients with NP and matched healthy controls for the state pain analysis (meanNP ± SDNP = 38.9 ± 9.8; meancontrols ± SDcontrols = 37.8 ± 11.1; P = 0.75, t = 0.32) nor for the trait pain analysis (meanNP ± SDNP = 39.0 ± 9.5; meancontrols ± SDcontrols = 37.9 ± 10.8; P = 0.74, t = 0.34). We found that for the top-10 features selected in the cross-network brain model for trait pain (model 5), NP patients with milder trait pain showed more correspondence with their matched healthy control than patients with greater pain (Fig. 7; Spearman rho = −0.58, P = 0.008). Although a similar trend was observed with the top-10 features selected in the brain model for state pain (model 2), this relationship was not statistically significant (Spearman rho = −0.38, P = 0.11).
This is the first study to reveal how dynamics in brain communication relate to fundamental characteristics and timescales of chronic pain, using a machine learning approach. Our key findings were (1) the most prominent networks in our models were the default mode, salience, and ECNs, (2) state and trait chronic pain are related to patterns of cross-network but not within-network dFC and sFC, (3) the cross-network brain–pain relationships were present in patients with NP but not non-NP, (4) dynamic connectivity patterns form the core of multivariate cross-network models of chronic pain in AS with only a minor contribution from sFC features, (5) the cross-network brain model for trait pain is more complex and comprised of more features than the model for state pain, and (6) patients with NP with milder trait pain show greater brain network similarity to healthy controls than patients with greater pain. This study demonstrates that measures of brain dynamics most sensitively reflects trait pain in patients with NP features.
We and others have previously shown that patients with chronic pain can exhibit altered cross-network sFC.1,16,30 However, brain communication and FC fluctuates over various timescales,17,20 and the characterization of dynamics provides information not captured by sFC.26 This is especially pertinent in the scope of cross-network communication, as intermodular/network connections are typically the most dynamic across the brain.44 Thus, this may underlie the finding here that most of the top features within the cross-network brain model of pain were dFC features. By contrast, patterns of within-network dFC and sFC were not associated with chronic state or trait pain. These findings may seem contradictory to other previous studies, which have found abnormalities in within-network functional communication in patients with chronic pain other than AS.4,23 However, we used an individualized functional mapping approach to delineate networks separately for each patient. Thus, abnormalities in within-network functional communication related to patients' pain may have been accounted for during the mapping of these individualized networks.
Also, previously unknown was whether these brain abnormalities represent a general state of chronic pain (ie, trait pain) or the patients' level of pain during the day of the scan (ie, state pain), which often fluctuates. In comparing the cross-network brain models for state and trait pain in patients with NP, key differences were found. The first was that many more brain connectivity features were selected in the multivariate model for trait rather than state pain. Second, the correlation between self-reported pain and model estimates made by the cross-network brain model of trait pain was marginally higher than that for state pain (Spearman rho = 0.72 vs 0.55, respectively). Thus, measures of patients' brain communication at rest were more highly and widely related to their trait compared with state pain. In comparison with healthy individuals, patients' brain networks related to trait rather than state pain were also increasingly abnormal with the level of their pain. One hypothesis for this amalgamation of findings is that as patients' pain often fluctuates over time, an assessment of pain averaged over a longer period may be more indicative of their current condition than an assessment of pain of the moment. Measures of resting-state dFC and sFC taken across the entire scan have also been shown to be test–retest reliable across neuroimaging sessions within individuals,7,8 capturing trait-like properties. Accordingly, trait-like brain measures captured during the resting-state was better able to reflect trait-like pain features across patients.
When the top features in the cross-network brain models for state and trait pain were examined, greater dFC with ECN was associated with less pain. This is consistent with our previous finding in healthy individuals, where greater cross-network dFC between the ECN and SN was associated with a better ability to cope with pain—as proxied by the individual's ability to prioritize cognitive task performance over attention to pain.6 In chronic pain, the dorsolateral prefrontal cortex, a hub of the ECN,34 has been shown to exhibit decreased gray matter across a broad range of chronic pain conditions.35 This region, typically ascribed to play an important role in cognitive control,29 also plays an important role in pain suppression.35 Thus, greater dynamic engagement of this area and its broader network in patients may be associated with a better ability to suppress pain. By contrast, greater dFC with limbic networks was associated with greater pain. This finding is consistent with a previous study on patients with persistent chronic back pain, which demonstrated that the brain representation of chronic pain predominated in emotion-/reward-related circuitry.13
Here, we found that although a multivariate model for state pain could be generated across all subjects, this was driven by patients with NP. Likewise, trait pain could be modelled by cross-network brain features in patients with NP only, and not in patients with non-NP or all patients together. This finding may reflect a greater sensitivity of dynamic measures of brain communication to behavioral measures that encompass dynamics as well, as NP typically involves fluctuating, spontaneous, and ongoing pain. Perhaps, in addition to sFC and dFC measures, other brain measures such as inflammation-linked proteins detected by PET,27 may be more sensitive to determine brain models that are highly associated with inflammatory pain or non-NP. Altogether, these findings highlight the importance of considering additional factors such as the type of pain presented when developing multivariate brain models for chronic pain, as heterogeneity in pain types may exist across patients grouped within the same diagnostic criteria. However, a limitation of this study was that we did not determine how well the findings would generalize for data that are acquired from a different scanner, or with different acquisition parameters.
Finally but importantly is the issue of the application of multivariate brain models of chronic pain for the diagnosis of chronic pain and treatment prognostication. The legal and ethical ramifications surrounding this topic have recently been discussed, and recommendations for the use of functional MRI offered by an international task force of experts.9 Findings from our study here support the task force findings that the application of machine learning and multivariate modeling to neuroimaging can provide great insight into the pathophysiology of chronic pain but should not be used to infer the presence or level of pain in an individual patient. Specifically, we found that the assessment of multivariate brain models on unseen/testing subjects in cross-validation was important for evaluating the goodness of the model, before interpreting associations between the independent (eg, brain measures) and dependent (pain) variables in the model. Although permutation testing showed that the cross-network brain models of AS-related pain in patients with NP were statistically significant in this study, predictions were not consistently accurate. Specifically, there was a tendency of these models to overestimate pain in patients with mild pain, and underestimate pain in patients with moderate to high levels of pain. Thus, although these models are useful for examining the association between multivariate patterns in brain connectivity and pain, estimates of pain in unseen subjects used for model evaluation purposes should not currently be used in lieu of self-reported pain in the clinic—which remains the gold standard.9
Conflict of interest statement
The authors have no conflict of interest to declare.
This work was supported by the Canadian Institute of Health Research (operating grant to K.D.D.); Strategy for Patient-Oriented Research (SPOR) funding of the Canadian Chronic Pain Network; and The Mayday Fund. J. Cheng and K. Hemington are recipients of a Canadian Institute of Health Research Doctoral Research Award. A. Kucyi was supported by a Banting fellowship from Canadian Institute of Health Research.
The authors thank Dr Adrian Crawley, Dr Judith Hunter, and Dr Paul Dufort for helpful insights and technical assistance with data analysis and interpretation, and Eugen Hlasny and Keith Ta for expert technical assistance in MRI acquisition.
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Keywords:© 2018 International Association for the Study of Pain
Ankylosing spondylitis; Pain; Dynamic functional connectivity; Machine learning