Altered Brain Complexity in Women with Primary Dysmenorrhea : A Resting-State MagnetoEncephalography Study Using Multiscale Entropy Analysis

How chronic pain affects brain functions remains unclear. As a potential indicator, brain complexity estimated by entropy-based methods may be helpful for revealing the underlying neurophysiological mechanism of chronic pain. In this study, complexity features with multiple time scales and spectral features were extracted from resting-state magnetoencephalographic signals of 156 female participants with/without primary dysmenorrhea (PDM) during pain-free state. Revealed by multiscale sample entropy (MSE), PDM patients (PDMs) exhibited loss of brain complexity in regions associated with sensory, affective, and evaluative components of pain, including sensorimotor, limbic, and salience networks. Significant correlations between MSE values and psychological states (depression and anxiety) were found in PDMs, which may indicate specific nonlinear disturbances in limbic and default mode network circuits after long-term menstrual pain. These findings suggest that MSE is an important measure of brain complexity and is potentially applicable to future diagnosis of chronic pain.


Introduction
Chronic pain, any continuous or recurrent pain lasting for more than three to six months [1,2], may cause reorganization of the central nervous system [3].It is a worldwide public health problem associated with mildly increased mortality [4].Primary dysmenorrhea (PDM), highly prevalent yet undertreated and affecting 40-90% of the reproductive-age females [5][6][7], is a pelvic pain during menstruation without identifiable structural lesion or anomaly in the internal female genital organs [8].PDM is a good clinical model for studying chronic pain because of its natural "on" (painful) and "off" (pain-free) states.PDM patients (PDMs) suffer from long-term recurrent menstrual pain, lasting Entropy 2017, 19, 680 2 of 27 for an extended period (8 to 72 h) during each menstrual cycle for years [9,10].This highlights the uniqueness of long-term PDM, which comprises the experiences of visceral acute tonic pain during menstrual cramp and recurrent pain during each menstrual cycle over the course of reproductive age.Such long-term menstrual pain shapes their brains and changes the way they perceive, modulate, and react to pain, leading to reduced quality of life, various mental and physiological health problems such as pain catastrophizing, depression, anxiety, and sleep disorders [7,11,12], and high comorbidity with many functional pain disorders later in life [13,14].Alterations in brain structures [15][16][17][18] and functions [13,[19][20][21][22][23][24][25][26] in PDMs have been reported, albeit far too little attention has been paid to the changes of cortical dynamics in PDMs.
The brain encompasses both regular and irregular neuronal interactions.The former is often regarded as linear, predictable, synchronous, or oscillatory and the latter is regarded as nonlinear, unpredictable, asynchronous, or nonoscillatory [27].The irregularity and unpredictability of brain activity can be regarded as neural complexity, which is related to the brain functions and the information processing between neurons [28,29].However, up-to-now, neural activities in the brain are typically analyzed using linear approximations, such as power-spectrum or time-frequency analyses.It is noteworthy that nonlinear interactions are thought to be as important as, if not more important, and more sensitive than linear interactions in characterizing brain dynamics [30].These interactions can be reflected by brief neuronal transients between synaptic reentrant loops and are embedded in time-series neurophysiological signals [31].The complexity of brain signal patterns reveals the neurophysiological information [28,32].Quantification of moment-to-moment temporal variability would provide a useful metric of brain dynamics [33], which may not be resolved by conventional spectral-based analysis.Entropy-based analysis, such as sample entropy [34], is a powerful tool to quantify complexity in nonlinear dynamics of neuronal activities.
However, there remains a paucity of evidence on the spontaneous neural complexity at rest in chronic recurrent menstrual pain.Recently, we applied MSE estimation to MEG signals in PDMs in the presence of painful menstruation (state-related changes) for pain level prediction [26].We found that MSE calculated from source activities could be used to predict pain scores, and the degree of hemispheric asymmetry in both source-level and sensor-level brain complexity reveals the intensity of pain.
Pain chronicity in PDM leads to functional neuroplasticity changes [13] and structural reorganization [18] (trait-related changes).In this study, we further extend our work with a large study cohort (156 participants) to examine whether PDMs' brain complexity in the absence of painful physiological state differs from those in healthy female controls (CONs).Complexity and spectral features of brain activity were extracted from resting-state MEG signals.MSE analysis revealed significant alterations in brain complexity, whereas only limited alterations were detected through spectral analyses.The correlations between brain complexity features and clinical manifestations were also investigated.This paper is organized as follows: Section 2 elucidates the study sample, clinical and psychological assessments, brain signal acquisition and data analysis, and statistical analyses to investigate the group differences between PDMs and CONs.Section 3 presents our results.In Section 4 we discuss and compare our findings with previous studies.

Participants
In this study, we included a subset of the participants from our multimodal imaging studies of PDM in Taiwan [11].Readers should refer to our recent studies [13,24] for detailed inclusion and exclusion criteria for PDMs and CONs.CONs had to meet all the same inclusion criteria, except that they must have no menstrual pain experience.All PDMs underwent pelvic ultrasonography to exclude organic pelvic diseases and were clinically diagnosed by a registered gynecologist.No analgesics were used within 24 h prior to the experiment [24].
Data from 82 PDMs and 79 age-matched CONs collected during pain-free periovulatory phase (Day 12-14 of menstruation) were included in our group analysis dataset.Due to the incompleteness of psychological inventory answers in a few participants, psychological data of 80 PDMs and 76 CONs were eventually included in our statistical analyses.This study was conducted in accordance with the Declaration of Helsinki.Written informed consent form and psychological inventories were approved by the ethics committee of Institutional Review Board of Taipei Veterans General Hospital, Taiwan.Before the study, all participants assessed for eligibility signed the written informed consent form.

