Abstract
The physical properties of fabric causing an uncomfortable tactile perception under certain clothing pressure has always been a difficult problem in the field of fabric comfort research. According to a large number of works in the literature, the amygdala was recognized as the key brain region for negative perceived emotions. In order to investigate the fabric factors causing the signal changes in the amygdala brain region, functional magnetic resonance imaging was used to monitor the amygdala brain region and its anatomical sub-brain region under the same degree of compression stimulation from several different corsets, and the percent signal changes (PSCs) were extracted and analyzed. The results showed that there was a significant positive correlation between the PSCs of the centromedial group of the amygdala and the average dynamic friction coefficient (MIU) of the fabric at the level of 0.05, and a general linear model was established (R2 = 0.998, p = 0.019). These results indicated that the surface friction properties of the fabric successfully attracted the attention of the central amygdala, and the attention increased linearly with the increase of MIU. This finding not only laid a foundation for exploring the brain perception mechanism of fabric discomfort, but also provides a possibility for further quantification of fabric discomfort perception by using the amygdala brain region.
The brain perception of fabric pressure comfort has important practical value and scientific significance in the field of fabric comfort perception representation. However, the pressure discomfort sensing mechanism, 1 the determination of the critical value of discomfort, 2 the influencing factors and the quantitative characterization of fabric contact comfort 3 have always been a major problem in the research field of fabric contact comfort. According to the formation principle of human perception, the physical stimulation of fabric was transformed into nerve potential signals by human skin receptors, which were transmitted to the central nervous system from the afferent nerve, and then into the cerebral cortex for comparison, judgment and calculation through the central nerve, thus forming comfort perception. 4 Therefore, starting from the cerebral cortex, the in situ characterization of fabric pressure comfort could be truly realized.
Among many brain regions in human body, the amygdala (AMYG) is probably the key brain region to represent the discomfort perception of fabric contact pressure, because the AMYG has long been a key brain region in the production and regulation of cognitive function and emotional behavior. Abnormal changes of the AMYG not only play an important role in the pathogenesis of various diseases, but are also recognized as the root brain region of sadness,5,6 fear, 7 anxiety,8,9 visceral pain 10 and other negative perceptions. According to the general theory, when people were in the state of “mindfulness,” which is a kind of concentrated and peaceful mind, bilateral AMYG activity would be reduced. 11 Moreover, the mindfulness trait was negatively correlated with bilateral AMYG activity, and the depressive symptoms were positively correlated with right AMYG activity. 12 When there was slight discomfort, only the contralateral AMYG was activated, but when the stimulus intensity increased, both AMYG brain regions were activated and the activation intensity increased. In particular, for fear perception, the longitudinal changes in the resting state functional connectivity of the AMYG, especially the left AMYG, persisted for several hours or even a week. 13 Patients with social difficulties, however, experienced no discomfort with the removal of the AMYG, even if they were face-to-face with a stranger. 14 Previous studies have shown that the emotional dimension of human perception of breathing discomfort (unpleasurable) is processed in the right anterior insula and AMYG. 15 Kanosu et al. 16 also found that the bilateral blood oxygen level dependent (BOLD) signal in the AMYG was enhanced when the body felt warmer tactile discomfort during cooling. Tan et al.17 analyzed the human brain stimulated by heat pain in fabric contact, and found that the contralateral AMYG was activated at 41°C, while the bilateral AMYG was activated at 51°C. Other studies had shown that abusive thoughts increased AMYG–visual cortex connectivity in adolescents. 18 Although a minority of studies had suggested a corresponding role on the AMYG in appetitive and affectively positive emotion, 19 the critical functional role of the AMYG is still often characterized as negative, which has been frequently proved by numerous studies based on fMRI (functional magnetic resonance imaging), EEG (electroencephalograms), SPECT (single photon emission computed tomography) and PET (positron emission tomography), as well as vivo brain morphometry using structural magnetic resonance imaging (MRI). The most typical case was that a significantly stronger activation in the AMYG occurred when uncomfortable visceral sensations were produced. 20 Furthermore, even uncomfortable residential environments could also induce significant activation in the AMYG. 21 In other words, “the AMYG: sensory gateway to the emotions”, as Aggleton and Mishkin stated. 22 Particularly worth mentioning is that although the event related potentials (ERPs) method had the smallest time resolution among the various techniques for assessing brain perception, which could reach hundreds of microseconds 23 and therefore was very suitable for rapid identification of dynamic comfort, from the perspective of spatial resolution, both the EEG and ERPs methods are limited by the volume conductor effect and individual skull differences, resulting in low spatial resolution. In recent years, the use of fMRI, which produces images using the electromagnetic principle, has greatly improved the spatial resolution, with a maximum up to 25–100 μm, 24 making up for the defect of the current brain monitoring technology. Therefore, the technique of fMRI used in this study was very innovative in the representation of changes in brain response to clothing contact stimulation.
