The major issue in the evolution of housing prices is risk of housing price contagion. To model this issue, we constructed housing multilayer networks using transfer entropy, generalized variance decomposition, directed minimum spanning trees, and directed planar maximally filtered graph methods, as well as China’s comprehensive indices of housing price and urban real housing prices from 2012 to 2021. The results of our housing multilayer networks show that the topological indices  of new first-tier cities  rank higher than those of conventional first-tier cities .  Owing to the rapid development of China’s real estate market, housing is a source of concern for ordinary residents and investors, whether for living or investment purposes. Moreover, the factors that influence and cause changes in housing prices are a hot topic. As information exchange becomes increasingly common, obtaining housing price information from various regions has become easier, potentially leading to a correlation effect between housing prices in different regions. Changes in housing prices in one region may cause changes in housing prices in other regions. Therefore, it is necessary to study the relationship between housing prices in different regions to avoid the risk of contagion between regions when housing prices in one place collapse and cause real estate in most regions to experience a downturn through the aforementioned linkage. Moreover, such investigations can improve the effectiveness of housing price control measures and provide useful advice with respect to reducing the systemic risk of real estate.Research on the correlation of housing prices between cities can be divided into two categories: studies related to the spillover correlation of housing prices using spatial measurement methods and those that investigate the correlation between sequences using time series   investigThe aforementioned studies revealed a positive spatial network spillover effect related to housing prices. Time-series analysis methods are more prevalent in housing price linkage research than spatial econometric models. Early research focused primarily on the “ripple effect”, which posits that housing prices have the characteristics of continuous transmission in space. Using data on British urban housing prices, MacDonald et al. 1993)  and Alex93  and AIn addition to using the VAR model, additional research has been conducted on the level of systemic risk in the real estate industry and the associated risk contagion following the subprime mortgage crisis. Li et al. (2019)  used theThe multilayer network method is rarely used to study the relationship between housing prices in the literature reviewed above. However, owing to the shortcomings caused by incomplete information from a single-layer network, we first constructed a multilayer network based on the comprehensive indices of housing prices (CIHP) and real housing prices of 31 major Chinese cities using the GVD and transfer entropy (TE) methods. Subsequently, we use the directed minimum spanning tree (DMST) and directed planar maximally filtered graph (DPMFG) methods to simplify each layer of the network and analyze the source and central cities in the housing price correlation network. The Multiplex Infomap method was used to conduct a community analysis of the multilayer network and study the geographical location and economic characteristics of cities with similar housing price fluctuation characteristics.The remainder of this paper Is structured as follows. In The TE method measures the transfer of housing price information between two cities, whereas the GVD method measures the impact of housing prices in other cities on housing prices in a given city. The correlation network created by these two methods is asymmetric, which corresponds to the asymmetric phenomenon of housing price fluctuation contagion in reality. Therefore, these two methods can describe the relationship between housing prices while also considerably reducing the bias that occurs in single-layer networks owing to the use of a multilayer network. Because the housing price correlation networks constructed by these two methods are all fully connected networks (except for the self-loop), it is difficult to grasp the key information. Consequently, we used the DMST and DPMFG methods to simplify the networks and build simplified multilayer housing price networks.According to Schreiber (2000)  and ChenBased on Diebold and Yilmaz (2014) , we can Because the row sum of the GVD is not always 1, the elements in the generalized variance matrix are standardized to better analyze the spillover relationship between housing prices and can be calculated as follows:Subsequently, the variance decomposition matrix can be obtained as:The diagonal of the obtained GVD matrix is set to 0; only the elements related to housing price overflow are retained. The processed variance decomposition matrix is:Randomly select a node as the root node;Travel all edges and find the smallest entry edges of all points except for the root node. Then, sum up the weighted values of edges to form the new graph. Determine the final minimum arborescence if no cycles exist in the new graph;(1)Choose a node ((2)Set the new edge weight of node (1)Return to Step 2 if the new weight graph contains rings;If a ring exists in the new graph, shrink the ring to a point and change the edge weight. The procedure to change edge weights is as follows:(1)Find a loop in the graph;(2)Remove the edge with the highest weight among the loops, but keep the graph connected;(3)Repeat this process until there are no loops in the graph (but they are still connected) and obtain the minimum spanning tree.Expand the new graph if rings do not exist by the loop-breaking method  ,24. The The housing price correlation network built using the two aforementioned methods is fully connected and has a total of ., 2020)  and a DP., 2020) . The DMSThe network generated using the DMST method is extremely clear and easy to process, but too few edges are retained, and some critical information is frequently overlooked. To retain more edges, it is necessary to make the network as simple as possible while also ensuring that the retained information is sufficient for analysis of the characteristics of the network structure and to identify critical nodes in the network. Thus, we adopt the DPMFG method, which is similar to the DMST method. The calculation steps of the DPMFG method are as follows.(1)By summing symmetric elements, convert the directed network into an undirected network;(2)N − 2) edges remaining;Use the undirected PMFG to simplify a fully connected network to a network with only 3 ((3)Restore each edge in the simplified undirected PMFG network to two directed edges, and keep the direction and weight of the side with the highest weight value as the edge and weight of the directed PMFG. Thus, the network is simplified to a directed PMFG network.Unlike the aggregate algorithm, which simply aggregates the topology parameters from each single-layer network, the multilayer algorithm used in our study also considers connections between points from different layers. Domenico et al. (2013)  and Dome(1)Degree CentralityWhen considering a multilayer network, a multilayer adjacency tensor can be used as an object for the complex relationship of the multilayer network. According to Domenico et al. (2013) , the mulThe degrees of nodes are determined by the sum of each layer in the aggregated multilayer network calculation. In reality, the relationship between two nodes may differ between layers. Thus, when the degrees of each layer are directly summed, errors may occur. The same issue arises in the subsequent calculations of various centrality metrics. For multilayer networks, the association between different layers and whether the nodes between the layers can be connected need to be considered comprehensively. This method directly calculates various centrality measures as a whole, which can better reflect the actual relationship. Using the previously introduced multilayer adjacency tensor, we can directly calculate the multilayer degree centrality vector using the following formula:(2)Eigenvector CentralityEigenvector centrality is an indicator commonly used to describe the importance of a node that often has a high eigenvector centrality when its neighbors also have a high eigenvector centrality. The eigenvector centrality vector in a multilayer network can be used as the solution to the tensorial equation ((3)PageRank CentralityPageRank centrality quantifies how well a node is connected to other nodes. In general, if a node is connected to many other nodes, its PageRank value will be higher. The PageRank calculation simultaneously considers the PageRank value of the node connected to a node; if the PageRank value of the associated node is higher, the PageRank value of the considered node will also be higher. For the multilayer PageRank centrality calculation, we can start from the steady-state solution of the equation . (2015) ), and ujInfomap is a stochastic and fast algorithm used to identify the best modular description of network flows according to the map equation, which measures the length required to communicate dynamics in a network and takes advantage of the information theory duality between finding regularities in data and compressing the data. Flow dynamics in multilayer networks are more complex than in single-layer networks because a random walker moves both intralayer and interlayer, and empirical interlayer weights are usually lacking. According to Daniel Edler et al. (2017)  and DomeWe use To ensure a unique ergodic solution in directed networks, we use teleportation at a rate We derive the recorded steps along links For directed networks, the results are robust to the variation of teleportation rate ., 2015) . In the The map equation can express the description length based on the rates at which a random walker enters and exits modules and visits nodes within modules, which can be used to calculate the rates for a multiplex network. For module codebook Now, we have expressed the description length of a random walker in terms of the three rates at which it enters and exits modules and visits state nodes of physical nodes within modules. Subsequently, we can obtain the two-level map equation in terms of multilayer networks with the per-step average description length   and Zhan. (2020) , the imp(1)Because the order of magnitude of the indicators may differ, the data must be standardized before calculating the entropy value of each indicator. The indicators selected herein are all positive; therefore, the standardization formula for each indicator is:(2)To avoid 0 and negative values when calculating entropy, it is necessary to and add 0.1 to all values.