Demographic, Menstrual Features, Pain Experiences, and Psychological Characteristics
Demographic data included age, body mass index (BMI), and handedness; menstrual features included age at menarche, years of menstruating, and averaged menstrual cycle length.Menstrual pain experiences were evaluated only in PDMs.Different aspects of recalled overall menstrual pain intensity over the last six months were evaluated in PDMs using McGill Pain Questionnaire (MPQ) [66,67] and verbal numerical rating scale (VNRS).MPQ total pain rating index (PRI-Total) composes four components: sensory, affective, evaluative, and miscellaneous; MPQ present pain index (PPI) is a 1-to-5 intensity scale (1 = mild, 5 = excruciating).VNRS was reported as menstrual pain recalled score with a range of 0 to 10 (0 = not at all, 10 = the worst imaginable pain).
Quality of life, personality traits, depressive mood, anxiety, and pain catastrophizing were assessed in all participants.The International Quality of Life Assessment Short-form-36 (IQOLA SF-36) Taiwan Standard Version 1.0 [68,69] (hereinafter, SF-36) was used to assess long-term physical and mental quality of life.The Chinese version of Basic Personality Inventory (BPI) [70] was used to assess personality traits, especially the personal emotional adjustment scale cluster (depression, anxiety, and hypochondriasis scales).Psychological inventories for anxiety and depression included Spielberger State-Trait Anxiety Inventory (STAI) [71], Beck Depression Inventory-IA (BDI-IA) [72], and Beck Anxiety Inventory (BAI) [73].Pain Catastrophizing Scale (PCS) [74] was used to study the negative appraisal style of pain.

Resting-State Magnetoencephalography (MEG) Signals Acquisition
A whole-head 306-channel neuromagnetometer (Vectorview, Elekta Neuromag, Helsinki, Finland) comprising 102 triple sensors (two orthogonal planar gradiometers and one magnetometer) was used to record the resting-state MEG signals.Electrooculography (EOG) from two vertical (VEOG) and two horizontal (HEOG) electrodes were recorded.A 3D digitizer (Isotrak 3S10002, Polhemus, Colchester, VT, USA) was used to identify the initial locations of four head position indicator (HPI) coils and three anatomical landmarks (nasion and bilateral preauricular points).The online sampling rate was 1000 Hz; online bandpass filter was 0.03-330 Hz; notch filter was 60 Hz.EOG signals exceeding 600 µV and MEG signals exceeding 6000 fT/cm were online-artifact rejected.MEG signals recorded from 102 gradiometers were excluded due to the susceptibility to distant noises, leaving signals from 204 planar gradiometers for further analyses.
Participants sat comfortably in a magnetically shielded room with their heads surrounded by the MEG helmet.Eye-closed resting-state MEG signals were recorded for three minutes in which the participants were instructed to relax, eliminate eye movements, and focus only on their breathing.

Preprocessing
Eight-second epochs were extracted from the three-minute eye-closed recordings without temporal overlap to avoid potential temporal dependency and were eliminated if their amplitudes in any channel at any time point exceeded 2000 fT/cm.To prevent the MEG recordings from the interference of eye movement and eye blinks, epochs with an amplitude of any EOG channel exceeding 250 µV were also eliminated.This resulted in an average of 14 (standard deviation = 5) artifact-free eight-second epochs and 8000 data points per epoch (with a sampling rate of 1000 Hz).For each epoch, MEG signals were projected onto a signal subspace using the signal space projection method [75].The projected signals were then passed through a 0.5-90 Hz band-pass filter followed by a 55-65 Hz band-stop filter for the elimination of power line interference.To remove the trend of the recordings, zero-mean adjustment was applied to signals of each channel.

Source Reconstruction
Maximum contrast beamformer [76] was used to estimate brain activity from MEG signals.
To obtain the approximate source signal y(t) of the dipole source θ, a spatial filter w θ was applied to the MEG recordings m(t): The spatial filter was obtained by applying the unit-gain constraint w T θ l θ = 1 and minimizing variance of the signal y(t): where E[•] denotes the expectation operator, l θ denotes the lead field vector of the dipole source θ, and α is the Tikhonov regularization parameter [77], which can restrict the norm of w θ .The estimated brain activity can be calculated by multiplying the MEG signals by the spatial filter ŵθ .

Feature Extraction
Three types of scale-invariant features were extracted from the estimated source activity, including brain complexity features (sample entropy, multiscale sample entropy, Shannon spectral entropy, Lempel-Ziv complexity), brain spectral features (relative band power, median frequency, spectral edge Entropy 2017, 19, 680 5 of 27 frequency), and indices of hemispheric asymmetry (A).For each epoch and each subject, we calculated the features of each brain region using the following methods.

Sample Entropy
Sample entropy (SE) proposed by a previous study [34] can be used to measure complexity.Two parameters, m and r, in SE refer to the length of the patterns to be compared (m = 2 in this study) and the tolerance range, respectively.Value r is usually set by c × σ, where c is a constant (c = 0.25 in this study) and σ is the standard deviation of the signal.Given a signal containing N sample points, x = [x 1 , x 2 , . . . ,x N ].First, a vector of length m was defined by: Next, for 1 ≤ j ≤ N − m and j = i, the distance of two vectors x m (i) and x m (j) was calculated as the maximum value of the difference between corresponding elements, as follows: For each i, i = 1, . . ., N − m, if dist(x m (i), x m (j)) ≤ r then x m (i) and x m (j) were matched and the number of matching count, l m r , was increased by one.Then we defined vectors of length m + 1 by: and calculate the number of matching l m+1 r .Once the l m r and l m+1 r were obtained, the SE of the signal x can be obtained as follows: Multiscale Sample Entropy MSE can be used to further measure complexity over different time scales [36].The coarse-grained time series z τ = [z τ 1 , z τ 2 , . . ., z τ N/τ ] of the original time series x = [x 1 , x 2 , . . . ,x N ] is obtained according to scale factor τ: We can obtain the multiscale SE of each time scale factor τ (τ is set from 1 to 100 in this study) by applying the SE method to each time series z τ j [26].Given m = 2, r = 0.25 × σ, N = 1000 Hz × 8 s/epoch = 8000 data points per epoch, and τ = 1 to 100, we had 80 to 8000 data points (N/τ = 8000/100 to 8000/1) for multiscale time-series data.The amount of data points was sufficient for SE calculation, as recommended in [34,78] (at least 10 m and preferable 30 m , that is, 100 to 900).Moreover, a minimum of 50 data points was also reported in EEG/MEG [52,79] and fMRI [28,60] studies.Figure 1 illustrates examples of time series data ranging from fine to coarse scales.Sample entropy (SE) proposed by a previous study [34] can be used to measure complexity.Two parameters, m and r, in SE refer to the length of the patterns to be compared (m = 2 in this study) and the tolerance range, respectively.Value r is usually set by  × , where c is a constant (c = 0.25 in this study) and  is the standard deviation of the signal.Given a signal containing N sample points,  = [ 1 ,  2 , … ,   ].First, a vector of length m was defined by: Next, for 1 ≤  ≤  −  and  ≠  , the distance of two vectors   () and   () was calculated as the maximum value of the difference between corresponding elements, as follows: For each i,  = We can obtain the multiscale SE of each time scale factor  ( is set from 1 to 100 in this study) by applying the SE method to each time series    [26].Given m = 2, r = 0.25 × , N = 1000 Hz × 8 s/epoch = 8000 data points per epoch, and τ = 1 to 100, we had 80 to 8000 data points (N/τ = 8000/100 to 8000/1) for multiscale time-series data.The amount of data points was sufficient for SE calculation, as recommended in [34,78] (at least 10 m and preferable 30 m , that is, 100 to 900).Moreover, a minimum of 50 data points was also reported in EEG/MEG [52,79] and fMRI [28,60] studies.Figure 1 illustrates examples of time series data ranging from fine to coarse scales.

