Demographic and clinical data

This study included 350 participants—70 HCs, 100 patients with CM, 40 patients with CMFM, 35 patients with FM, 30 patients with CTTH, and 75 patients with EM. Of them, the data of 56 HCs and 80 patients with CM were included in the training dataset. Table 1 provides a summary of the demographic and clinical characteristics of all the participants in the training dataset. The two groups in the training dataset did not significantly differ in terms of age or sex. Anxiety (HADS_A) and depression (HADS_D) scores were higher in the CM group than in the HC group (HADS_A, p < 0.001; HADS_D, p < 0.001). The testing dataset consisted of the data of 14 HCs, 20 patients with CMs, 40 patients with CMFM, 35 patients with FM, 30 patients with CTTH, and 75 patients with EM (Table 2). The groups in the testing dataset did not significantly differ in terms of age. However, the FM group included significantly more women than those in the CM, EM, and CTTH groups (CM, p = 0.02; EM, p < 0.001; CTTH, p < 0.001). Similar to the findings for the groups in the training dataset, anxiety and depression scores were lower in the HC group than in the other pain disorder groups (anxiety: CM, p < 0.001; CMFM, p < 0.001; EM, p < 0.001; FM, p < 0.001; CTTH, p = 0.001. depression: CM, p = 0.007; CMFM, p < 0.001; FM, p = 0.001; CTTH, p = 0.043). As expected, the patients with CM or CMFM had more monthly headache days than did those with EM (CM, p < 0.001; CMFM, p < 0.001). The CTTH group had lower headache severity in the last year than did the CM, CMFM, and EM groups (CM, p = 0.001; CMFM, p < 0.001; EM, p < 0.001). The MIDAS scores were higher in the patients with CM or CMFM than in those with EM (CM, p = 0.023; CMFM, p = 0.002). Notably, psychometric scores were comparable among the CM, CMFM, CTTH, FM, and EM groups.

Table 1 Demographics and clinical profiles of participants in the training dataset Table 2 Demographics and clinical profiles of participants in the testing data sets Aberrant FC within distinct network in pain disorders

FC measures revealed significant alterations in node strength within specific networks for the pain disorder groups compared with the HC group. In the PN, beta connectivity and gamma connectivity were decreased in the CM, CMFM, and EM groups (all p < 0.05 with FDR corrections and t-values represented using colour coding). In the gamma band, a large portion of pain-related areas exhibited alterations. However, in the beta band, more areas (except the left SI and SII) were preserved in the EM group than in the CM and CMFM groups. Decreased connectivity in the theta and alpha bands was observed only in the CM group. Moreover, although the CTTH group exhibited decreased PN connectivity in the gamma band, the FM group exhibited intact FC. In general, in the PN, patients with CM presented widespread spatial and multifrequency deteriorations. These discriminative connections were illustrated by adjacency matrices spanning from the delta to gamma bands between the HC and pain disorder groups (left part of Fig. 2), and these features were topographically displayed on axial MRIs in different frequency bands (right part of Fig. 2).

Fig. 2

Aberrant pain-network connectivity in pain disorders. Differences in oscillatory connectivity within the pain-related network between patients with distinct pain disorders and healthy controls (HCs). The t-value matrix presents statistical results for groups with a spatial-oscillatory pattern. The t values are then mapped onto brain images in the axial view, with colours representing corresponding values. CM, chronic migraine; FM, fibromyalgia; CMFM, CM with comorbid FM; CTTH, chronic tension-type headache; EM, episodic migraine; L, left; R, right. Ins, insula; MF; medial frontal; SI, primary somatosensory; MI, primary motor; SII, secondary somatosensory; ACC, anterior cingulate cortex; L, left; R, right; *, corrected p < 0.05

In the DMN (Fig. 3a), we noted a decrease in beta and gamma connectivity in the CM, CMFM, and EM groups (all corrected p < 0.05 with t-values represented using colour coding). However, the CMFM group exhibited the highest number of affected brain areas, followed by the CM and EM groups. In addition, decreased gamma band connectivity was observed in the CTTH and FM groups. The CTTH group exhibited only a few alterations only in the right medial frontal and left precuneus areas. In summary, the CM and CMFM groups exhibited a significant decline in DMN function, whereas the CTTH and EM groups exhibited minimal deviations in FC. In the SMN (Fig. 3b), we observed decreased theta and gamma connectivity in the SI, SII, and MI areas in the CM, FM, and EM groups (all corrected p < 0.05 with t-values represented using colour coding). Altered alpha connectivity and beta connectivity were noted in the right MI area in the CM group. Decreased connectivity was detected in few SMN areas in the CMFM and CTTH groups. However, the CM group exhibited abnormal connectivity between most SMN areas across various frequency bands. In the VN (Fig. 3c), the CMFM and FM groups exhibited decreased connectivity, whereas the CM and CTTH groups exhibited normal connectivity. Regarding Ins–DMN connectivity (Fig. 3d), alterations in connectivity in the beta and gamma frequency bands were observed in the CM, CMFM, and FM groups. Only the FM group exhibited a reduction in theta connectivity. Taken together, these findings indicate that each pain disorder has neuropathological mechanisms that might be characterised by aberrant network connectivity, as depicted in Fig. 4, from the perspectives of networks and frequency bands.