(3)Determine the proportion of the (4)Calculate the information entropy of the (5)Calculate the difference coefficient of the (6)Calculate the weight of (7)Calculate the comprehensive index of housing price (https://www.datayicai.com/readReport/267) (accessed on 27 January 2022) reported by the Yicai website . Because the selected regions are all in developed urban areas, the number of third-tier cities is relatively small.We select the capital cities of China’s provinces  and five well-developed cities  as samples for our study. Therefore, a total of 33 cities are included for analysis; the time span runs from January 2012 to August 2021. The Wind database is used to calculate the housing price index. For subsequent research and analysis, we employ two methods to divide the selected cities. One method involves dividing them into eastern, central, and western regions according to their geographical location ; the method other entails dividing them into first-tier, new first-tier, second-tier, and third-tier cities according to the “Ranking of Cities’ Business Attractiveness in China 2021”  (accessed on 2 December 2021). The selected cities and time intervals are consistent with the CIHP.The real housing price data used in our statical analysis were collected from the Anjuke website , and three periods (one quarter), respectively.Subsequently, we use the DMST and DPMFG methods to translate the TE matrix and GVD matrix, which are generated by the CIHP and real housing prices, into two different four-layer networks. The characteristics of a multilayer network topology are used to describe the influence and contagion of housing prices in various locations.We depict the multiplex networks of CIHP and the real housing price. To visualize the node cities with more edges in the complex network more intuitively, we use the node degree (the sum of outgoing and incoming degrees) as the node size. The larger the node, the more cities with which the city’s housing price is linked in the network. Generally, cities with more connecting nodes play an important role in the housing price association network. When a city’s housing prices are affected, the central city is not only more vulnerable to the impact of changes in housing prices in other cities, but changes in its housing prices can also spread to others cities.The amount of information required to analyze central cities is insufficient if the number of edges in the simplified network obtained from the DMST is small and the degree difference of each node is not large. Hence, for the DMST-simplified network, we only examine the source nodes, that is, nodes with only outgoing degrees and no incoming degrees. To a considerable extent, the source nodes can represent the source of housing price correlation, which is of significance for analyzing the contagion source of housing price changes and preventing and controlling abnormal housing price changes. In other words, we analyze the source node of the DMST-generated simplified network and the center node of the DPMFG-generated simplified network.The multilayer network structure of the CIHP and real housing prices can is shown in The source cities of the CIHP DMST network are Guangzhou and Xiamen, whereas the source cities of the DMST network of real housing prices are Shenzhen and Guangzhou. Therefore, there are three source cities: Guangzhou, Xiamen, and Shenzhen. The CIHP in the source cities is high, particularly in Shenzhen and Guangzhou, which are the top two among all investigated cities. Xiamen is ranked slightly lower, in sixth place. These results show that the source of the contagion of housing price changes is often a city that has a rapidly rising housing prices, which plays a leading role for all cities. Thus, when housing prices in such cities rise or fall, the effect is distributed to other cities, causing housing prices in other cities to change.The four-layer price complex networks simplified by the DPMFG show that the core cities differ depending on the complex networks. In the network constructed using the CIHP and TE methods, the top cities with the highest degree of nodes are Lanzhou, Changsha, Qingdao, and Wuhan. Only Shenzhen and Shanghai have slightly larger node sizes than the first top central cities among the four traditional first-tier cities. The top central cities are replaced by Shenyang, Tianjin, Hangzhou, and Haikou in the network built using the CIHP and GVD methods. The degree of the first-tier cities is higher than that determined using the TE method, although only a medium degree, with a large gap compared to the top cities.From the perspective of the network built using real housing prices and the TE method, Qingdao, Harbin, and Yinchuan are the most prominent cities, ranking far higher than Beijing and Taiyuan. Only Beijing ranks in the middle of the first-tier cities, with the other three cities ranking extremely low. Zhengzhou and Xi’an rank far higher than other cities in the network constructed using real housing prices and the GVD method, whereas the first-tier cities rank lower.Excluding some second-tier cities (Lanzhou and Harbin) and third-tier cities (Haikou and Yinchuan), the rest of the top-ranked cities are new first-tier cities. Qingdao, in particular, has a high degree in the two DPMFG-simplified networks built using the TE method, which is at the heart of the comparison. Conversely, Qingdao has a low degree for networks constructed using the GVD method. The traditional notion that first-tier cities should have a substantial impact on the housing prices of other cities is not reflected in the four DPMFG-simplified networks presented above. Except for Beijing and Shenzhen, which are in the middle of the network built using the TE method, the ranking in the other cases is extremely low.The light- and dark-green stripes in We calculate the multi-PageRank centrality with reference to Domenico et al. (2015)  and the Notably, the eigenvector centrality value for the network derived from the DMST is 0 because the calculation of the eigenvector requires each point to be reachable, whereas the DMST network cannot satisfy this condition c,d. RegaAlthough Tianjin ranks first in terms of the multi-centrality of real housing prices, Qingdao ranks first in multi-degree-out centrality, indicating that Qingdao has the characteristics of a highly central city  or in the same coastal special economic zone as Shenzhen (Xiamen) and thus do not have a large gap relative to the first-tier cities. The first-tier cities are not all part of the same community according to the community clustering diagram of real housing prices. Except for Beijing and Guangzhou, which are in the same community, Shenzhen and Shanghai are in separate communities with other cities and are separated by a considerable distance. For example, Shanghai is in the same community as Hefei, Chengdu, Kunming, and Yinchuan, whereas Shenzhen is not clearly in the same community as the other cities. In general, the community clustering result obtained by using the CIHP is more effective for first-tier cities and is highly correlated with their actual economic level and geographical location.The three cities of Tianjin, Qingdao, and Shenyang, which are among the top 10 cities in various categories of multi-centrality, are in the same community clustering of the CIHP, as are Jinan, Wuhan, and Changsha. Tianjin and Qingdao remain in the same community in terms of real housing price clustering, whereas Shenyang is a member of a separate community. Jinan and Wuhan are also in the same community as Tianjin and Qingdao, whereas Changsha is not in the same community as Tianjin or Shenyang. The clustering results of the two communities show that the central cities with a higher importance are more likely to share the same characteristics and attributes, making it easier for them to be grouped together.It can be concluded that the multilayer complex network community clustering results obtained from the CIHP are superior; these results not only accurately divide the first-tier cities into the same community but also cluster the cities with higher rankings as per the multilayer network structure characteristics into the same community. There is still a substantial gap between the outcomes of real housing prices and the actual situation, and the outcomes of community division are less effective than those from the CIHP. Therefore, the multilayer complex network constructed using the CIHP is more consistent with the actual situation and has a high degree of recognition with respect to identifying important nodes.Focusing on the risk contagion of housing prices, we used the TE and GVD methods to construct a fully connected network with respect to housing price correlation. Subsequently, we simplified this network using the DMST and DPMFG, yielding two different four-layer multiplex network graphs of the CIHP and real housing prices, respectively. By analyzing the source cities from the DMST network, we found that the source cities are Guangzhou, Xiamen, and Shenzhen, which are all among the top cities in the CIHP. In addition, according to the node size of the DPMFG network, the central city is not a traditional first-tier city; rather, new first-tier cities appears more frequently in the central location.Calculation the multi-centrality of multilayer networks shows that traditional first-tier cities do not rank extremely high in the various categories of multi-centrality. However, Tianjin, Qingdao, and Shenyang, which are new first-tier cities, occupy the central position in the multilayer networks. Furthermore, new first-tier cities replace first-tier cities as the core of the price fluctuation correlation network. Subsequently, we used the Multiplex Infomap method to cluster multilayer networks and found that the community cluster based on the CIHP is most effective. The first-tier cities and some cities near Shanghai are members of the same community, as are Tianjin, Qingdao, and Shenyang, with high network structure indicators.The methods of building multilayer networks and dynamic topology extraction can also be applied to financial networks. For example, when building stock/bank multilayer networks, we can use the closing prices of multiple stocks as the research object, build a multilayer financial network through VD and TE methods, and build dynamic financial networks for crisis early warning research. The method used in the present study has good applicability in the financial field.In the future, we will consider using machine learning to identify early warning signs of rising housing prices. We intend to convert housing data into a symbolic sequence (0 and 1) corresponding to price rises and falls. Through the sliding window method and multilayer network structured indicators  constructed above as the characteristics  of a machine learning model, various machine learning models can be used to forecast the rise or fall in housing prices.


