King’s stage at PET was derived from ALSFRS-R and was regressed out against whole-brain metabolism in the whole sample. The full factorial design confirmed the hypothesis that differences among groups ) existed overall. Comparisons among stages and between each group and HC were performed. We included age at PET and sex as covariates.Three hundred ninety ALS cases with King’s stages 1, 2, and 3  contains supplementary material, which is available to authorized users. Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease affecting upper and lower motor neurons, leading to muscle weakness and wasting that progressively spreads across body regions. In about 50% of cases, also prefrontal regions are involved, causing various degrees of cognitive impairment of the frontotemporal type . Death uIn recent years, King’s staging system has been proposed for ALS, mainly based on the extension of the disease across body regions . It defi18F-2-fluoro-2-deoxy-d-glucose-PET (18F-FDG-PET) since it is a measure of neuronal injury and degeneration in vivo [Published data about the neuroimaging correlates of King’s stages are limited to few magnetic resonance imaging (MRI) studies based on small samples –9. The a in vivo .18F-FDG-PET at diagnosis between 2008 and 2015 at the ALS Centre of Turin  were considered eligible for the study (n = 406). The present study includes patients whose brain 18F-FDG-PET scan was included in the analyses performed in previous publications.Patients diagnosed with definite, probable, and probable laboratory-supported ALS according to El Escorial revised diagnostic criteria , who und18F-FDG-PET/CT and who had a normal neurological assessment were considered eligible as controls. Otherwise, major systemic illnesses, major vision disturbances, psychiatric illnesses, and diseases affecting brain functioning and metabolism represented exclusion criteria.Forty healthy controls (HC) were included. Subjects who were referred to the PET center for suspected lung cancer but in whom no oncologic disease was detected with C9ORF72, SOD1, TARDBP, and FUS genes. All the coding exons and 50 bp of the flanking intron-exon boundaries of SOD1, of exon 6 of TARDBP, and of exons 14 and 15 of FUS have been PCR amplified, sequenced using the BigDye Terminator v3.1 sequencing kit (Applied Biosystems Inc.), and run on an ABIPrism 3500 genetic analyzer. These exons were selected as the vast majority of known pathogenic variants are known to lie within these mutational hotspots. A repeat-primed PCR assay was used to screen for the presence of the GGGGCC hexanucleotide expansion in the first intron of C9ORF72.All patients underwent genetic analysis for 18F-FDG-PET was performed according to published guidelines [18F-FDG was injected. The acquisition started 60 min after the injection. In the patient group, a whole-body scan was performed setting head first. In the control group, a separate brain scan was performed after the whole-body one with a time difference of 15 min. The 18F-FDG-PET acquisition procedure was performed in the same environmental conditions in patients and controls, according to published guidelines [idelines . Patientidelines . PET/CT King’s staging is based on the spreading of motor symptoms in three different body regions  and on the use of non-invasive ventilation (NIV) and enteral nutrition. We used the algorithm proposed by Balendra et al.  to calcun = 390). Indeed, stages 1, 2, and 3 correspond to involvement of 1, 2, and 3 body regions respectively, whereas stages 4A and 4B correspond to the reaching of milestones related to functional impairment .Since our aim was to evaluate the metabolic changes related to the different regional extent of ALS, we focused on patients classified as King’s stages 1, 2, and 3  or the Kruskal-Wallis test was used for quantitative, continuous variables. The homogeneity assumption needed for ANOVA was evaluated through Levene’s test. In the case of significant Levene’s test, the Kruskal-Wallis test was employed instead of ANOVA.The demographic and clinical characteristics of patient groups  and HC were compared as follows. The 18F-FDG-PET template [SPM12 implemented in Matlab R2018b  was used for image spatial normalization to a customized brain n = 390), King’s stage  was regressed out against whole-brain metabolism. The SPM12 multiple regression routine was implemented with age at PET and sex as covariates and the height threshold was set at p < 0.001 (p < 0.05 FWE corrected at cluster level). We used the full factorial design as implemented in SPM12 to test the hypothesis that differences among groups  exist overall . In case the hypothesis was confirmed, comparisons between groups defined according to King’s stage were performed through the two-sample t test model of SPM12. For both analyses, age at PET and sex were used as