Between July 2021 and March 2022, a total of 85 patients diagnosed with CTN and 79 age- and sex-matched HCs were prospectively recruited from the Department of Radiology at Hangzhou First People's Hospital, Zhejiang University School of Medicine. Written informed consent was obtained from all participants prior to their involvement in this prospective study. The study was conducted in accordance with the ethical guidelines and principles outlined in the Declaration of Helsinki and was approved by the local ethics committee of Hangzhou First People's Hospital, Zhejiang University School of Medicine (IRB# No. 202107002).

The inclusion criteria for CTN patients were as follows: (1) diagnosis of CTN based on the third edition of the International Classification of Headache Disorders (ICHD-3), with magnetic resonance imaging (MRI) evidence of neurovascular compression (NVC) showing morphological changes (atrophy or dislocation) in the trigeminal nerve root (1); (2) unilateral pain in the distribution of one or more branches of the trigeminal nerve; (3) paroxysmal facial pain triggered by specific factors (e.g., light touching of the face, opening of the mouth, etc.); (4) normal brain signals on conventional MRI T1WI and T2WI scans; (5) no additional neurological or sensory deficits; (6) no prior surgical or invasive procedures for CTN; (7) no contraindications to MRI; (8) right-handedness; and (9) all patients underwent microvascular decompression, confirming the presence of NVC rather than just contact.

The exclusion criteria were as follows: (1) CTN patients who had undergone previous surgical treatment; (2) presence of headaches or other paroxysmal or chronic pain conditions; (3) family history of headache or other pain in first-degree relatives; (4) presence of other somatic or psychiatric conditions; (5) left-handedness; and (6) contraindications to MRI.

All participants underwent MRI scans using a 3.0 T MRI scanner (Siemens, MAGNETOM Verio, Germany) equipped with an eight-channel phased-array head coil. The structural data were acquired using 3D T1 weighted images (magnetization-prepared rapid gradient-echo) and the functional images were acquired using gradient echo-echo planar imaging. The imaging parameters were as follows: for 3D T1 weighted images, 176 slices were acquired with a repetition time (TR) of 1,900 ms, an echo time (TE) of 2.52 ms, a slice thickness of 1 mm, a field of view (FOV) of 256 × 256 mm², a voxel size of 1 × 1 × 1 mm³, and a flip angle of 9 degrees. For functional images, 240 volumes were acquired with a TR of 2,000 ms, a TE of 30 ms, a slice thickness of 3.2 mm, a voxel size of 3.44 × 3.44 × 3.20 mm³, a flip angle of 90 degrees, a FOV of 220 × 220 mm², and a scan duration of 8 min. Participants were instructed to keep their eyes closed, remain awake, and breathe calmly throughout the scan, controlled breathing throughout the scan to ensure they were in a resting state.

The rs-fMRI data preprocessing was performed using the DPABI and SPM12 toolbox in MATLAB (MathWorks, MA, USA). The preprocessing pipeline involved the following steps: (1) discarding the initial 10 volumes to achieve a steady-state MRI signal; (2) correcting for slice timing and head motion using motion correction parameters; (3) co-register the structural MRI image (T1-weighted) to the mean functional image created after motion correction; (4) the T1-weighted structural images were then segmented and normalized to the Montreal Neurological Institute (MNI) space to obtain deformation information using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL); (5) normalizing the images to the MNI space by deformation fields derived from tissue segmentation of structural images as described above and resampling to a voxel size of 3 × 3 × 3 mm³; (6) detrending the BOLD signal by removing the linear trend; (7) removing noise through regression of Friston-24 head motion parameters, cerebrospinal fluid signals, and white matter signals; and (8) band-pass filtering was applied in 0.01–0.08 Hz. Nine patients and seven HCs were excluded due to excessive head motion (displacement > 3 mm, rotation > 3°) or framewise displacement (FD_Jenkinson) > 0.2. The final analysis included 76 patients with CTN and 72 HCs.

After image pre-processing, the calculation of BEN was performed using BENtbx software (21), which can be accessed at https://cfn.upenn.edu/~zewang/software.html. BEN was computed at each voxel using Sample Entropy (SampEn) (31). SampEn is an approximate entropy measure that quantifies the temporal coherence of a time series by assessing the likelihood that a small section of the data matches with other sections as the window length increases. The matching criterion is determined by a threshold set as a multiple (r) of the standard deviation of the entire time series. In this study, a window length of 3 and a cutoff threshold of 0.6 times the standard deviation were used (21). Further information on BEN calculation can be found in the original BENtbx paper (21). The resulting entropy values of all voxels constituted the BEN map, which was then smoothed with an isotropic Gaussian kernel (full width at half maxima = 6 mm) to mitigate structural brain differences among individuals that may arise during spatial normalization to the MNI space.

For demographic and clinical continuous variables, normality was assessed using the Shapiro-Wilk test. Normally distributed variables were reported as mean ± standard deviation, and group comparisons were conducted using two-sample t-tests. Non-normally distributed variables were reported as median (interquartile range), and group comparisons were performed using the Mann-Whitney U test. Gender differences between groups were examined using the chi-square test.

In the DPABI software, differences in brain entropy between patients and HCs were assessed using a two sample t-test, and then multiple comparison correction based on Gauss random field (GRF) theory was applied with significance thresholds set at voxel-wise p < 0.001 and cluster-wise p < 0.05. To account for potential confounding factors, such as age, sex, education, and head motion, these variables were included as covariates in the analysis. Additionally, partial correlation analysis was performed to explore the associations between the average BEN values of significant brain areas and the neuropsychological assessments, regressing out the covariates of age, sex, education, and head motion.