After the first-round (Preliminary Baseline Survey) ultrasound-based examination for thyroid cancer in response to the accident at the Fukushima Daiichi Nuclear Power Plant in 2011, two rounds of surveys  have been carried out in Fukushima Prefecture. Using the data from these surveys, the geographical distribution of thyroid cancer incidence over 6 or 7 years after the disaster was examined.Children and adolescents who underwent the ultrasound-based examinations in the second- and/or third-round  survey in addition to the first-round survey were included. With a discrete survival model, we computed age, sex, and body mass index standardized incidence ratios (SIRs) for municipalities. Then, we employed spatial statistics to assess geographic clustering tendency in SIRs and Poisson regression to assess the association of SIRs with the municipal average absorbed dose to the thyroid gland at the 59-municipality level.P = 0.17 and 0.54, respectively). Poisson regression showed no significant dose-response relationship: the estimated relative risks of lowest, middle-low, middle-high, and highest areas were 1.16 , 0.55 , 1.05 , and 1.24 .Throughout the second- and third-round surveys, 99 thyroid cancer cases were diagnosed in the study population of 252,502 individuals. Both flexibly shaped spatial scan statistics and maximized excess events test did not detect statistically significant spatial clustering  in Fukushima Prefecture. In response to this situation, the Fukushima Health Management Survey (FHMS), which included an ultrasound-based screening program for thyroid cancer (thyroid ultrasound examination [TUE]), was launched in order to monitor the long-term health of the children and adolescents in Fukushima Prefecture.1,2The accident at the Fukushima Daiichi Nuclear Power Plant (FDNPP), caused by the Great East Japan Earthquake of March 113,4 Nevertheless, the first-round survey diagnosed 116 thyroid cancers (including suspected cases), once again raising the question of a link between radiation and thyroid cancer5 as well as the possibility of overdiagnosis without clinical symptoms by the introduction of ultrasonography to a large population survey.6 As summarized by the recently updated review by United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR),7 most studies examining the geographical distribution of thyroid cancer detection rates  in the first-round survey did not show dose-response relationships with regional differences in radiation dose or any statistical spatial clustering of thyroid cancer detection rates.8–10The first-round (Preliminary Baseline) survey, scheduled to run for 3 fiscal years from October 2011, was conducted to establish the baseline information of thyroid cancer prevalence for subsequent surveys. Since the exposure dose of radioactive iodine in Fukushima was estimated as far smaller than that from the CNPP accident, it was expected that an increased occurrence of thyroid cancer was unlikely.11 Using the results of the second-round survey, two studies reported no statistically significant association between the estimated radiation dose and thyroid cancer diagnosis.12,13 Some studies also indicated that the detection rates of thyroid cancer in the second-round survey were associated with the mean external radiation dose in air based on published regional counts of thyroid cancer cases,14,15 although the results could not be adjusted for the age at diagnosis and prevalence and incidence could not be distinguished.16TUEs were continued after the first-round (Preliminary Baseline) survey at 2-year intervals from 2014 onwards. To date, the results of the second-  and third-  rounds of the survey  have been finalised.17 but studies using the second-round survey evaluated the situation only 3 or 4 years after the FDNPP accident.Importantly, assessments of thyroid cancer incidence should be evaluated through multiple surveys based on the observation interval period between them. In the European areas affected by CNPP accident, the number of thyroid cancer cases increased rapidly from 4 years after the accident, and the incidence of thyroid cancer among children (under 15 years of age) peaked at 10 years after the accident,This study thus aimed to statistically examine the geographical variability in thyroid cancer incidence among children and adolescents in Fukushima Prefecture over longer periods compared to previous studies by assessing the data up to the third-round TUE . Spatial cluster detection methods and Poisson regression combined with a discrete survival model were employed to identify areas with excess risk of thyroid cancer incidence and the potential association of geographic indicators of radiation doses with the distribution of thyroid cancer incidence after the first-round TUE.th, 2020 was the data source for this study. The target population for the first-round TUE included children and adolescents (<19 years of age at the time of the accident), which was then expanded in the second-round TUE to include children who were born from April 2, 2011 to April 1, 2012. In the third-round TUE, the current scheduling plan involves testing persons up to the age of 20 years once every 2 years and testing once every 5 years for those who are older. The sizes of the registered population in the first-, second-, and third-round TUEs were 367,579, 359,184, and 345,544, respectively. In this study, we focused on persons who lived in Fukushima Prefecture when the FDNPP accident occurred and who had been tested in the first-round TUE and no thyroid cancer were diagnosed, and at least one of the two subsequent TUEs, resulting in 359,206 target subjects.The Fukushima Medical University conducted the TUEs and compiled the database of the examination results. The dataset as of December 818 Written informed consent for the study was obtained from the parents of every participant. This study using the TUE database was approved by the Ethics Committee of the Fukushima Medical University .Each TUE involved two stages. The primary examination involved ultrasonography; if large nodules  or cysts  were found, or if a definitive diagnosis was clinically required, confirmatory examination by fine-needle aspiration cytology (FNAC) was recommended to confirm the malignancy. We regarded the malignant or highly suspicious of malignancy diagnoses based on confirmatory testing as a diagnosis of thyroid cancer for this study. The details of the TUE protocol are provided elsewhere.i is the index of the municipality based on the residential address at the time of the disaster. io and ie are the number of observed and expected diagnosed cases at the second- and third-round TUEs, respectively. The expected number of cases was obtained from the estimated probability of thyroid cancer diagnoses using the following discrete survival model at the individual level:j and t are the indexes of the subject and the round of TUE (either 2 or 3), respectively. α and kβ are coefficients to be estimated. Suppose a pseudo-observation unit of the combination of the subject and the round of TUE. The unit is defined only for the case that the subject j who takes the tth TUE but is not diagnosed with thyroid cancer in the earlier TUE (s). jty is defined as the diagnosis indicator that takes the value one if subject j was diagnosed at the tth TUE and zero otherwise. jtd is the interval length (in years) of examination dates between the examination date of the tth TUE and that of the most recent prior TUE. jtkx is the kth associated individual factor to be adjusted for the computation of SIR. Sex, age, body mass index (BMI)19 at the examination, and the dummy variables of the round of TUE were considered as the adjusting factors for this study. We regarded BMI <5 or BMI >50 as recording errors of the database and applied an available value from an other-round survey to the incorrect/missing values.For this study, the standardized incidence ratio (SIR) at the municipality level for the study subjects (not diagnosed with thyroid cancer at the first-round TUE) was defined as:kβ), can be interpreted as the associated hazard ratio of one-unit increase in the explanatory variable as in the Cox proportional hazard model. The model can be fitted as a binomial generalized linear model with a complementary log-log link function by treating the jty as independent Bernoulli observations with the probability of jtλ for subject j at the tth round TUE. This type of survival model is suitable for interval-based observations of event occurrence.20 The inclusion of the offset variable, log jtd, corresponds to the adjustment of person-years for a constant hazard model.The exponential value of the