All of above suggests that the AMYG plays a critical role in the origin of fabric tactile discomfort, in all probability. In other words, it might be a characteristic brain region representing the perception of fabric tactile discomfort. Therefore, this study focused on the signal changes of the AMYG brain region under certain fabric contact pressure stimulation, and attempted to explore whether there was a significant correlation between fabric properties and the AMYG brain region, so as to explore the possibility of using the AMYG brain region to represent fabric discomfort.
Materials and methods
Subjects
Seven female volunteers without history of mental illness and metal implantation were selected as the volunteers for this project. All volunteers were healthy, with a similar age (25 ± 2 years old) and a similar body shape (mean height = 1.54 ± 0.05 m, mean weight = 48.74 kg, mean body mass index = 20.6 ± 1.11 kg/m2, mean belly fat thickness = 0.95 ± 0.18 cm, mean lower chest circumference = 74 ± 2.33 cm, mean waist circumference =68.57 ± 2.13 cm, mean abdominal circumference =73.86 ± 3.09 cm). Due to the fact that tactile perception would be influenced by memory, personality, expectation and other psychological factors,25,26 after full knowledge and understanding of fMRI scanning, they accepted simple training in the scanning procedures of this project, and eventually they all signed informed consent voluntarily. The study was approved by the ethics committee of Zhejiang Sci-Tech University.
Materials and apparatus
Three popular metal-free boneless corsets with different fabric structures (weft knitted, spacer knitted and warp knitted) were selected as fabric samples for this experiment. The reason for choosing test samples without metal was that there should be no metal in the subsequent fMRI test, otherwise it would be adsorbed by the powerful magnetic field of the instrument, thus causing unnecessary harm. The requirement of no bones was mainly to avoid the impact of bones on the fabric and human skin contact. The number of experimental samples was limited by the working time of the instrument and the time the human body could withstand continuous scanning, according to a doctor's advice that each person could receive continuous stimulation of three samples at most at one time, at the same time, in order to avoid the participants undergoing fMRI experiments at a different time when their different psychological and physiological states could cause disturbance to the final result. Finally, three samples were selected. The length and width of the corsets were 50 and 25 cm, respectively. Both ends of the samples were hook and loop fasteners. In this way, the experimental corsets could be stretched or relaxed quantitatively.
A YG141N digital fabric thickness gauge was utilized to measure the fabric thickness and a YG026MB-250 universal electronic fabric strength tester was applied to test the tensile properties, load-bearing tensile properties, elongation deformation properties, stress relaxation properties and fatigue resistance. A KES-FB system was used to measure the bending properties, surface friction properties and touch feelings of warmth or coolness of the fabrics. FMRI scanning were conducted on Ingenia 3.0T medical fMRI equipment. The time of echo was 30 s, time of repetition was 3 s and layer thickness was 3 mm in the functional and structural images, and the total functional and structural image scanning times were 190 s (the pre-scanning time was 10 s and scanning time was 180 s) and 300 s, respectively. The 3D-GRE T1WI sequence structure image scanning was from left to right.
Tests of basic physical and mechanical properties of fabric samples
All of the physical and mechanical properties of fabrics were tested in the constant temperature (20 ± 2°C) and humidity (65 ± 5% RH) physics laboratory of Zhejiang Sci-Tech University. All samples were pre-conditioning for 24 h before testing. Tensile testing proceeded according to Chinese standard GB/T39231-2013 The first part of the fabric tensile property —— the measurement of fracture strength and elongation at break (strip method).