Shannon Spectral Entropy
We applied Shannon entropy [80] to amplitude components of the normalized power spectrum density (PSD n ) as probability in Shannon entropy.Shannon spectral entropy (SSE) is a method to quantify the flatness of the PSD n , which implies the irregularity of signal.The SSE is defined as the following equation:   8) where PSD n () is normalized PSD of the total power between 0.5 Hz and 90 Hz and is written by the following equation: A high value of SSE means that the power spectral density is uniformly distributed whereas a low value of SSE means that the spectral concentrates at few frequencies.White noise has a high value of spectral entropy, whereas a signal composed of sinusoids has a low value of spectral entropy.

Lempel-Ziv Complexity
The analysis of Lempel-Ziv complexity (LZC) [81] is based on a finite symbol sequence, so the given signal must be coarse-grained by transforming it into a sequence with only a few symbols.Readers may consult Appendix A for the estimation and equations of LZC we used.

Shannon Spectral Entropy
We applied Shannon entropy [80] to amplitude components of the normalized power spectrum density (PSD n ) as probability in Shannon entropy.Shannon spectral entropy (SSE) is a method to quantify the flatness of the PSD n , which implies the irregularity of signal.The SSE is defined as the following equation: where PSD n ( f ) is normalized PSD of the total power between 0.5 Hz and 90 Hz and is written by the following equation: A high value of SSE means that the power spectral density is uniformly distributed whereas a low value of SSE means that the spectral concentrates at few frequencies.White noise has a high value of spectral entropy, whereas a signal composed of sinusoids has a low value of spectral entropy.

Lempel-Ziv Complexity
The analysis of Lempel-Ziv complexity (LZC) [81] is based on a finite symbol sequence, so the given signal must be coarse-grained by transforming it into a sequence with only a few symbols.Readers may consult Appendix A for the estimation and equations of LZC we used.

Relative Band Power
In this study, the frequency band for analysis was set between 0.5 and 90 Hz and six frequency sub-bands were defined: δ (0.5-4 Hz), θ (4-8 Hz), α (8-12 Hz), β (12-30 Hz), Lγ (30-55 Hz), and Hγ (65-90 Hz).For each frequency sub-band (B), we calculated the relative band power (RP(B)) as the ratio of the overall power in that frequency sub-band to that of the entire frequency band: where PSD( f ) is the power spectrum density of frequency f.

Median Frequency
Median frequency (MF) is a measure which summarizes the information of the entire power spectrum [56] and can be defined as the frequency which accounts for 50% of the total power.MF can be regarded as a rough representation of the distribution of power spectrum.It is written by the following equation: Spectral Edge Frequency Just like median frequency, spectral edge frequency 90 (SEF90) is defined as the frequency which accounts for 90% of the total power.SEF90 has been applied to study the depth of anesthesia [82] and Alzheimer's disease [64], and it is written as the following equation: 2.5.3.Regional Features of Resting-State Networks Brain complexity and spectral features were calculated from the estimated source activity at each voxel and were averaged across all eight-second epochs.For cortical-level analysis, 90 brain regions (45 regions in each hemisphere) were defined using an automated anatomical labeling (AAL) template [83] with a 1 mm × 1 mm × 1 mm resolution, which is available in the MRIcro medical image viewer freeware [84].The AAL label of each voxel was obtained by registering the AAL template to each participant's MRI T1 anatomical images using IBASPM (Individual Brain Atlases using Statistical Parametric Mapping) [85], an extension of the image analysis academic software toolkit Statistical Parametric Mapping version 5 (SPM5).To be noted, AAL region whose averaged voxel number across all participants was less than 10 voxels (that is, volume smaller than 10 mm 3 ) were excluded from further statistical analysis.Subsequently, brain features were averaged across all voxels within each region, yielding one representative mean value for each brain feature at each brain region.

Asymmetry Features
Subsequently, the indices of hemispheric asymmetry (A) for each region were calculated by using: where R and L denote one of the features in the corresponding brain regions in the right and left hemispheres, respectively.The more positive the A was, the larger the MSE value in the right hemisphere compared to that in the left hemisphere for that feature; the more negative the A was, the larger the MSE value in the left hemisphere compared to that in the right hemisphere for that feature.[110] were performed in each group.Since some of the psychological data were not normally distributed, Mann-Whitney U tests (α = 0.01, two-tailed) were subsequently applied to compare group differences.Median, interquartile range (IQR, 25% to 75%), p values, and Mann-Whitney U scores were reported accordingly.