coefficient, exp.Since each pseudo-observation was modelled in the form of an independent Bernoulli trial with a rare probability of event occurrence, it should be reasonable to consider that the aggregated behaviors of the observation approximately follow a Poisson distribution, 21 proposed flexibly shaped spatial scan statistics (Flexscan) to search for irregularly shaped clusters of regions with elevated risk using likelihood ratio statistics to compare risks inside and outside possible topologically connected areas. The region with the highest likelihood ratio is called the ‘most likely cluster,’ whose statistical significance can be assessed using Monte Carlo simulation under the null assumption of homogeneous risk. Since the test statistic is obtained as the highest likelihood ratio in the entire study region, this method avoids the problem of multiple testing. Flexscan is expected to detect elevated risk regions along the areas with high doses and display them on the map, even if the true cluster is non-circular . For the technical details, see An alternative hypothesis based on the null hypothesis is that regions with a higher risk compared to the others existed. Tango and Takahashi22 has the highest power for detecting the general spatial clustering tendency of incidence rates.23 In this method, the clustering tendency is measured using the C-index with a pre-fixed scale parameter corresponding to the geographic size of clustering. Since testing the multiple C-index with different scale parameters in searching for the optimal (most probable) scale results in the multiple comparisons, MEET involves computing the multiple-comparison adjusted P-value of clustering with the aid of Monte Carlo simulation. For the technical details, see A clustering tendency of incidence can also be identified as a positive spatial autocorrelation of the relative risks, meaning that SIRs are likely to be similar between areas with closer distance. Such clustering tendency may suggest that SIRs are spatially structured by the distribution of other geographic factors. Tango’s MEETk,i is the dummy variable of the kth dose-range group in the ith municipality . It should be noted that kth group. In accordance with a previous study,13 we referred to the UNSCEAR’s updated information of municipal average absorbed doses in the thyroid gland in the first year after the accident by considering both internal and external exposures. Since the currently available data in the report were only those for infants, we prepared four area groups based on these data  by assuming that the area division reflects general degrees of radiation exposure to the residents . Poisson regression shares the same assumption of the Poisson process for spatial clustering tests:24 In all analyses, the level of significance was set at P < 0.05.All analyses were carried out in the R version 4.0.2  environment using the glm function for the discrete survival and Poisson regression, the R package rflexscan version 0.4.0 for Flexscan, and Tango’s R script for MEET.Figure P-value (0.167) associated with the cluster was not significantly low. MEET also did not detect a substantial clustering tendency in regional thyroid cancer incidence at all spatial scales tested. Figure P-value . This indicates that the municipal SIRs of thyroid cancer were not geographically clustered/structured.Table The Poisson regression models did not detect statistically significant relationships between thyroid cancer incidence and regional mean estimated radiation dose Table . AccordiThe results of the series of analyses in this study showed no substantial geographical variability in the incidence of thyroid cancer in Fukushima Prefecture after the first-round TUE. This is the first study to examine regional differences in the diagnosis rate of thyroid cancer using cohort samples who underwent the first-round TUE and following them until 6 or 7 years since the FDNPP accident in 2011. The long-term observation period increased the statistical power by increasing the number of diagnosed cases, the follow-up assessment of the first-round TUE recipients allowed analysis of incidence rather than prevalence, and individual-level adjustment for intervals between examinations (corresponding to person-years) and for sex, age, and BMI at the time of the examinations allowed us to assess regional differences in thyroid cancer diagnosis rates in a more reliable manner.25 and Ukraine,26,27 suggesting strong radiation-related increased risks of thyroid cancer, such as 2.15  excess odds ratio per Gy with the 0.56 Gy mean thyroid dose for the participants in the Belarus study.25 According to the updated UNSCEAR’s report,7 the absorbed doses to the thyroid gland of the whole population in Fukushima Prefecture were about two orders of magnitude smaller than those in Belarus after the CNPP accident. The mean estimated absorbed thyroid dose in the first year among the non-evacuee population in Fukushima Prefecture was about 5 mGy, and only 0.5% of them were estimated to have received >20 mGy. The low levels of radiation exposure may explain our statistically insignificant results.After the CNPP accident, there were several case-control studies of children and adolescents who had undergone ultrasound examinations in Belarus12,13 We confirmed these findings using the third-round TUE data with a different approach. The AIC values suggested that the fitted Poisson models were statistically inferior to the null model, which assumed homogenous incidence over the region. It is possible that our adjustment for individual BMI attenuated the association between detection rate and radiation dose measures. Our analysis confirmed that a high BMI is associated with an increased hazard ratio for the development of thyroid cancer. However, the addition of the collective dose measurement variable at the individual level did not substantially change the coefficient for BMI.Previous studies using the results of the second-round TUE to analyze the association between exposure dose estimates and the detection rates of thyroid cancer showed no significant association.P = 0.08), and the highest dose group had the highest relative risk . The most likely cluster of Flexscan overlapped with high radiation dose areas, including the municipalities in the vicinity of FDNPP. To interpret these results, care is needed in understanding the sensitivity of thyroid cancer detection without symptoms in the ultrasound examination. Although the sensitivity of diagnosis by testing was assumed to be the same everywhere for the statistical analysis, the implementation of FNAC, which confirms the diagnosis of thyroid cancer, involved subjective judgments by doctors and patients, suggesting that the procedure was most likely performed at times and in areas where the risk was perceived to be high.13,16 This may result in higher detection rates in some areas with higher absorbed doses.Despite these statistically insignificant results, the relative risk estimates for different dose area-groups showed a marginal positive trend  made it difficult to estimate the accurate geographic distribution of radiation exposures. Toki et al results . Additio27 Our results for the discrete survival model showed that the incidence of thyroid cancer decreased in the third-round TUE compared to the second-round TUE, even though it was still approximately 7 years after the FDNPP accident. This finding indicated that there was no increasing trend of thyroid cancer in Fukushima. One possibility could be that the third-round TUE could have been more restrained in the implementation of confirmatory testing, because of the potential overdiagnosis6 from the results of the first-round TUE.In the CNPP accident, the incidence of thyroid cancer among children in the exposed areas remained high for approximately 30 years after the accident.28 the sensitivity of ultrasound screening at the first-round TUE was estimated to be around 0.6–0.7, suggesting that some of the prevalent cases at the first-round TUE may not have reached the indication of FNAC and detected at the second- or third-round TUEs, which may also explain the reduced incidence in the third-round TUE under the assumption that there was essentially no radiation-induced thyroid cancer incidence.In another study using a mathematical model of thyroid cancer development,P-value of the tests may have been underestimated, but no significant clustering tendency was found. While this study used Poisson regression to analyze the geographic relationship between the absorbed dose and incidence in the style of an ecological analysis, it could also be conducted as an individual-level analysis by adding the