2.3 Experimental Paradigm
The thermal stimulus test was conducted in the morning every day. Before the experiment, each participant was told to stay relaxed and not to have a particular thought other than to pay attention to the stimulus. Because the incisor area is the most sensitive area to temperature, the thermal stimuli sites were selected as the central areas of the maxillary and mandibular incisor areas [2]. In a pilot study, 36°C was used as the starting point for thermal stimulation and the temperature was gradually increased while subjects reported their subjective sensations. When the stimulus temperature reached 45°C, subjects reported being able to slightly feel the temperature of the stimulus. The pilot study gradually increased the temperature at intervals of 1°C., 2°C., 3°C., and 4°C. It found the subjects did not subjectively perceive a significant difference in temperature stimulation at 1°C and 2°C intervals. The reason for that may be that the temperature change was small and did not exceed the oral temperature adaptive temperature threshold. In contrast, when the interval was more than 3°C, the subjects were able to perceive a more substantial temperature change. Therefore, in this study, 45°C was used as the starting stimulation temperature and 3°C was used as the temperature stimulation increment. The four thermal stimuli were 45°C, 48°C, 51°C, and 54°C, each of which had a duration of 8 s. The thermal chip was moved slightly after each recording to avoid sensitization or habituation at the same stimulus site. After the stimulation of the maxillary incisor and mandibular incisor at the same temperature, the stimulus at the next temperature was presented. After each stimulus, the subjects were asked to rate its level of pain on the Visual Analogue Scale/Score (VAS), with 0 indicating no pain, and 10 indicating severe pain, with other ratings indicating different degrees of pain.
2.4 Data Analysis
Preprocessing. The original acquired EEG signals were mixed with background noise, power frequency interference, and other artifacts. Therefore, the EEGLAB toolbox (version 13.6.5b) (Delorme and Makeig, 2004) of MATLAB R2016b (The MathWorks, Natick, MA, USA) was used to conduct baseline correction and remove baseline drift of EEG data. A band-pass filter of 0.5 Hz to 80 Hz was used to filter the data. The 50 Hz power frequency interference was filtered out with a trap of 49.5–50.5 Hz. Independent component analysis (ICA) was used to remove eye movement and muscle artifact components. The pre-processed data were used for subsequent analyses.
Frequency Analysis. Frequency analysis was performed using the periodogram method in MATLAB [10]. Then, the average power of six frequency bands were calculated: delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), low beta (13–20 Hz), high beta (20–30 Hz), and gamma (30–45 Hz). The trends of the average power of the EEG delta, theta, alpha, low beta, high beta, and gamma bands were analyzed in accordance with the temperatures of the different thermal stimuli applied to the oral mucosa. The electrodes were selected and grouped into five main regions to compute global frequency changes, based on previous studies: the frontal, central, left parietal, right parietal, and occipital areas [11]. The frontal region included the F3, Fz, F4, Fc3, Fcz, and Fc4 electrodes, the central region included the Cz, Cpz, and Pz electrodes, the left parietal region included the C3, Cp3, and P3 electrodes, the right parietal region included the C4, Cp4, and P4 electrodes, and the occipital region included the O1, OZ, and O2 electrodes (Fig. 1).
Directed Transform Function. Directed Transform Function (DTF) is a physical quantity that describes the direction and strength of information transfer between the signals of each channel. The strength of the causal relationship between channels can be judged by the size of the DTF value, as proposed by Kaminski and Blinowska [12]. It is a method to quantitatively characterize causal connections of frequency domains based on a multivariate autoregression (MVAR) model, and it extends Granger causality analysis to variables of any dimension [13]. Studies have confirmed that using DTF methods to assess the connectivity patterns of the cerebral cortex is effective [14]. The causal connection strength \({\gamma }_{ij}^{2}\left(f\right)\) from channel \(j\) to channel\(i\)can be expressed as:
$$\gamma _{{ij}}^{2}\left( f \right)={\left| {{H_{ij}}\left( f \right)} \right|^2}/\sum\limits_{{m=1}}^{k} {{{\left| {{H_{im}}\left( f \right)} \right|}^2}}$$
1
In the formula, \(H\left(f\right)\) is the transfer matrix and \({\gamma }_{ij}^{2}\left(f\right)\) is the normalized DTF matrix. In this paper, the calculation of DTF was determined by eConnectome toolbox developed by He et al. [15].
\({DTF}_{mean}\) . This is the average value of the DTF matrix that is used as an indicator that directly describes the causal connection strength of the EEGs. In the causal network, \({DTF}_{mean}\) is defined as the ratio of the actual number of connected edges to the possible total number of connected edges [16]. The calculation formula is as follows:
$$DT{F_{mean}}=\frac{1}{{k\left( {k - 1} \right)}}\sum\limits_{{i \in K}} {} \sum\limits_{{j \ne i \in K}} {DT{F_{ij}}}$$
2
In the formula, \({DTF}_{ij}\) represents the directional transfer function matrix from channel \(j\) to channel \(i\), \(k\) is the number of nodes, \(K\) is the set of all nodes in the causal network, and the value of \({DTF}_{ij}\) is the edge of the causal network. Higher values of the \({DTF}_{mean}\) indicate there are more node connections, and it also reveals the degree to which the nodes coordinate activities, from a global point of view, in the causal network.
Graph Theory. Graph Theory is a mathematical theory and method for quantitative research and analysis of network topology. Complex network analysis based on graph theory can mathematically quantify the changes in topological properties of network structures; hence, it is widely used in the research on brain networks. It is necessary to set a threshold to transform the DTF matrix into a binary directed matrix to establish a functional network using causal analysis as a measure of network connectivity. When a threshold (T) is given, all the elements greater than T in the DTF matrix are set to 1, indicating that there is a causal connection between the corresponding nodes; all elements less than T are set to 0, indicating that there is no connection between the corresponding nodes. Without causality of the node itself, all diagonal elements of the connection matrix are set to 0.
The clustering coefficient and global efficiency are two important parameters of small-world network properties and are mainly considered in this study. The clustering coefficient (C) is a physical quantity that represents the degree of closeness between nodes and adjacent nodes in the network, and it is an index to measure the degree of grouping of the network [17]. The calculation formula is:
\(C=\frac{1}{N}\sum\limits_{{i \in K}} {{c_i}}\) , \({c_i}=\frac{{2{e_i}}}{{{k_i}({k_i} - 1)}}\) (3)
where \({c}_{i}\) is the clustering coefficient of node\(i\), \({e}_{i}\) is the number of adjacent actual connected edges of node \(i\), and \({k}_{i}\) is the degree of node \(i\). In the network, the average of the clustering coefficients of all networks is the clustering coefficient \(C\) of the network.
Global efficiency (E) reflects the global transmission capability of the network [18] and measures the comprehensive index of the speed of information transmission in the network. In a network, the higher the global efficiency, the faster the rate of information transfer between nodes. The formula for calculating global efficiency is:
$$E{\text{=}}\frac{1}{{N(N - 1)}}\sum\limits_{{i,j \in V,i \ne j}} {\frac{1}{{{l_{ij}}}}}$$
4
where \({l}_{ij}\) is the characteristic path length from node \(i\) to node \(j\).