Brain Features
To investigate the effect of long-term menstrual pain on brain complexity, spectral, and hemispheric asymmetry features, permutation testing based upon t-statistics [111] were performed to deal with the multiple comparisons problem.In permutation tests, all participants were randomly divided into two groups with the same size as the original data set (80 PDMs vs. 76 CONs).This procedure was repeated 5000 times (5000 permutations) for each brain region and for each feature to compare group differences.Each time a new t-test compared two randomly divided "groups" and gave one t-score.As a result, a distribution of 5000 t-scores was created.Only p-values within the 5% of the lower or higher values (α = 0.05) were considered statistically significant for complexity and spectral features, or 1% (α = 0.01) for asymmetry features.To further examine whether there is global or network-wise effect of long-term menstrual pain on MSE, we performed the following four independent t-tests (two-tailed, α = 0.05) by comparing the averaged MSE values in two-groups across (i) the whole brain for each scale factor; (ii) each network for each scale factor; (iii) each network in each hemisphere for each scale factor, and (iv) all scale factors in each brain region.In addition, to delineate significant hemispheric asymmetry (lateralization) in each group, for each significant between-group hemispheric asymmetry feature, we further examined significant within-group hemispheric asymmetry by comparing the mean value of that feature in the left versus right hemispheres in each group using Wilcoxon sign-rank tests (α = 0.05, two-tailed) (as reported in Supplementary Materials Tables S2-S4).BrainNet viewer visualization tool [112] was used to depict the significant differences.

Correlations between Pain Experiences, Psychological Traits, and Brain Features
To understand how clinical and psychological levels of long-term menstrual pain correlate with the altered brain complexity and spectral features (physiological level), we analyzed how PDMs' menstrual pain experiences, anxiety, depression, and pain catastrophizing characteristics were correlated with brain features that differed significantly between PDMs and CONs.Spearman correlations (α = 0.01, two-tailed) were carried out in IBM SPSS Statistics 22.0 software.

PDMs and CONs had Similar Demographic Characteristics and Menstrual Features
Table 1 shows the demographic characteristics and menstrual features from 80 PDMs and 76 CONs.As expected, PDMs and CONs had similar demographic characteristics and menstrual features, indicating that PDMs in this study were otherwise-healthy females.Hence, any group differences found in further analyses were not likely to be contributed by demographic and menstrual features.1 also shows the clinical manifestations of menstrual pain experiences in 80 PDMs.PDMs in our study have been suffering from moderate-to-severe menstrual pain (7 in the 0-10 scale; IQR: 6-8) lasting for two days (IQR: 1-3) every month for about eight years (IQR: 6-10).The recalled present pain index (McGill Pain Questionnaire PPI) of menstrual pain over the last six months also showed that PDMs experienced moderate-to-severe menstrual pain (3 in the 1-5 scale; IQR: 2-4).  2 displays the results of quality of life, personality traits, anxiety, depression, and pain catastrophizing characteristics in both PDMs and CONs.After long-term menstrual pain, PDMs manifested significantly lower quality of life in both physical well-being (p < 0.00001) and mental well-being (p < 0.00001).Group differences regarding the psychological traits and mental health conditions were more alarming: compared to CONs, PDMs exhibited higher personal emotional adjustment problems (anxiety, p = 0.00068; depression, p = 0.00003; hypochondriasis, p < 0.00001), anxiety (BAI, p = 0.00014; state anxiety, p = 0.00007; trait anxiety, p < 0.00001), pain catastrophizing characteristics (helplessness, p < 0.00001; magnification, p < 0.00001; rumination, p < 0.00001), and marginal significantly higher of depressive mood (p = 0.01307).Figure 2 shows the group differences between PDMs and CONs in brain complexity featured by MSE, and are quite revealing in several ways.First, significant group differences only emerged at larger scale factors (SFs) beginning from SF 52 (Figure 2a,b).Second, counts of significant group differences within each scale factor-interval were SFs 1~50 (0), 51~60 (4), 61-70 (8), 71~80 (6), 81~90 (10), and 91~100 (14).SF 92 was the most frequent feature (count = 4) that differentiated the brain complexity of PDMs from CONs, followed by SF 81 and SF 99 (3 counts each) (Figure 2a).Third, what stands out from the bird's-eye view in Figure 2c is that MSE values in PDMs were mostly lower (blue spheres) than those in CONs, and the differences emerged mainly in the right hemisphere.Table 3 reveals that compared to CONs, PDMs showed decreased MSE in chronic pain-related brain regions such as limbic/subcortical regions (amygdala, hippocampus, parahippocampal gyrus), default mode network (angular gyrus, inferior parietal lobule, precuneus, inferior temporal gyrus, middle temporal gyrus), and pain sensory-related regions such as sensorimotor network (rolandic operculum, thalamus), indicating a loss of complexity in chronic pain-related regions after long-term menstrual pain.Conversely, PDMs demonstrated higher MSE values than did CONs at the anterior cingulate cortex (ACC), the key region in salience network and also an important pain-regulating region.No significant group differences in all global or network-wise tests were found.regions that revealed significant MSE group differences were grouped into five SF-intervals for demonstration: SFs 51~60, 61-70, 71~80, 81~90 and 91~100.Brain regions where MSE measures in PDMs were higher or lower than those in CONs are represented in red or blue spheres, respectively.Size of sphere represents the count of scale factors that showed significant group differences.PDM, primary dysmenorrhea patients; CON, healthy female controls; L, left hemisphere; R, right hemisphere; LIMBIC, limbic network; DMN, default mode network; SAN, salience network; SMN, sensorimotor network; ECN, executive control network; AMYG, amygdala; ANG, angular gyrus; ITG, inferior temporal gyrus; CAL, calcarine; ROL, rolandic operculum; IPL, inferior parietal lobule; LING, lingual gyrus; IFGoperc, opercularis of inferior frontal gyrus; SOG, superior occipital gyrus; CUN, cuneus; PHG, parahippocampal gyrus; FFG, fusiform gyrus; MTG, middle temporal gyrus; MOG, middle occipital gyrus; ACG, anterior cingulate gyrus; THA, thalamus; HIP, hippocampus; PCUN, precuenus.(c) Brain regions that revealed significant MSE group differences were grouped into five SF-intervals for demonstration: SFs 51~60, 61-70, 71~80, 81~90 and 91~100.Brain regions where MSE measures in PDMs were higher or lower than those in CONs are represented in red or blue spheres, respectively.Size of sphere represents the count of scale factors that showed significant group differences.PDM, primary dysmenorrhea patients; CON, healthy female controls; L, left hemisphere; R, right hemisphere; LIMBIC, limbic network; DMN, default mode network; SAN, salience network; SMN, sensorimotor network; ECN, executive control network; AMYG, amygdala; ANG, angular gyrus; ITG, inferior temporal gyrus; CAL, calcarine; ROL, rolandic operculum; IPL, inferior parietal lobule; LING, lingual gyrus; IFGoperc, opercularis of inferior frontal gyrus; SOG, superior occipital gyrus; CUN, cuneus; PHG, parahippocampal gyrus; FFG, fusiform gyrus; MTG, middle temporal gyrus; MOG, middle occipital gyrus; ACG, anterior cingulate gyrus; THA, thalamus; HIP, hippocampus; PCUN, precuenus.