municipality-level absorbed-dose group variables to the individual-level discrete survival analysis used to estimate the expected values, resulting in a virtually identical result (see This study had several limitations. First, in this study, the tests of spatial clustering and Poisson regression were based on the results of estimating the expected number of municipalities in advance by the discrete survival model, so the uncertainty inherent in the estimation of the expected number was not taken into consideration for the spatial analysis. As a result, the sult see .29 It is also important to note that the number of people who have not been examined by TUE is on the increase, and that follow-up assessments for individuals aged ≥18, who often move out of the region when they graduate from high school, are particularly getting more difficult to follow in later TUEs. Although we adjusted for age in our analysis, we cannot deny the possibility that there is still a bias due to the number of people who have not been examined. Furthermore, our analysis may depend on the size and shape of municipalities used to estimate the level of absorbed radiation doses. Spatially aggregated measurements reducing the exposure variability may result in larger uncertainty in estimating the radiation effects.30 Hence, it is desirable to verify our study result using individual-level measurements analysis of both internal and external radiation doses.Second, as argued above, there would remain potential biases in the observed incidence. It is necessary to conduct a more detailed analysis of the temporal and geographical differences in the confirmatory testing implementation of FNAC to evaluate the detection rates of thyroid cancer.14 rather than only radiation effects. An increase in BMI owing to a reduction in outdoor exercise due to radiation anxiety31 may increase the risk of thyroid cancer in the longer term. In this case, instead of using BMI as an adjustment factor, it is important to carefully monitor regional differences in changes in BMI among the children and adolescents in Fukushima Prefecture.Third, considering the primary purpose of the FHMS thyroid screening as a health-supportive program, it would be desirable to account for wider contextual factors, such as phycological stress,In conclusion, our analysis of cohort data combining information from three thyroid examinations from fiscal years 2011 to 2017 showed no substantial geographic variation in the observed incidence of thyroid cancer after the FDNPP accident among municipalities in Fukushima Prefecture, and no statistical support for a positive dose-response relationship to the updated regional estimates of absorbed dose.


Stroke disease leads to a partial or complete disability affecting muscle strength and functional mobility. Early rehabilitation sessions might induce neuroplasticity and restore the affected function or structure of the patients. Robotic rehabilitation minimizes the burden on therapists by providing repetitive and regularly monitored therapies. Commercial exoskeletons have been found to assist hip and knee motion. For instance, unilateral exoskeletons have the potential to become an effective training system for patients with hemiparesis. However, these robotic devices leave the ankle joint unassisted, essential in gait for body propulsion and weight-bearing. This article evaluates the effects of the robotic ankle orthosis T-FLEX during cooperative assistance with the AGoRA unilateral lower-limb exoskeleton (hip and knee actuation). This study involves nine subjects, measuring muscle activity and gait parameters such as stance and swing times. The results showed a reduction in muscle activity in the Biceps Femoris of 50%, Lateral Gastrocnemius of 59% and Tibialis Anterior of 35% when adding T-FLEX to the AGoRA unilateral lower-limb exoskeleton. No differences were found in gait parameters. Nevertheless, stability is preserved when comparing the two legs. Future works should focus on evaluating the devices in ground tests in healthy subjects and pathological patients. Ischemic stroke is caused by an abrupt obstruction of blood flow to a part of the central nervous system . Stroke Commonly, patients with stroke suffer difficulties performing activities of daily living due to their lack of mobility . This ocThese rehabilitation approaches allow to recover the motor control and the person’s autonomy can be restored . In the Currently, in rehabilitation robotic technologies are wearable robotic exoskeletons and robotic orthoses that can control the movements of different joints in the training process providing power and assistance . ExoskelHowever, commercial and unilateral exoskeletons have a limitation concerning the ankle performance because some of them lack it or have it as a rigid mechanism which causes the joint to have no rotational movement and restricts the range of motion when walking . FurtherThe AGoRA unilateral lower-limb exoskeleton is a structure with rigid actuators located at the center of rotation of the hip and knee joints allowing flexion and extension movement of these joints and passive hip movement in adduction/abduction . It has On the other hand, the robotic orthosis, T-FLEX, is a powered ankle-foot orthosis to assist and rehabilitate ankle dysfunctions. It has two actuation systems in the frontal and posterior part of the leg. Attached to these mechanisms are tendons composed of a flexible and an elastic mechanism that performs the dorsi-plantarflexion movements of the ankle . PreviouConsidering this, the main contribution of this work is the biomechanical evaluation of adding ankle actuation to a hip and knee exoskeleton by comparing 3 modes: (1) the AGoRA exoskeleton (hip and knee), (2) the integration of the T-FLEX orthosis (ankle), and (3) a baseline of the person without wearing the devices. Therefore, the analysis of these comparisons through physiological and kinematic sensory analysis can become essential in the design and development of future lower-limb exoskeletons with ankle actuation for gait assistance for people with mobility impairments. This can be observed in changes generated in muscle activity of four gait-relevant muscles and in gait parameters such as swing and stance times. The assessment was conducted in nine healthy subjects walking on a treadmill for 6 min for the three modes. Moreover, the study analyzes stability and qualitative results such as a questionnaire to observe the perception received by the users wearing the devices.This section describes the design and control of the AGoRA unilateral lower-limb exoskeleton and the T-FLEX robotic orthosis acting together. Likewise, this section explains in detail the experimental protocol with the different stages used to evaluate the devices and the perception of the users.The AGoRA unilateral lower-limb exoskeleton see a is a reThe T-FLEX robotic orthosis is added to the exoskeleton see b, which The exoskeleton comprises a multilevel control design that considers the change of some parameters to assist the user’s gait cycle. This multilevel control is composed of a low-level controller that is equal to the standard controller as a PI controller. In this case, a PI controller is implemented to apply a current controller . A mid-lThe robotic device T-FLEX is implemented to assist the movements in the ankle joint. The main goal is to apply estimated torques that complement the dorsi-plantar flexion ankle movements. T-FLEX was developed with a different concept than the AGoRA unilateral lower-limb exoskeleton, in this case, T-FLEX, lacks a rigid structure . AdditioNine healthy male adults participated in the study. This protocol included three modes , with AGoRA unilateral lower-limb exoskeleton (WE) and with the AGoRA unilateral lower-limb exoskeleton and the T-FLEX orthosis (WE&T)) to analyze the effect of the T-FLEX orthosis on the AGoRA unilateral lower-limb exoskeleton. According to SENIAM guidelines, participants were instrumented with surface electrodes and an EMG acquisition module .To monitor muscle activity, four muscles relevant to the gait cycle  were useThe processing performed in the study was accomplished using MATLAB software . Inertial sensors data was acquired with a sampling frequency of 128 Hz and was segmented and normalised to 0–100% of the gait cycle. Each gait cycle is obtained by consecutive peak heel strikes in the angular velocity of each foot as shown in Electromyographic signals (EMG) were acquired with a sampling frequency of 1024 Hz. To extract the average linear envelope during the gait cycle, raw EMG signals were filtered with a band-pass filter to remove noise and artefact contamination . SignalsFinally, the RMS value was calculated and averaged for each gait cycle to refer to the signal’s average power.