27
Five samples were taken for each fabric sample, with an effective size of 10 cm × 5 cm, 150 mm away from the cloth edge. The rising speed was 100 mm/min and the descending speed was 300 mm/min. According to Chinese standard FZ/T 70006-2004 Test Method for elastic resilience of knitted fabric,
28
the force at constant elongation, elongation rate at fixed force, elastic recovery rate and stress relaxation rate were measured. The calculation formulas are as follows:
In Equation (1), L0 represents the length (original length) of the specimen after pre-tension, in millimeters, and L1 is the length stretched to a predetermined stress in millimeters.
In Equation (2), L1 is the length of the specimen stretched to a fixed load value, L0 is the length of the sample after applying pre-tension and L0′ is the length of the specimen (including the plastic deformation) when the pre-added tension was re-applied after resetting after the tensile test; all units are millimeters.
As for the stress relaxation rate, the tensile rate of the specimen was 50 mm/min, the predetermined stop time was 3 min and the predetermined elongation was 20%. The number of stretch–shrinkage cycles was one. After stretching once between zero elongation and constant elongation, the maximum force F1 was recorded immediately, the elongation was maintained for 3 min and then the force value F0 of the specimen was recorded. The calculation formula was as follows:
For the force at constant elongation, the two ends of the length of the sample were evenly fastened in the gripper, the instrument started to apply 1N pre-tension, and then when the tension reached the predetermined elongation value of 20%, the instrument was stopped for 1 min and the tensile force value was automatically recorded by the instrument. The test results were represented by the average value of the data of five samples.
FMRI scanning
FMRI experiments were conducted on each sample under the same 20% stretching stimulation to explore the response of the AMYG brain region to fabric perception under the same stretching condition of different fabrics. Based on analysis of the literature,29–31 it could be concluded that the garment pressure would reached about 1.428 kPa when the elongation of the elastic fabric was 20%, about 2.196 kPa when the elongation reached 30% and 3.338 kPa when the elongation was 40%. For the adjusted girdle, the garment pressure might be greater than that of normal elastic fabric due to its high density at the same elongation. Research results showed that when the pressure exceeded 1.5 kPa, the human body would start to feel uncomfortable, and when the pressure exceeded 2.46 kPa, it reached the category of extremely uncomfortable. 32 Therefore, when the elongation of the girdle was about 20%, the human body would produce an uncomfortable perception. Besides, this extension length was also the result of taking normal human health into account. Before the fMRI test, each sample was stretched to 20% and marked with a line, then returned to normal. During the fMRI scan, the sample was in direct contact with the skin of the waist and abdomen of the human body, and quickly stretched to the marking line, which was fixed by hook and loop fasteners, so that the human skin was kept stimulated by 20% clothing contact pressure.
The temperature and humidity of the experimental environment were 20 ± 2°C and 65 ± 5% RH, respectively. First of all, all participants entered the laboratory 1 hour before the formal test to adapt to the test environment. During this period, all participants wore a loose-fitting tank top, shorts and a hospital gown to avoid interference from other clothing pressures. At the same time, we reintroduced fMRI scanning precautions to the participants to ensure safety factors and keep them relaxed and awake psychologically. Then, the pre-scan training was started. Finally, in order to avoid interference caused by the noise of the instrument, each participant wore earplugs during the formal experiment. If any discomfort occurred during the test, the participant could lift her leg at any time to signal the operator to stop the test.
For fMRI experiments, a block design 33 was adopted. Each subject was asked to lie flat with her eyes closed but keeping the brain awake. To avoid the interference of noise, the subjects were also given earplugs. After resting for 30 seconds, 20% stretch fabric surface tactile stimulation to the waist of the human body was applied and lasted for 30 seconds, and each process was repeated three times.
Data analysis
SPM12 (Statistical Parametric Mapping) was used for image preprocessing, individual analysis and group analysis. 34 Anatomy was used to select the brain region as a brain ROI (region of interest). 35 The so-called ROI was referred to a mask file, which was used to filter out and remove all the activated areas that were not in this brain region. The remaining activation clumps within the mask brain region were analyzed. 36 In other words, all the analysis of this topic were only conducted in this ROI. The specific algorithm flow is shown in Figure 1.

Algorithm flow of region of interest (ROI) analysis. FMRI: functional magnetic resonance imaging; PSCs: percent signal changes.