Brain Spectral Features, Other Complexity Features, and Their Hemispheric Asymmetry
No significant group differences were found in relative band power, median frequency, spectral edge frequency, Shannon spectral entropy, and Lempel-Ziv complexity.Significant group differences were only disclosed in the hemispheric asymmetry (asymSpectral) of high gamma relative band power, median frequency, and spectral edge frequency.PDMs showed left-lateralized asymSpectral mainly in the frontal regions, including ORBmid and ORBinf, and lingual gyrus, as seen in Figure 4 and Table 5.Overall, results from brain temporal and spectral features indicated that MSE might be more sensitive than spectral analyses in extracting spontaneous neurophysiological complexity of long-term menstrual pain over multiple time series.S4).Blue spheres depict the brain regions with enhanced left lateralization in PDMs compared to CONs.PDM, primary dysmenorrhea patients; CON, healthy female controls; L, left hemisphere; R, right hemisphere; g., gyrus; IFG, inferior frontal gyrus; MFG, middle frontal gyrus; ORBmid, orbital MFG; ORBinf, orbital IFG, orbital; LING, lingual gyrus; RP, relative band power; δ, RP(); θ, RP(); α, RP(); β, RP(); Lγ, RP( ); Hγ, RP(ℎℎ ); MF, median frequency; SEF, Spectral edge frequency; SSE, Shannon sample entropy; LZC, Lempel-Ziv complexity.

Correlations between Multiscale Sample Entropy and Pain Experiences/Psychological Characteristics
Table 6 presents the relationships between significant findings in MSE and PDMs' clinical pain experiences as well as their psychological characteristics.Spearman correlation analysis revealed that the higher the depression scores, the higher the brain complexity in the hippocampus (rho = 0.303, p = 0.0064; Figure 5a), thalamus (BPI-Depression: rho = 0.329, p = 0.0029; BDI: rho = 0.318, p = 0.0041; Figure 5b), and angular gyrus (BDI: rho = 0.304, p = 0.0060; scale factor 88: rho = 0.291, p = 0.0087).Brain complexity in the Rolandic operculum was negatively correlated with physical well-being (rho = −0.296,p = 0.0085; Figure 5c), and its asymmetry index was negatively correlated with depression score (rho = −0.304,p = 0.0061).Brain complexity in the fusiform gyrus was positively correlated with pain magnification catastrophizing thought (rho = 0.300, p = 0.0072).Brain complexity in the left inferior temporal gyrus was positively correlated with pain recalled score (rho = 0.323, p = 0.0045).Interestingly, these relationships appeared primarily at larger (coarse) scale factors, suggesting that brain complexity at larger scale factors might reflect macroscopic changes at the psychological and/or behavioral levels.

Discussion
In this study, we investigated the resting-MEG signals during pain-free state after long-term menstrual pain in a large study cohort (156 participants).The major finding of this study is that PDMs presented loss of complexity in brain regions associated with sensory, affective, and evaluative components of pain, including the thalamus, hippocampus, and anterior cingulate gyrus, even in the absence of menstrual pain.Our results demonstrated that MSE analysis serves as a good probe for changes of brain complexity sculptured by long-term pain experience.

Measures of Neural Complexity
PDMs experienced mental health consequences, including anxiety, depression, and pain catastrophizing characteristics.Our results are consistent with previous studies in depression, anxiety disorders, autistic spectrum disorder, bipolar disorder, and schizophrenia [35,42,61,64,113] that support the loss of complexity theory.Hornero et al. [47] reported that patients with Alzheimer's disease, characterized by degeneration of the nervous system that decreases regional dynamical complexity, exhibited less complex and more regular neural activities at rest.Similar "slowing effect" in Alzheimer's patients, that is, an increase of regularity of the signal and a reduction in complexity, was observed by Labate et al. [114,115] using entropic complexity measures.On the other hand, Brookes et al. [58] demonstrated that patients with schizophrenia, characterized by loss/breakdown of local synchrony (more disordered and increased randomness) and dysconnectivity between distributed brain regions, manifested significantly increase in task-induced entropy.In our study, PDMs were found to exhibit loss of complexity in pain-related brain regions.Complexity has been reported to reflect the increase of transitions between stable and synchronous microstates through neuronal reentrant loops [116].We speculate that the loss of complexity in PDMs could be attributed to the chronic stress elicited by recurrent menstrual pain.In our previous structural brain study, gray matter volume loss in regions of pain transmission, sensory processing, and affect regulation was found in PDMs [17].Two resting-state fMRI studies reported trait-related hypoconnectivity between DMN and salience network during non-painful state [13,24].The loss of complexity in PDMs may result from inter-regional structural disconnections or decreased neuronal coupling interactions, and the possible underlying mechanisms include loss of neurons [17] or loss of local connectivity [13,24].