(1)Test without exoskeletons (WOE): This test consisted of walking without wearing the devices. Besides this, training was performed using IMU sensors to customize the device’s assistance according to the person’s gait.(2)Test with the AGoRA unilateral lower-limb exoskeleton (WE): In this test, the AGoRA unilateral exoskeleton is attached to the participant. The operating system is initialized with the person in a bipedal stance on the treadmill. This is done to calibrate the reference positions for the hip and knee joints. Then, the information received by the IMU from the tip of the toe is validated, and the gait detection module is executed. Finally, the person starts to walk, and the exoskeleton starts to assist this activity by applying various forces on the hip and knee joints.(3)Test with the AGoRA unilateral lower-limb exoskeleton and T-FLEX robotic orthosis (WE&T): This test is performed with the two devices, the AGoRA unilateral lower-limb exoskeleton and the T-FLEX orthosis. A calibration step is also performed with the person in a standing position on the treadmill to obtain the reference values of the AGoRA exoskeleton joints. The data obtained by the right IMU is validated, and both gait detection modules of the two devices are executed. This is shown in The protocol proposes three modalities , with AGoRA unilateral lower-limb exoskeleton (WE) and with the AGoRA unilateral lower-limb exoskeleton and the T-FLEX orthosis (WE&T)) in order to evaluate the benefit of adding the T-FLEX robotic orthosis to the AGoRA unilateral lower-limb exoskeleton. After instrumenting the person as shown in The QUEST  is a staThe statistical analysis was analyzed with the SPSS software . The normality of data was checked with the Shapiro–Wilk test. Due to the non-normality of the muscle activity data a Friedman Test is performed to evaluate if there are significant differences in each muscle: Biceps Femoris (BF), Vastus Medialis (VM), Lateral Gastrocnemius (LG) and Tibialis Anterior (TA) for the three conditions: without exoskeleton (WOE), with the AGoRA unilateral lower-limb exoskeleton (WE) and with AGoRA and T-FLEX exoskeletons (WE&T). After this, a post hoc test is performed using the Wilcoxon Test to evaluate which conditions have differences.p) was less than 5% (p < 0.05) were considered statistically significant.On the other hand, the spatio-temporal parameters estimate the left foot data has a non-normal distribution; therefore, the Friedman Test is performed and, due to the fact that in the right foot, the data shows the normal distribution, a 1-way ANOVA is performed for the analysis of the data. The differences in which the probability  data to determine if there were significant results regarding having the AGoRA unilateral lower-limb exoskeleton and the addition of the T-FLEX orthosis.Three trials were performed for each subject. Physiological and spatio-temporal parameters were measured as muscle activity of four muscles of each leg and times of the swing and stance phases. This section describes the results obtained from the study.Muscle activity is reported in four muscles for each leg: Biceps Femoris (BF), Lateral Gastrocnemius (LG), Tibialis Anterior (TA) and Vastus Medialis (VM) during gait activity. Data is recorded for 6 min for each muscle and reported as the average RMS value of each gait cycle for the entire session.p-values showing whether there are significant differences between the different conditions in the leg actuated by the devices. As well as Muscle activity data for the BF and VM of the right leg are illustrated in a bar graph in On the other hand, To analyse the qualitative part, the results of the QUEST surveys of perception of the devices characteristics are analysed. Different characteristics such as dimensions, weight, adjustability, safety, ease of use, comfort and effectiveness were evaluated to know the perception of all participants towards the devices. p-values. It can be observed that there are no significant differences when comparing the items in the two conditions.In addition, This paper presents the first physiological and biomechanical evaluation of the use of the AGoRA unilateral hip and knee exoskeleton and the T-FLEX robotic orthosis in healthy subjects. This study allowed the development of an unassisted test that can be taken as a baseline and two assistance tests with the AGoRA unilateral lower-limb exoskeleton and the T-FLEX orthosis, which could be evaluated to observe the effects of adding the ankle assistance of a device with a soft structure such as the T-FLEX orthosis to the AGoRA unilateral lower-limb exoskeleton. On a larger scale, significant reductions were observed in the combined assistance of the two devices, which demonstrates the potential effect it can have on the rehabilitation of people with stroke.With T-FLEX, the muscle activity of the LG and TA is reduced due to the adequate energy provided by the device to the ankle motion. In ankle exoskeletons, such as WAXO, it was observed a reduction in the GL muscle when comparing walking with the device and normal gait . MoreoveOn the other hand, the TA muscle is in charge of the initial swing phase where hip flexion, knee flexion and ankle dorsiflexion are activated simultaneously. The main objective of TA muscle during gait contributes ankle flexion in antagonism with LG . In AEXOMoreover, the assistance of T-FLEX generates the AGoRA unilateral lower-limb exoskeleton to interact more effectively with the person by reducing the BF muscle activity. This is observed in a study of a knee–ankle–foot robot for gait rehabilitation that the muscle activity decreases when the device is placed in assistance mode, which corresponds to effective device assistance to the subjects when walking . MoreoveIn addition, it can be observed that adding T-FLEX regulates the weight of the device; therefore, it generates greater assistance in knee flexion/extension reflected in the reduction of the BF muscle. The opposite occurs in a weight-bearing gait rehabilitation hip and knee exoskeleton, where it is observed that TA and BF muscle activity increases, which may indicate an absence in ankle joint actuation that is compensated by increasing the activity of these muscles in healthy subjects .Consequently, it is observed in this comparison that the applied weight of the two devices (17 kg + 3 kg) to the person does not affect and even appropriately interacts, decreasing the muscle activity of 3 muscles  and compensating the activity of the VM muscle.In this comparison, the LG and TA muscle activities increase because there is no device to assist the ankle, i.e., the positive mechanical power needed for walking and the redirection of the center of mass in the stance phase. When T-FLEX is removed, the LG and TA have to support the weight of the AGoRA unilateral lower-limb exoskeleton that the T-FLEX helped to keep before and the BF and VM are compensated because the AGoRA unilateral lower-limb exoskeleton strategy is adequate enough to not sense the device’s weight. This is confirmed when using a unilateral hip and knee exoskeleton, TA muscle activity increases at heel strike (plantar flexion) to compensate ground reaction forces. This causes the TA muscle activity to increase in order to control the rate of foot plantar flexion . EquallyHowever, the AGoRA unilateral lower-limb exoskeleton is designed to assist in conjunction with the T-FLEX orthosis and weight-bearing AGoRA robotic walker . TherefoIn this comparison, it can be observed that the exoskeleton alters only the activity of the VM muscle. This muscle activity is reduced because both devices are synchronized with each other, generating a reduction of the muscle knee extensor VM which also acts in weight-bearing conditions with different knee positions . The othIt is essential to highlight that when comparing the two legs for stability purposes, in Besides this, the use of T-FLEX did not affect the user’s stable gait. The tendon-driven actuators with T-FLEX allow the dorsi-plantarflexion motion to be reproduced, simulating tendon stiffness and strength. It is observed that this principle is maintained in this study since it generates a constant stiffness in the ankle, causing it to assist and develop stability in the gait cycle .Gait parameters (swing and stance times) did not present significant differences in the modes with the devices in healthy subjects. The device could cause people to alter their gait due to the weight of the system. However, there are articles with healthy subjects that support these