Machine learning was conducted using a script within the MATLAB environment. In our study, we utilized the Automated Anatomical Labeling (AAL) atlas version 3 as a mask, and for each voxel, we extracted the corresponding BEN value as a feature. This process resulted in a total of 54,948 MRI features, each corresponding to a specific voxel defined by the AAL atlas. Previous studies have demonstrated the reliability and reproducibility of the temporal complexity of rs-fMRI (32).

Considering the limited availability of subjects in human neuroimaging studies, which can impact the generalization ability of the study, we employed a 10-fold cross-validation strategy. In each iteration of cross-validation, one-tenth of the samples were held out as a test set, while the remaining subjects were used for training the classifier. This process was repeated until all subjects were used as test samples. Within each fold of cross-validation, we first performed a two-sample t-test between the two groups to remove features with p > 0.001 and then utilized four widely recognized feature selection methods based on filter approaches: fisher score (FSCR), relief-F (RELF-F), minimum redundancy maximum relevance (MRMR), and conditional mutual information maximization (CMIM). To address redundancy, features exhibiting a Spearman's correlation of 0.7 or higher were eliminated to reduce the presence of redundant information.

Moreover, in our effort to address the challenges associated with the “curse of dimensionality” and mitigate the risk of overfitting, we followed Harrell's guideline, which recommends that the number of selected features should be <10% of the sample size, with a final feature count of approximately 10 (33–35). Consequently, we selected the top 10 non-redundant features (36, 37) as the input for four distinct machine learning classifiers: logistic regression (LR), k-nearest neighbor (KNN), random forest (RF), and support vector machines with radial basis function kernel (RBF-SVM). In response to the question of whether selecting more or fewer features would significantly improve classification performance, we conducted additional experiments. We validated the results using the first 5 features and the first 20 features, respectively. The results for these different feature selection scenarios were analyzed and compared to the results obtained using the top 10 features. To ensure the generalizability of the biomarkers and avoid overfitting and spurious results (38), we utilized standard/default parameter settings for all experiments, rather than extensive hyperparameter tuning, a choice consistent with the previous study (39). We implemented 16 cross-combinations of feature selection methods and classifiers (4 feature selection methods × 4 classifiers). Finally, the results of each repetition were averaged to produce the final classification outcome.

To further validate the significance of our classification results, we conducted permutation tests on classification metrics (accuracy, sensitivity, specificity and area under the curve [AUC]). In these permutation tests, we generated four null distributions of classification metrics (AUC, accuracy, sensitivity and specificity) for each classifier using a non-parametric permutation approach with 2,000 permutations. The p-value was determined by calculating the proportion of the 2,000 permutations for which the classification metrics of the original data were equal to or larger than the classification metrics of the permuted data. The classification metrics of each classifier were considered statistically significant if the p-values were <5% (p < 0.05).

Demographic and clinical information for the final 76 CTN patients [56 (13) years, 52 females] and 72 HCs [54.5 (14) years, 47 females] were presented in Table 1 and Supplementary Table 1. There were no significant differences in gender (p = 0.685), age (p = 0.066), and head motion (p = 0.954), and while significant differences were observed in Mini-Mental State Examination (MMSE, p < 0.001), the quality-of-life score of patients with trigeminal neuralgia (p < 0.001), self-rating depression scale (SDS, p < 0.001), self-rating anxiety scale (SAS, p < 0.001) between the two groups.

Compared to HCs, CTN patients exhibited distinct patterns of BEN changes in the brain (Table 2, Figure 1). Specifically, increased BEN was observed in the thalamus (voxel p < 0.001, cluster p < 0.05, GRF correction, cluster size > 32 voxels) and pons (voxel p < 0.001, cluster p < 0.05, GRF correction, cluster size > 32 voxels), suggesting enhanced neural activity and complexity in these areas. Conversely, decreased BEN was found in the inferior semilunar lobule (voxel p < 0.001, cluster p < 0.05, GRF correction, cluster size > 32 voxels), indicating disrupted neural processing and complexity in this region. Further analyses revealed a low positive correlation between the average BEN values of the thalamus and neuropsychological assessments (SAS and SDS), regressing out the covariates of age, sex, education, and head motion (Figure 2, Table 3).

The classification metrics, including AUC, accuracy, sensitivity, and specificity, are presented in Figure 3. Among the 16 combinations of machine learning methods utilized in our study, the CMIM-RF method demonstrated the highest performance in classifying CTN patients and HCs based on BEN changes, achieving an AUC of 0.801, and the AUC of most classifiers above 0.75.

Supplementary Tables 2–5 presents the results of permutation tests for classification metrics. The outcomes of these permutation tests consistently revealed statistical significance (p < 0.05) across all classification metrics of CMIM-RF, including accuracy, sensitivity, specificity, and AUC. The accuracy and AUC of the other classifiers were also statistically significant (p < 0.05). These results provide robust evidence that the pattern of complexity alterations captured by BEN can effectively distinguish CTN patients from HCs, further underscoring its potential as a diagnostic tool for CTN.

Moreover, it is noteworthy that our findings remain stable across different feature selection scenarios. Specifically, the results obtained using the first 5 features and the first 20 features, as illustrated in Supplementary Figures 1, 2, exhibited similar performance, reinforcing the reliability, and consistency of our findings.