Clinical Implications of Altered Brain Complexity at Rest in Chronic Pain
In this study, PDMs demonstrated loss of complexity in considerable pain-related brain regions (Table 3), including regions in the default-mode network (DMN), limbic regions, sensorimotor network (SMN), and salience network (SAN) compared to healthy female controls.
DMN, ECN, SMN, and SAN are largely influenced by chronic pain experiences [24,117,118] and are highly interactive with the descending pain modulatory system [24].In healthy individuals, DMN emerges at rest, mainly deactivated towards stimuli or task [117], and has also been reported to involve in the modulation of pain experience [118].In our previous resting-state fMRI connectivity study, trait-related hypoconnectivity between DMN and salience network was observed during non-painful state [24].Loss of complexity in the DMN regions in PDMs, even during pain-free state, may add to prior research findings in resting-state fMRI pain studies that reveal decreased functional connectivity of the anterior to posterior parts of DMN in chronic pain patients [24,118], indicating a maladaptive state in chronic pain patients.In addition, hemispheric asymmetry of brain complexity and spectral features in the anterior parts of DMN differed significantly between PDMs and CONs, implying that differences in the hemispheric asymmetry pattern might provide additional neurophysiological information related to chronic pain [26,119,120].
The hippocampus and parahippocampal gyrus, though located in the limbic region, are also regarded as core regions associated with DMN [89].Hippocampus is substantially involved in emotional learning, and parahippocampal gyrus is thought to be involved in stress-related disorders and anticipatory anxiety [121].As long-term menstrual pain serves as a chronic stressor in life, this explains that the asymmetry of brain complexity in the parahippocampal gyrus was found to be positively associated with anxiety level in PDMs in this study.Brain complexity in the left thalamus and the right hippocampus were positively associated with depression level.On the other hand, the amygdala is a well-known region related to the affective-motivational dimension of pain [122] and shows altered resting-state activities in chronic pain conditions [123].The complexity of the amygdala was also found to be decreased in PDMs in this study, implying that emotional processing could be altered.
In this study, loss of complexity was found in the sensorimotor regions, including the thalamus and Rolandic operculum, in PDMs.Sensorimotor network (SMN) is involved in the processing of sensory-discriminative dimension of pain.Cross-network functional connectivity in the sensorimotor cortex is associated with measures of physical function and is influenced by chronic pain [117].Thalamus, in particular, is a key region in ascending pain modulatory system that transmits sensory/nociceptive stimuli to cerebral and has reciprocal connections with cerebral cortex [124].Our results support the evidence that indicates damage in thalamus leads to severe chronic pain [124].
In contrast, activity in salience network is normally anticorrelated with that in DMN [117].Anterior cingulate cortex (ACC) engages in the emotional/motivational component of pain perception [125,126] and is a key region in the salience network (SAN) [102], which is activated when we constantly engage and focus on the pain but is normally deactivated when pain is gone.In a structural brain study [17], the gray matter volume of ACC was found the be increased in PDMs.We found that MSE in ACC is higher in PDMs compared to that in healthy controls, which suggest excessive attention processing of potential pain salience even in the absence of pain.Together with the negative findings in the between-group grand-averaged MSE global and network-wise tests, our findings suggest that brain complexity of PDM females does not alter globally or systematically, but at specific brain regions at some temporal scales.

Entropy with Multiple Scales Corresponding to Various Ranges of Frequency
Previous studies have found distinct results for different scales in MSE and suggested that a single scale is not enough for the analysis of biological signals [36,38,40,54,113,127,128]. However, the interpretation of the biological mechanisms reflected by multiple scales has not been well-established.A known fact is that there is a close relationship between the temporal scales in MSE and the frequencies of the signals: the small scale (fine scales) factors reflect the complexity of oscillations at higher frequencies whereas larger scale (coarse scales) factors reflect those at lower frequencies [43,46,129].Recently, Courtiol et al. [129] have used simulated white noises and experimental EEG data to investigate how the values of MSE across different scales change along with different power spectra of the signals.The procedure of temporal averaging in MSE can be regarded as performing downsampling or low-pass filtering on the original signals.Therefore, according to Nyquist-Shannon's sampling theorem, the MSE at scale factors can detect the irregularity of signals with frequencies less than ( f s /τ)/2, where f s is the sampling rate of the original signals.Previous studies have linked the signals with high frequencies to information processing in local region whereas those with low frequencies to long-range communication between brain regions [46,130].Together with the previous findings that the entropy of brain signals reflects the information processing in the brain, it is possible that MSE at different temporal scales may reveal the brain dynamics with different spatial scales [129].Power spectral analyses in chronic pain patients at rest suggests an increased EEG power in lower frequency bands, including theta and alpha bands [131,132].In our previous study, we also successfully predicted current pain level in PDMs during menstruation using low frequency components [26].In this study, MSE group differences only emerged at large scale factors (τ = 52~100), approximately below 10 Hz, implicating that the loss of complexity in PDMs might be related to dysfunction of the distributed/global processing and inter-region communication in the brain after long-term pain experience.

MSE Versus Spectral Analyses
Increased theta, alpha, beta, or delta band power in chronic pain patients at rest has been reported [131].In our recent study, the combination of MSE and spectral features could accurately predict current pain intensity in PDMs during painful menstruation [26].The present study further extends the MSE and spectral analyses to capture brain complexity alterations shaped by long-term menstrual pain during non-painful state.The possible explanations of the findings that MSE features revealed more differences than spectral features might be due to the symptoms of PDM and the study state (pain-free state).First, primary dysmenorrhea, as regarded as "primary" [2], is a chronic pain syndrome without identified structural lesion or anomaly in the affected area (female genital organs).Other chronic pain disorders that involved tissue damage or systemic symptoms, such as chronic low back pain (CLBP) and fibromyalgia, might suffer from constant peripheral nociceptive feedbacks [122] and are thus more likely to show systemic and rhythmic changes in central nervous system that can be captured by linear analyses, such as spectral analysis.Second, although PDMs do suffer from significant negative cognitive and emotional consequences when compared to healthy females including depression, anxiety [7,11], they are considered as otherwise-healthy females who do not suffer from cognitive impairments or mental dysfunctions.This is reasonable to consider that local linear synchrony neural activities in PDMs are similar to those in CONs when spontaneous pain (menstrual pain) does not exist.On the other hand, MSE can effectively capture distributed and long-range dynamics mixed by different brain regions and time scales.

Limitations
There are some limitations in the present study.First, regional features of MSE were defined using an automated anatomical labeling (AAL) template, which is relatively coarse in spatial resolution comparing to voxel-wise analyses.Second, other MSE measures [38,39] could be used to explore brain complexity in chronic pain.Finally, categorization and nomenclature of the resting-state networks vary across different studies, thereby warrant cautious interpretation of their functions.