results when comparing spatio-temporal parameters such as swing phase, stride and step length, and cadence wearing and not wearing the robotic device. Panizzolo et al. found that this may be an indicator of preserved walking comfort while using an assistive device , whereasIn general, the categories that had only positive scores correspond to the dimensions, safety and effectiveness for the mode with the AGoRA unilateral lower-limb exoskeleton and safety with the addition of T-FLEX. When the statistical analysis was performed, it could be observed that there were no significant differences when comparing the two modes; however, it could be observed that concerning the weight of the device, the addition of T-FLEX generated 33% more between somewhat and not very satisfied. Furthermore, participants indicated ease of use for both devices. This suggests that people found it easy to walk with these devices on the treadmill at an established velocity.An important measure to be improved is user comfort since it is one of the factors that showed the least favourable results in the questionnaire with values of 3.89 and 3.44, respectively, for both conditions. This can be improved with weight-bearing foams in the user’s vest, which can enhance the weight distribution of the device and generate greater comfort for the user. Additionally, the device satisfaction value of the two tests is approximately 4, which indicates a correct perception of the users when using the devices.Two devices were evaluated together for the first time: a hip and knee exoskeleton known as AGoRA unilateral lower-limb exoskeleton and an ankle orthosis known as T-FLEX. Tests were performed on nine subjects walking on a treadmill at a speed of 1 km/h without the devices, with the AGoRA unilateral lower-limb exoskeleton and with the addition to the AGoRA unilateral lower-limb exoskeleton of the T-FLEX orthosis. These tests evaluated the biomechanical effect of adding ankle actuation to a hip and knee exoskeleton.In the analysis of muscle activity, reductions were found in the muscle activity of the BF, LG and TA when adding T-FLEX to the AGoRA unilateral lower-limb exoskeleton, besides compensating the activity of the VM muscle by not increasing its muscle activity according to the weight that is being added to the person with the two devices. This reduction indicates both the assistance of the exoskeleton in hip and knee flexion/extension and the assistance of T-FLEX in the dorsi-plantarflexion movement in the gait cycle.No differences in gait parameters were found. However, stability was found by comparing both legs. This indicates that the devices did not negatively affect the user’s gait by allowing synchronization of the assistance with the person’s natural gait.Therefore, it is concluded that ankle actuation in a rigid hip and knee exoskeleton is required to improve the user’s locomotion, reducing muscle activity and maintaining stability, which indicates the importance of adding ankle actuation. These analysis can become essential in the design and development of future lower-limb exoskeletons for gait assistance for people with mobility impairments. In addition, the user’s comfort should be improved by means of supports in the exoskeleton vest for greater comfort and thus less concentration of the weight of the device in the upper area.Future works should focus on ground tests evaluating both devices and should also include a weight bearing device, known as the AGoRA walker to evaluate the performance in healthy subjects. This is done to have a baseline for future studies with stroke patients.


With the emerging need for human–machine interactions, multi-modal sensory interaction is gradually pursued rather than satisfying common perception forms , so developing flexible, adaptive, and stiffness-variable force-sensing devices is the key to further promoting human–machine fusion. However, current sensor sensitivity is fixed and nonadjustable after fabrication, limiting further development. To solve this problem, we propose an origami-inspired structure to achieve multiple degrees of freedom (DoFs) motions with variable stiffness for force-sensing, which combines the ductility and flexibility of origami structures. In combination with the pneumatic actuation, the structure can achieve and adapt the compression, pitch, roll, diagonal, and array motions (five motion modes), which significantly increase the force adaptability and sensing diversity. To achieve closed-loop control and avoid excessive gas injection, the ultra-flexible microfiber sensor is designed and seamlessly embedded with an approximately linear sensitivity of ∼0.35  Human–machine integration involves a deep interaction among humans, machines, and environments. Tactile (or force information) plays an indispensable role as one of the indispensable media, together with visual and auditory signals ,2,3. It According to the mounting location, force-sensing devices can be divided into two categories: one is mounted on the ground or the desktop, and the other is mounted on the human body ,9. The fMost traditional pressure or force sensors are made from rigid substrates, such as silicon and metal . Due to (1)A low-cost, easy-to-use, origami-inspired force-sensing device with a sandwich structure is proposed; the utilization of common Eco-Flex 50, polydimethylsiloxane (PDMS), and cardboard provide the structure with multi-DOF motions to sense various types of forces.(2)A microfiber sensor with a double-layer structure was designed to improve sensitivity by eliminating strain at the edges. It was seamlessly integrated into the origami-inspired system through a multilayer casting technique.(3)A pneumatically variable sensing system sensitivity is introduced to solve the traditional problem of fixed sensor sensitivity and further expand the adaptability of sensors to different application scenarios.Therefore, based on the investigation above, our work proposes the origami-inspired structure for force-sensing, which can be potentially utilized as a wearable device for collecting human motion signals, as shown in This paper integrates the origami-inspired structure (made of ordinary cardboard) with an ultra-flexible microfiber sensor to create a multi-DOF force-sensing system with variable stiffness. The subsequent sub-section covers the design and fabrication process of the origami structure and microfiber sensors, followed by the integration between the origami structure and microfiber.Z direction. However, aiming to increase dexterity and achieve multiple actuation modes, the whole origami structure was built on the commonly used cardboard. Meanwhile, the middle points of ceases were all processed with diamond cutouts to remove the fixed distance constraint shown in ® 5011 to compact the structure. The glue is used to ensure the airtightness of the force-sensing system.Using the glue ensures no air leaks at the bonding locations and achieves the stiffness maintenance of the whole sensing system. In this paper, the glue ERGO® 5011 is a robust, fast-drying glue from the Swiss company ergo, and is suitable for silicone bonding. The glue ERGO® 5011 is also very efficient, taking only about 10–20 s to dry and position, ensuring the connection precision of the crease joints. To achieve conformal contact and even pressure on the wrist, the green square surface contacting the skin shown in Origami structures, consisting of rigid parts and flexible hinges, have the potential to sustain large force renderings without buckling while being conformal to the skin at the same time. Other advantages, such as low cost, lightweight, and a simple fabrication process, facilitate the development of wearable origami technologies. The structure was folded from a hexahedron with a size of In this section, the proposed ultra-flexible microfiber sensor can adhere to the contact surface and easily integrate into our origami structure above, to achieve closed-loop control and sensitive pressure awareness. This design (in our work) was adopted mainly from the following two perspectives. Considering the excellent reconfigurability of the microfiber sensor in our scenario, the substrate and microfiber sensor were two separate parts. We only needed to build substrate channels with different shapes for mounting the microfiber sensor, simplifying the fabrication and design process. Meanwhile, most microfluidic or microchannel sensors were fabricated with a sandwich structure, which weakened the deformation of the inner sensing element, leading to a lower sensitivity. Therefore, our pressure sensor was composed of PDMS and liquid metal, where PDMS functioned as the substrate material and