In this project, the AMYG cortex was extracted to make a ROI, and anatomical brain regions in the AMYG were also extracted to make sub-ROIs. Finally, Marsbar
37
was utilized to extract the PSC (percent signal change, or % signal change) of the ROI, which denoted the PSC of the BOLD response within the ROI. The so-called PSC was calculated through the time series, which could be simply equivalent to the percentage of BOLD signal values of all voxels in the task time phase in the BOLD signal values of all voxels in the rest time series. Therefore, the calculation formula38,39 could be simplified as
Obviously, the PSC itself was calculated relative to the baseline (which could be the mean of the entire time period), and thus contained the concept of the baseline itself.40,41 Therefore, compared to the activation intensity obtained by the comparison calculation, the calculation of the PSC need not be a control condition, which was more intuitive and understandable. 42 The higher the PSC, the more attention the brain region paid to the stimulus.
Results and discussion
Results of basic physical and mechanical properties of fabric samples
The summary and comparison table of the physical and mechanical properties of various sample garments obtained by the test is given in Table 1.
Summary and comparison table of basic performance and physical and mechanical properties of samples
As can be seen from Table 1, Sample 1 was the heaviest, and its surface property was in the middle among the three. It had excellent transverse tensile ductility and elastic recovery rate, but its longitudinal modulus was very low, and it was easy to stretch and deform. Sample 2 had medium thickness, the best surface performance, was the most smooth and flat, had high breaking strength, and excellent elastic recovery rate, low elongation under the same tensile force, was not easy to stretch to deformation and its bending stiffness was in the middle. Sample 3 was the thinnest, had the worst surface performance, the lowest elongation at break, was difficult to stretch and had the lowest bending stiffness but the largest bending hysteresis moment.
Production results of ROI-AMYG and sub-ROIs-AMYG
In order to avoid the interference effect of other brain regions, the brain region of the AMYG was made into a ROI. All analyses were only performed in the ROI-AMYG, rather than in the whole brain. The ROI-AMYG shown in Figure 2 was made, calculated and depicted by Anatomy, Marsbar 37 and BrainNet Viewer, 43 respectively.

Full view of the region of interest- amygdala on (a) the transparent brain, (b) the surface of the brain, (c) the brain mask (zero was the edge of the mask) and (d) visualization and statistics.
Coordinates of the center of mass of the ROI-AMYG in the MNI (Montreal Neurological Institute) space were (–0.531, –0.297, –22.1). The voxel size was 5177 mm. The maximum/minimum in the X, Y, Z directions were (–33/35, –13/5, –34/–10).
Production results of the sub- ROI-AMYG
Actually, the AMYG is not a unitary homogeneous structure but rather a complex of many subnuclei, which could be described using different parcellation schemes, such as the myeloarchitecture method, cytoarchitecture method and chemoarchitecture method. One of the most widely accepted classification schemes is distinguishing medial amygdaloid nuclei alongside the stria terminalis (AStr) and the superficial group (SF) from the centromedial group (CM) and the laterobasal complex (LB), 44 as shown in Table 2.
Detailed anatomical structures of the amygdala cortex
In order to identify sub-brain regions in the AMYG that paid the most attention to fabric, these four sub-brain regions were respectively made into sub-ROIs by Anatomy, and then the sub-ROIs was displayed by BrainNet Viewer. Sub-ROIs are shown in Table 3 and Figure 3.
Definition information of sub-regions of interest (ROIs) in the amygdala
AStr: stria terminalis; SF: superficial group; CM: centromedial group; LB: laterobasal complex.

Definition of the sub-regions of interest in the amygdala: (a) stria terminalis; (b) superficial group; (c) centromedial group and (d) laterobasal complex.
Results and discussion of PSCs in the ROI-AMYG and sub-ROIs-AMYG
Limited by experiment times and interference from individual differences, in order to avoid excessive experimental errors, the extraction results of PSCs of seven subjects are presented one by one, instead of using the average method for analysis, because some individual differences might be caused by differences in psychological and physiological effects among individuals.45,46 By eliminating individual outliers, experimental results of most subjects were selected for analysis. Finally, the PSC results of the ROI-AMYG and sub-ROIs-AMYG under the stimulation of the same contact pressure of all kinds of samples are obtained as shown in Table 4 and Figure 4.