Conclusions
The brain encompasses both regular and irregular neuronal activities interacting at different spatial and temporal scales.Pain chronicity leads to functional neuroplasticity changes and structural reorganizations, yet the neural complexity, which is reflected by the moment-to-moment temporal variability of nonlinear neural activities, altered by chronic pain is understudied.In this study, we investigated the resting-state magnetoencephalographic signals during pain-free state in 80 PDMs with long-term menstrual pain history and 76 CONs.Revealed by multiscale sample entropy (MSE), PDMs exhibited loss of brain complexity in pain-related brain regions including regions in the default-mode network, limbic circuits, sensorimotor network, and salience network.Significant correlations between MSE values and psychological states (depression and anxiety) found in PDMs may indicate specific nonlinear disturbances in limbic and default mode network circuits after long-term menstrual pain.Our findings suggest that MSE is an important measure of brain complexity and is potentially applicable to future diagnosis of chronic pain.

Supplementary Materials:
The following are available online at www.mdpi.com/1099-4300/19/12/680/s1,Table S1: Reported RSNs of each AAL brain regions.Table S2.Lateralization of MSE within PDM and CON groups sorted by scale factor intervals and hemispheric asymmetry alteration in PDM.Table S3: Lateralization of MSE within PDM and CON groups sorted by hemispheric asymmetry alteration in PDM and brain region.Table S4: Lateralization of spectral features within PDM and CON groups.

Figure 1 .
Figure 1.Examples of time series data for an 8-s epoch over a range of representative scale factors (τ) from fine to coarse scales: 1, 5, 30, 60 and 90.The x-axis represents time and the y-axis represents the estimated brain activity index.

Figure 1 .
Figure 1.Examples of time series data for an 8-s epoch over a range of representative scale factors (τ) from fine to coarse scales: 1, 5, 30, 60 and 90.The x-axis represents time and the y-axis represents the estimated brain activity index.

Figure 3 .
Figure 3. Hemispheric asymmetry of multiscale sample entropy (asymMSE) group differences from resting-state MEG brain signals during pain-free state.Significant group differences were found across all scale factor-intervals with the most differences seen between SFs 31~60.(a) Count of each SF that showed significant group differences (permutation testing with 5000 iterations, p < 0.01, twotailed); (b) Group differences in hemispheric asymmetry of MSE (asymMSE).The x-axis represents the scale factors (SFs) of asymMSE ranging from 1 to 100; the y-axis represents the AAL brain regions which were categorized into different RSNs (indicated by thick lines and text in different colors) for functional attribution; the color bar represents between-group t-values after 5000 permutation tests (α = 0.01) as listed in TableS2, with the most positive t-values (PDMs > CONs) shown in bright yellow and the most negative t-values (PDMs < CONs) shown in bright blue; (c) Altered hemispheric asymmetry of MSE in PDMs.Brain regions that revealed significant asymMSE group differences were grouped into six SF-intervals for demonstration (TableS2): SFs 1~30, 31~40, 41~50, 51~60, 61-80 and 81~100.CON group exhibited mostly left-lateralization.Compared to CONs, grey, red, and blue spheres indicate the brain regions with loss of hemispheric asymmetry, right-lateralization, and leftlateralization in PDMs, respectively.Size of sphere represents count of scale factors that showed significant group differences.PDM, primary dysmenorrhea patients; CON, healthy female controls; LIMBIC, limbic network; DMN, default mode network; SAN, salience network; SMN, sensorimotor network; ECN, executive control network; L, left hemisphere; R, right hemisphere; MFG, middle frontal gyrus; ORBmid, orbital MFG; ROL, rolandic operculum; PUT, putamen; HES, Heschl gyrus; SFG, superior frontal gyrus; ORBsupmed, medial orbital SFG; SFGmed, medial SFG; ACG, anterior cingulate gyrus; CAU, caudate; IFGoperc, opercularis of inferior frontal gyrus; AMYG, amygdala; PHG, parahippocampal g.; SFGdor, dorsolateral SFG; HIP, hippocampus; THA, thalamus.

Figure 3 .
Figure 3. Hemispheric asymmetry of multiscale sample entropy (asymMSE) group differences from resting-state MEG brain signals during pain-free state.Significant group differences were found across all scale factor-intervals the most differences seen between SFs 31~60.(a) Count of each SF that showed significant group differences (permutation testing with 5000 iterations, p < 0.01, two-tailed); (b) Group differences in hemispheric asymmetry of MSE (asymMSE).The x-axis represents the scale factors (SFs) of asymMSE ranging from 1 to 100; the y-axis represents the AAL brain regions which were categorized into different RSNs (indicated by thick lines and text in different colors) for functional attribution; the color bar represents between-group t-values after 5000 permutation tests (α = 0.01) as listed in TableS2, with the most positive t-values (PDMs > CONs) shown in bright yellow and the most negative t-values (PDMs < CONs) shown in bright blue; (c) Altered hemispheric asymmetry of MSE in PDMs.Brain regions that revealed significant asymMSE group differences were grouped into six SF-intervals for demonstration (TableS2): SFs 1~30, 31~40, 41~50, 51~60, 61-80 and 81~100.CON group exhibited mostly left-lateralization.Compared to CONs, grey, red, and blue spheres indicate the brain regions with loss of hemispheric asymmetry, right-lateralization, and left-lateralization in PDMs, respectively.Size of sphere represents count of scale factors that showed significant group differences.PDM, primary dysmenorrhea patients; CON, healthy female controls; LIMBIC, limbic network; DMN, default mode network; SAN, salience network; SMN, sensorimotor network; ECN, executive control network; L, left hemisphere; R, right hemisphere; MFG, middle frontal gyrus; ORBmid, orbital MFG; ROL, rolandic operculum; PUT, putamen; HES, Heschl gyrus; SFG, superior frontal gyrus; ORBsupmed, medial orbital SFG; SFGmed, medial SFG; ACG, anterior cingulate gyrus; CAU, caudate; IFGoperc, opercularis of inferior frontal gyrus; AMYG, amygdala; PHG, parahippocampal g.; SFGdor, dorsolateral SFG; HIP, hippocampus; THA, thalamus.