liquid metal functions as the sensitive element. The design of the strain sensor was derived from the conventional wire-type strain sensor, with liquid metal embedded in PDMS in the form of a microfluidic channel. Both the base material and the sensitive element have excellent stretchability, and the sensor designed in this paper mainly adopted a strain-gate structure. This combination increased the total length of the microfluidic channel, improving the sensor’s resistance and sensitivity. The diameter of the substrate channel was adjustable at around 0.5 mm, and the total length was around 20 mm. As for the size of the microfiber sensor, we could control the diameter of the footprint to become adjustable from 0.5–0.6 mm.Based on the previous design section, this section executes the fabrication and assembly of the origami model and microfiber sensor. We conducted the feasibility tests for our fabrication to evaluate the sensing capacity and origami kinematics. The details are in the following subsections.To achieve sensitive pressure awareness and a high reconfigurable structure, we leveraged liquid metal  are mixed thoroughly for 2–3 min, and the mixtures are set aside under the cool condition. After finishing the preparation stage, the silicone mixture filled half of the mold’s depth for making the outer layer. Then the mold with a half mixture solution will be put into the vacuum thermostat (within 70 degrees Celsius) for about an hour. The next step is manually putting the creased cardboard into the mold and compact pattern layer. After checking that the surface fits, the rest of the silicone mixture solution will be poured into the mold until filled to make the inner layer. The mold will be placed in a vacuum oven (within 80 degrees Celsius) for about half an hour. During the final curing process, the pre-prepared microfiber sensor is laminated to the inner layer of the cured foldable structure. The installation timing can be chosen when the Eco-Flex layer is not fully cured, or when the inner layer has good adhesion. The finished model is folded according to the previous folds, and the joints are glued with universal ERGOThis section discusses the kinematic analysis and simulation study for this proposed origami structure. The performance tests for our microfiber sensor were operated to evaluate the sensing stability and feasibility. Meanwhile, the calibration experiment was also operated to build the relationship between resistance and applied pressure. Moreover, the online acquisition experiment was conducted to verify the pressure generating and sensing capability. Finally, the variable stiffness experiment was conducted to prove that the pneumatic actuation can cause the variable stiffness of the structure to affect the sensitivity of the sensor. The details will be further given in the following subsections.Most force-rendering display device kinematics remain unchanged when mounted on the body as they consist of rigid segments and joints ,32. To aL shown in The foldable structure is modeled as two square planes with the side length of In our scenario, we choose to actuate this origami module by the pneumatic method described previously. Due that the pneumatic channels being distributed symmetrically, the effects of the resultant force renderings are to drive the four legs of the origami model separately for generating motions. The acting direction of the resultant force rendering can be equivalently along the r. Here, we further define that When both planes form a certain angle as roll or pitch motion occurs, there always exists a virtual ball tangent to two planes through point H, the top plane can be described as the point set lying in the top plane H below:As we have defined the normal vector Based on the characteristics of this point set, the mid-points From the derivation above, when the target position of this origami structure is set, we can determine the lengths of In this subsection, we review the modal analysis of this foldable structure to verify the multiple motion modes to meet the requirements to realize various force-sensing types. Here, we only focus on this origami structure to accurately show all possible motion modes. The model has no external workload in this case.Z direction shown in From the results of the modal analysis shown in A further explanation of this experimental setup can verify the versatility of the origami structure’s motion; further experiments on the adaptation tests were carried out. The experiment setup in This subsection presents a finite element mechanical simulation of the microfiber sensor to highlight the direct forces on the microfluidic tube more intuitively, allowing a direct comparison between the commonly used sandwich structure and the dual-layer structure proposed in this paper. Just as the following simulation presents  and baseThe mechanical properties of the microfiber sensor are characterized by an Instron 5943 Testing System . The basic setup of a mechanical test is shown in In this test, repeated compression tests over ten cycles with peak pressures of 10 N, 20 N, 100 N, and 200 N were performed. According to the test results shown in a–d, the In In this section, the simplified experiment is reviewed to verify the feasibility of our system. The origami actuator is driven by pressurized air, and the microfiber sensor is embedded seamlessly into the origami structure to monitor the pressure in real-time. A customized circuit board with a Wi-Fi unit is used to control each air pump and solenoid valve to change the direction of the airflow, read the electric signal from the pressure sensor, and communicate with smart devices, such as computers, to transmit pressure data and receive commands. Following this working principle, the air path diagram according to this system is shown in The final experiment is to verify that the pre-pressure value can affect the sensor sensitivity. The external pressure or calibration load is applied by the Instron system. The basic setup of the mechanical test is shown in In this work, we propose an origami-inspired structure with variable stiffness to achieve multiple degrees of freedom (DoF) motions for force-sensing. The foldable structure is embedded with microfiber sensors through a multiple-layer integration fabrication. Finally, motion modal simulations and adaptability testing experiments demonstrate the flexibility of the origami-inspired structure. Additionally, the calibration and test experiments have successfully verified that the structure’s stiffness can be changed through pneumatic actuation to adjust the sensitivity of force-sensing. Although we verified that the origami sensing system could realize force-sensing, the experiments in our current work were conducted under ideal conditions without external loads.The additional contact loads are considered when the structure is in contact with the skin in a wearing situation. Therefore, further experiments on wearable sensing tests, and a more adaptive origami structure might be further promoted to increase its wearability and interactivity.Moreover, the current modal analysis further demonstrated its flexibility due to combining the soft materials with the origami structure, and its ability to adapt to irregular and variable surfaces, such as the human skin surface. Therefore, the multi-mechanical-mode demonstration is more oriented towards passive force-sensing.While the perception of component forces along the x, y, and z directions are not considered in this paper, the current work only considers the change in sensitivity of the overall sensing system due to changes in pressure caused by external forces, so that only one sensing microfiber is introduced to capture the force information. However, it should be acknowledged that the introduction of several microfiber sensors will significantly enhance the ability of the current system to sense component forces from different directions. Meanwhile, the foldable structure design and the placement of the sensors might be thoroughly reconsidered, as will the decoupling of the component signals from each other. In the future, our foldable pressure-aware system can be embedded with multiple microfiber sensors and investigate the optimal parameters for body-mounted force rendering displays. More physical signals will be considered, such as angle and displacement measurements, and more functional components will be centralized in the system to detect human signals. Due to the low fabrication costs, a high integration level, and suitable sensing range, our wearable system can become affordable daily. It can be used at home according to the medical instructions from doctors.