The results of extracting percent signal changes of the region of interest (ROI)-amygdala (AMYG) stimulated by fabric samples
AStr: stria terminalis; SF: superficial group; CM: centromedial group; LB: laterobasal complex.

(a) Average percent signal changes (PSCs) of each region of interest (ROI) and (b) the distribution of PSCs in various samples. AMYG: amygdala; AStr: stria terminalis; SF: superficial group; CM: centromedial group; LB: laterobasal complex.
From Table 4 and Figures 4(a) and (b), the PSCs of the CM brain region in AMYG were larger than those of the other brain ROIs, regardless of the sample. In other words, in spite of the differences in the physical and mechanical properties of the three samples, the CM brain region in the AMYG was always the most concerned with fabric stimulation, even more so than the whole AMYG. This might be because other brain regions in the AMYG would not pay much attention to the fabric contact stress stimulation and focus instead on other stimuli, thus distracting the entire AMYG from the fabric stimulation.
The variability in PSCs observed in Figure 4 was inescapable, as they fluctuated slightly up and down sometimes because signal detection arose from a complex mixture of neuronal, metabolic and vascular processes 47 ; the analysis of BOLD-fMRI might be greatly hindered and further severely corrupted by multiple non-neuronal fluctuations of instrumental, physiological or subject-specific origin (cardiac pulsatility artifacts including cerebrospinal fluid movement, vessel pulsation, tissue deformation and so on 48 ).
Correlation analysis between PSCs and physical properties of fabric
Since there were only three experimental samples selected, they were not suitable for principal component analysis or other mathematical statistical methods. In order to determine which properties of the fabrics caused the difference in PSCs of the AMYG brain region, after the above individual analysis, Pearson correlation analysis between the PSCs of the AMYG and its sub-brain regions and physical and mechanical performance indicators of samples was conducted and the result is shown in Table 5.
Pearson correlation coefficients between physical and mechanical properties and percent signal changes of each brain region of interest
*The correlation was significant at the 0.05 level (bilateral).
AMYG: amygdala; AStr: stria terminalis; SF: superficial group; CM: centromedial group; LB: laterobasal complex.
As can be seen from Table 5, among various fabric properties, only the dynamic friction coefficient, the mean coefficient of dynamic friction (MIU), had a significant positive correlation with the PSC of the CM brain region at the level of 0.05.
Establishment of a quantitative linear model
In order to clarify the quantitative relationship, the general linear model of MIU and PSC of the sub-ROI-CM were constructed, as shown in Figure 5, which showed a significant linear fitting effect (y = 0.302x + 0.648, R2 = 0.998, p = 0.019). The results showed that the surface dynamic friction of fabrics attracted the special attention of the CM, and the attention increased linearly with the increase of MIU.

Linear fitting model of the MIU of fabrics and percent signal changes (PSCs) of the sub-region of interest (ROI)-centromedial group (CM).
Discussion on the variation of the percent signal change in the central amygdala with fabric surface performance
What must call for special attention was the central AMYG, located in the CM, which is a critical part for emotional regulation in response to behaviors related to stress and pain. 49 On the one hand, a large proportion of neurons in and around the central AMYG had the ability to receive somatosensory information of a nociceptive nature. 50 On the other hand, the basolateral AMYG received polymodal inputs from all sensory systems and the thalamus, then projected to the central AMYG, which has been called the “nociceptive” AMYG, which was responsible for pain perception and modulation. 51 The central AMYG projected to the hypothalamus, the bed nucleus of the AStr and the brainstem, 52 so as to influence descending and top-down modulation of pain-related signals. It was not difficult to conclude from the above that there was a proven correlation between the central AMYG and negative perception.