Figure 4 .
Figure 4. Group differences of hemispheric asymmetry of spectral and other complexity features from resting-state MEG brain signals during pain-free state.Significant group differences were only disclosed in hemispheric asymmetry of high gamma relative band power, median frequency, and spectral edge frequency, and were left-lateralized mainly in the frontal regions in PDMs.(a) Group differences in hemispheric asymmetry.The x-axis of the matrix represents the hemispheric asymmetry of spectral and other brain complexity features; the y-axis represents the AAL brain regions which were categorized into different RSNs (indicated by thick lines and text in different colors) for functional attribution; the color bar represents between-group t-values after 5000 permutation tests (α = 0.01), with the most positive t-values (PDMs > CONs) shown in bright yellow and the most negative t-values (PDMs < CONs) shown in bright blue; (b) Hemispheric asymmetry alterations in PDMs were displayed (TableS4).Blue spheres depict the brain regions with enhanced left lateralization in PDMs compared to CONs.PDM, primary dysmenorrhea patients; CON, healthy female controls; L, left hemisphere; R, right hemisphere; g., gyrus; IFG, inferior frontal gyrus; MFG, middle frontal gyrus; ORBmid, orbital MFG; ORBinf, orbital IFG, orbital; LING, lingual gyrus; RP, relative band power; δ, RP(); θ, RP(); α, RP(); β, RP(); Lγ, RP( ); Hγ, RP(ℎℎ ); MF, median frequency; SEF, Spectral edge frequency; SSE, Shannon sample entropy; LZC, Lempel-Ziv complexity.

Figure 4 .
Figure 4. Group differences of hemispheric asymmetry of spectral and other complexity features from resting-state MEG brain signals during pain-free state.Significant group differences were only disclosed in hemispheric asymmetry of high gamma relative band power, median frequency, and spectral edge frequency, and were left-lateralized mainly in the frontal regions in PDMs.(a) Group differences in hemispheric asymmetry.The x-axis of the matrix represents the hemispheric asymmetry of spectral and other brain complexity features; the y-axis represents the AAL brain regions which were categorized into different RSNs (indicated by thick lines and text in different colors) for functional attribution; the color bar represents between-group t-values after 5000 permutation tests (α = 0.01), with the most positive t-values (PDMs > CONs) shown in bright yellow and the most negative t-values (PDMs < CONs) shown in bright blue; (b) Hemispheric asymmetry alterations in PDMs were displayed (TableS4).Blue spheres depict the brain regions with enhanced left lateralization in PDMs compared to CONs.PDM, primary dysmenorrhea patients; CON, healthy female controls; L, left hemisphere; R, right hemisphere; g., gyrus; IFG, inferior frontal gyrus; MFG, middle frontal gyrus; ORBmid, orbital MFG; ORBinf, orbital IFG, orbital; LING, lingual gyrus; RP, relative band power; δ, RP(δ);

Figure 5 .
Figure 5. Spearman correlation between multiscale sample entropy and pain experiences or psychological characteristics in primary dysmenorrhea patients (PDMs).The x-axis of each subfigure is the value of MSE or hemispheric asymmetry of MSE (asymMSE) in each PDMs; the y-axis is the pain and/or psychological scores.Spearman rho and p-values are listed for each correlation.(a) Brain complexity in the right hippocampus positively correlated with depression score; (b) Brain complexity in the left thalamus positively correlated with depression scores; (c) Brain complexity in the left Rolandic operculum negatively correlated with physical component score of quality of life; (d) Asymmetry of brain complexity in the parahippocampal gyrus was positively correlated with anxiety score.MSE, multiscale sample entropy; asymMSE, hemispheric asymmetry of MSE; BDI, Beck depression inventory; BAI, Beck anxiety inventory; PCS, pain catastrophizing scale; MPQ, McGill pain questionnaire; PRI, MPQ pain rating index; PPI, MPQ present pain index.

Figure 5 .
Figure 5. Spearman correlation between multiscale sample entropy and pain experiences or psychological characteristics in primary dysmenorrhea patients (PDMs).The x-axis of each subfigure is the value of MSE or hemispheric asymmetry of MSE (asymMSE) in each PDMs; the y-axis is the pain and/or psychological scores.Spearman rho and p-values are listed for each correlation.(a) Brain complexity in the right hippocampus positively correlated with depression score; (b) Brain complexity in the left thalamus positively correlated with depression scores; (c) Brain complexity in the left Rolandic operculum negatively correlated with physical component score of quality of life; (d) Asymmetry of brain complexity in the parahippocampal gyrus was positively correlated with anxiety score.MSE, multiscale sample entropy; asymMSE, hemispheric asymmetry of MSE; BDI, Beck depression inventory; BAI, Beck anxiety inventory; PCS, pain catastrophizing scale; MPQ, McGill pain questionnaire; PRI, MPQ pain rating index; PPI, MPQ present pain index.
2.6.Statistical Analyses 2.6.1.Demographic, Menstrual Features, Pain Experiences, and Psychological Characteristics Demographic data, menstrual features, menstrual pain experiences, and psychological scores of PDMs and CONs were processed in IBM SPSS Statistics 22.0 software (IBM Corp., Armonk, NY, USA).Prior to any inferential statistical testing, descriptive statistical tests and normality tests (Shapiro-Wilk test)

Table 1 .
Demographic characteristics, menstrual features, and clinical manifestations of menstrual pain experiences.PDMs and CONs had similar demographic characteristics and menstrual features.
Group differences were compared using Mann-Whitney U test (p < 0.01, two-tailed).Unit or range is bracketed after each item name.Data are presented as median (IQR).Menstrual pain recalled score, recalled PPI, and recalled PRI scores are average recalled menstrual pain intensities over the last six months.PDM, primary dysmenorrhea patients; CON, healthy female controls; BMI, body mass index; MPQ, McGill pain questionnaire; PRI, pain rating index; PPI, present pain index; y/o, years old; y, year, d, day.3.1.3.PDMs Displayed Significantly Higher Anxiety, Depression, and Pain Catastrophizing Characteristics than CONs Table

Table 2 .
Between-group comparison of psychological assessments.PDMs displayed significantly lower quality of life and higher anxiety, depression, and pain catastrophizing characteristics than those of CONs.

Table 5 .
Significant group differences in asymmetry of spectral and other complexity features (p < 0.01, 5000 permutation tests).