Fig. 3

Altered network connectivity in pain disorders. Differences in oscillatory connectivity within the default mode network (DMN), sensorimotor network (SMN), visual network (VN), and insula to DMN network (Ins-DMN) between patients with distinct pain disorders and healthy controls (HCs). The t-value matrix presents statistical results for groups with a spatial-oscillatory pattern. CM, chronic migraine; FM, fibromyalgia; CMFM, CM with comorbid FM; CTTH, chronic tension-type headache; EM, episodic migraine; IP, inferior parietal; MF; medial frontal; MT, medial temporal; Prc, precuneus; PCC, posterior cingulate cortex; LT, lateral temporal; SI, primary somatosensory; MI, primary motor; SII, secondary somatosensory; V1, primary visual cortex; L, left; R, right; *, corrected p < 0.05

Fig. 4

Summary of altered oscillatory connectivity within distinct networks in different pain disorders. CM, chronic migraine; FM, fibromyalgia; CMFM, CM with comorbid FM; CTTH, chronic tension-type headache; EM, episodic migraine; PN, pain-related network; DMN, default mode network; SMN, sensorimotor network; VN, visual network; Ins-DMN, insula to DMN

Classification model using network connectivity for CM

By utilising discriminative features obtained from FC between the HC and CM groups (as mentioned in the earlier text), which included oscillatory connectivity at various frequencies within the PN, DMN, SMN, and Ins–DMN, we established training datasets for constructing classifiers. We examined the performance of different classification models based on the combinations of these prominent networks: (1) PN, DMN, SMN, and Ins–DMN; (2) PN, DMN, and SMN; (3) PN, DMN, and Ins–DMN; (4) PN, SMN, and Ins–DMN; (5) PN and DMN; (6) PN and SMN; (7) PN and Ins–DMN; (8) PN; (9) DMN; (10) SMN; and (11) Ins–DMN.

The classification models exhibited varying accuracies, ranging from 74.3 to 92.6%, for differentiating between CM and HC in the training datasets (Fig. 5a and b) by using the discriminative features of the following networks: (1) PN, DMN, SMN, and Ins–DMN (SVM with median gaussian kernel; accuracy: 92.6%, sensitivity: 0.97, specificity: 0.86, AUC: 0.93); (2) PN, DMN, and SMN (SVM with median gaussian kernel; accuracy: 91.2%, sensitivity: 0.96, specificity: 0.84, AUC: 0.93); (3) PN, DMN, and Ins–DMN (SVM with median gaussian kernel; accuracy: 91.2%, sensitivity: 0.95, specificity: 0.85, AUC: 0.92); (4) PN, SMN, and Ins–DMN (SVM with linear kernel; accuracy: 91.2%, sensitivity: 0.97, specificity: 0.82, AUC: 0.9); (5) PN and DMN (SVM with median gaussian kernel; accuracy: 89.9%, sensitivity: 0.95, specificity: 0.82, AUC: 0.9); (6) PN and SMN (SVM with median gaussian kernel; accuracy: 89.7%, sensitivity: 0.96, specificity: 0.8, AUC: 0.9); (7) PN and Ins–DMN (SVM with median gaussian kernel; accuracy: 86.0%, sensitivity: 0.94, specificity: 0.75, AUC: 0.88); (8) PN (SVM with median gaussian kernel; accuracy: 88.2%, sensitivity: 0.95, specificity: 0.78, AUC: 0.9); (9) DMN (SVM with fine gaussian kernel; accuracy: 81.6%, sensitivity: 0.96, specificity: 0.61, AUC: 0.77), (10) SMN (SVM with median gaussian kernel; accuracy: 80.1%, sensitivity: 0.98, specificity: 0.53, AUC: 0.79), and (11) Ins–DMN (SVM with fine gaussian kernel; accuracy: 74.3%, sensitivity: 1.0, specificity: 0.37, AUC: 0.7). These results indicate the varying performance of different classification models based on the different combinations of prominent networks. Models with performance values below 0.75 were excluded from further validation, including those constructed from the DMN, SMN, and Ins–DMN alone. In addition, the averaged Shapley values for the eight classification models revealed the significance of each brain area within the networks for identifying patients with CM. Furthermore, these values were visually represented on axial MRIs (Fig. 5c and d). In particular, the connectivity of the MI, SI, SII, ACC, and insula areas was crucial for constructing a reliable classification model.