In fact, in addition to tactile stimuli, a negative visual, auditory and emotional stimuli could also cause differences between the AMYG subnuclei. For example, the visual attention of the central AMYG to pain was significantly reduced after compassion training, 53 and previous studies on auditory perception also showed that the signal changes related to positive auditory stimuli mainly occurred in laterobasal group, while the negative response mainly occurred in the SF and CM, which might be related to the lateralization or specialization of the AMYG function. 54 Among them, the central AMYG was more strongly connected to regions involved in sensory processing, while the bed nucleus of the AStr was more strongly connected to regions involved in motivational processing. 55 The work in the present study also provided evidence for the functional specialization of the human AMYG. The human AMYG is a gray matter complex composed of multiple nuclei. Although all the AMYG subnuclei are functionally related, each AMYG subnucleus shows functional specialization in processing tasks, such as emotion and perception, and it was recognized that negative stimulation was the most sensitive to the central AMYG, and hemodynamic response amplitude elicited by the negative stimuli was greater and peaked later than for neutral stimuli. 56 This might be related to the fact that the central AMYG is the primary regulator of behavioral and autonomic responses. Through its connections with the lateral and paraventricular hypothalamus, the central AMYG modulates the heart rate, blood pressure, corticosteroid release and skin conductance. The central AMYG’s projections to the ventral tegmental area, locus coeruleus and basal forebrain modulated arousal, vigilance and attention. 57 Other studies suggested that there were multiple circuits in the AMYG, the same neurons were grouped into one subcircuit and subcircuits of genetically identical neurons would serve specialized and functionally dissociable functions. 58 It was worth affirming that functional specialization of AMYG had been confirmed by many studies59,60
Therefore, when the surface dynamic friction coefficient of the fabric was small, the smooth fabric surface did not stimulate the metabolic activities of the central AMYG brain region, which was trended to show a comfortable state. At this point, the central AMYG brain region did not devote too much attention to it, which lead to a low percentage of signal change. In contrast, when the surface dynamic friction coefficient of the fabric was large, the stretching behavior of the fabric stimulated the metabolic activity of the central AMYG brain region, resulting in the perception of discomfort, and thus more attention was paid to it, resulting in an increase in the percentage of signal change.
In addition, some brain research results monitored by ERPs also verified the above research results. Tang et al. 61 compared the amplitude of the peak value at brain signal P3 when contacting fabrics with three different friction coefficients (linen > cotton > silk), and found that a higher contact friction would also lead to a higher P3 amplitude. There were also many other research results on tactile stimulation of brain signals, which showed that the increase of fabric friction coefficient could indeed cause more attention in the brain region,62,63 which also provided evidence that the PSC of the AMYG brain region would increase linearly with the increase of MIU. This was mainly because the increase of the friction coefficient of the fabric surface caused more uncomfortable signals or even pain signals, which increased the attention of the AMYG brain region to the stimulus, especially for the central AMYG brain region, and finally showed a linear increase in PSC.
Conclusion
The relationship between the signal response of the AMYG cortex of the human brain under fabric tactile stimulation was explored by fMRI technology in this study. It was concluded that the brain region in which the maximum PSC occurred was the CM in the AMYG, which would be obviously positively affected by the MIU of the fabric. Pearson correlation coefficients reached 0.999, and the correlation was significant at the 0.05 level (bilateral). The attention of the CM increased linearly with the increase of the MIU (R2 = 0.998, p = 0.019), which was because the AMYG brain region would show functional specialization (or functional lateralization) when stimulated by surface contact pressure from the fabric, and this functional specialization would increase with the increase of the friction property of the fabric surface. Although this phenomenon would also occur with emotional, auditory and visual stimuli, this was the first time it had been seen with contact stimuli from fabric surfaces. It is a breakthrough in the field of the fabric tactile comfort mechanism. In addition, this finding also provided a further research direction in the field of brain perception representation of fabric comfort in the future.
Footnotes
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by the National Natural Science Foundation of China (grant no. 52003245), the Fundamental Research Funds of Zhejiang Sci-Tech University (grant no. 2019Q077), the Zhejiang Provincial Natural Science Foundation of China (grant no. LQ18E030007), the General Scientific Research Fund of the Education Department of Zhejiang Province (grant no. 113129A4F21075), the Education and Scientific Research Foundation for Middle-aged and Young Scientist of Fujian Province, China (grant no. JAS180331), Open Funding of the Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, and Zhejiang Provincial Key Laboratory of Fiber Materials and Manufacturing Technology, Zhejiang Sci-Tech University (grant no. 2019QN05), the Natural Science Foundation of Shandong Province (grant no. ZR2020QF115), the Research Foundation of Zhejiang Sci-tech University (grant no. 11313132612042) and the National Natural Science Foundation of China (grant no. 52106205).