Fig. 5

Performance of classification models with distinct network features for CM versus HC. a Comparisons of model performance with distinct features. b Receiver operating characteristic curves and area under the curve (AUC) values for different models. c Averaged Shapley values from prominent models for different brain areas. d Shapley values are then mapped onto axial-view brain images and colour-coded. PN, pain-related network; DMN, default mode network; SMN, sensorimotor network; VN, visual network; Ins-DMN, insula to DMN. MT, medial temporal; LT, lateral temporal; IP, inferior parietal; PCC, posterior cingulate cortex; Prec, precuneus; MF, media frontal; Ins, insula; ACC, anterior cingulate cortex; MI, primary motor; SI, primary somatosensory; SII, secondary somatosensory; L, left; R, right

Generalisability of the classification model

To examine the generalisability of the eight classification models, we utilised an independent dataset containing the data of 20 patients with CM and 14 HCs. These models demonstrated high accuracies, ranging from 85.3 to 97.0% (all p < 0.0001), and excellent AUC values, ranging from 0.84 to 0.97 (Fig. 6a). In addition, we evaluated the performance of these models for distinguishing CM from other chronic pain disorders by using the following datasets. (1) The first dataset consisted of the data of 20 patients with CM and 40 patients with CMFM (Fig. 6b). The model yielded favourable results with accuracies ranging from 83.3 to 95.0% (all p < 0.0001) and AUCs ranging from 0.82 to 0.95. However, the model that incorporated features from the PN, SMN, and Ins–DMN exhibited a lower accuracy and AUC of 0.62. (2) The second dataset consisted of the data of 20 patients with CM and 35 patients with FM (Fig. 6c). Some models, specifically those incorporating features from (a) the PN, DMN, SMN, and Ins–DMN; (b) PN, DMN, and SMN; and (c) PN and DMN, displayed high accuracies (all p > 69.1% and p < 0.001) and AUC values (all p > 0.7). (3) The third dataset contained the data of 20 patients with CM and 30 patients with CTTH (Fig. 6d). Similar to the validations of CM versus FM, the three models exhibited high accuracies (all p > 76.0% and p < 0.0001) and AUC values (all p > 0.75). Moreover, the model performance for classifying different migraine subtypes was evaluated using a dataset comprising the data of 20 patients with CM and 75 patients with EM (Fig. 6e). With the exception of two models (one incorporating features from the PN, SMN, and Ins–DMN and another using PN features alone), both of which had AUC values below 0.7, all the other models exhibited high accuracies, ranging from 62.1 to 77.8% (all p < 0.001), and AUC values, ranging from 0.7 to 0.84. Finally, in terms of distinguishing the CM group from all other groups (Fig. 6f), three models demonstrated excellent performance, each with AUC values greater than 0.8. These models were based on (a) PN, DMN, SMN, and Ins–DMN; (b) PN, DMN, and SMN; and (c) PN and DMN. In summary, these findings indicated that appropriate classification models displayed favourable generalisability for identifying patients with CM in an independent dataset. Moreover, the connectivity features, primarily from the PN and DMN, may be significant for characterising the neuropathology of CM. Additionally, receiver operating characteristic curves from each validation model are plotted using decisive values (Fig. 7). Notably, receiver operating characteristic curves using predicted labels are depicted in Fig. 6.

Fig. 6

Validation of classification models for identifying patients with CM. Classification performance with distinct network features between (a) chronic migraine (CM) versus healthy controls (HCs), (b) CM versus CM with comorbid fibromyalgia (CMFM), (c) CM versus fibromyalgia (FM), (d) CM versus chronic tension-type headache (CTTH), (e) CM versus episodic migraine (EM). SEN, sensitivity; SPEC, specificity; AUC, the area under the curve. PN, pain-related network; DMN, default mode network; SMN, sensorimotor network; Ins–DMN, insula to DMN

Fig. 7

Receiver operating characteristic curves plotted using decisive values for distinct network features between (a) chronic migraine (CM) versus healthy controls (HCs), (b) CM versus CM with comorbid fibromyalgia (CMFM), (c) CM versus fibromyalgia (FM), (d) CM versus chronic tension-type headache (CTTH), (e) CM versus episodic migraine (EM). PN, pain-related network; DMN, default mode network; SMN, sensorimotor network; Ins–DMN, insula to DMN