covariates and the height threshold was set at p < 0.001 (p < 0.05 FWE corrected at cluster level). Although the scope of the study was the assessment of metabolic differences across King’s stages, for a more exhaustive characterization of patient metabolic state, each group defined according to King’s stage was compared with HC, through the two-sample t test model of SPM12, with age at PET and sex as covariates, setting the height threshold at p < 0.0001 (p < 0.05 FWE corrected at cluster level). In all the analyses, only clusters containing > 125 contiguous voxels were considered significant. Brodmann areas (BAs) were identified at a 0–2-mm range from the Talairach coordinates of the SPM output isocenters corrected by Talairach Client .In our sample (p < 0.001), ALSFRS-R total score (p < 0.001), and cognitive status as defined by diagnostic criteria published by Strong et al. [p = 0.019). However, a bivariate correlation analysis did not show any correlation between the site of onset and King’s stage (p = 0.36). Regarding the difference in ALSFRS-R total score, this could be expected since King’s stage has been calculated based on the ALSFRS-R score according to the algorithm published by Balendra et al. [Based on the ALSFRS-R at the time of PET, 165 patients (42.3%) were in King’s stage 1, 133 (34.1%) in stage 2, and 92 (23.6%) in stage 3. The demographic and clinical characteristics of patients belonging to the three groups and of the whole sample are reported in Table a et al. .Table 1Dp = 0.002). Nevertheless, both age and sex were included as covariates in the analyses.In the HC group, the median age was 66.5 years (interquartile range 55.0–72.0), and the male/female ratio was 2.64 (29/11). In the comparisons between each stage group and HC, we found no significant difference for age and sex distribution, with the exception of sex distribution between King’s stage 3 and HC . We identified clusters including the bilateral medial frontal gyrus , right precentral gyrus (BA 4), and right postcentral gyrus BA 2) The full factorial design resulted in a significant main effect of groups  and bilateral medial frontal gyrus (BA 6). When performing group comparisons, no significant difference was detected between King’s stage 1 group and King’s stage 2 group. King’s stage 3 group showed relatively hypometabolic clusters when compared with King’s stage 1+2 group, including left precentral and medial frontal gyrus (BAs 4 and 6) and right precentral, middle frontal, postcentral, and medial frontal gyrus . The comparisons between each stage group and HC resulted in agreement with such findings, showing the extension of frontal metabolic changes from stage 1 to stage 3, with the larger metabolic gap between stages 2 and 3. Posterior clusters, including occipital lobes in all comparisons, of relative hypometabolism in ALS patients as compared with HC have already been reported .The corticospinal tracts (CST) originate from neurons mainly situated in BA 4, corresponding to the primary motor cortex. Nevertheless, CST fibers rise also from neurons situated in other cortical regions, including the premotor and supplementary motor cortex (BA 6), and primary somatosensory cortex . Therefore, we identified a decreasing gradient of metabolism going from patients with King’s stage 1 to subjects with King’s stage 3 in cortical regions from which the corticospinal tracts originate. Furthermore, group comparisons suggested that the main metabolic gap is situated between stages 2 and 3. We detected no difference between subjects with King’s stages 1 and 2. A possible explanation is that patients showing the involvement of three body regions at diagnosis subtend a more rapid neurodegenerative process, involving the prefrontal cortex to a greater extent, as compared with patients with stages 1 and 2. Otherwise, the metabolic difference between stages 1 and 2 is probably under the threshold, being the neurodegenerative process slower and less extensive.Clusters of relative hypometabolism in subjects with King’s stage 3 as compared with patients with stages 1 and 2 included BAs 4, 6, and 3 and extended towards anterior regions (BAs 8 and 9). In a previous study, we identified a decreasing gradient of metabolism going from ALS with normal cognition to ALS with FTD, through cases with intermediate cognitive deficits (ALS-Ci) in frontal clusters including BAs 8 and 9 . Synapse18F-FDG-PET study [A ET study  on 146 pET study  and meta18F-FDG-PET study.The cross-sectional design of our study may have limited our findings. Nevertheless, patients were tested early after diagnosis and the cognitive impairment at that time point likely reflects the speed of lesion spreading to non-motor cortical areas of the brain. Besides, we can assume that King’s stages come in succession along the disease course. Indeed, in a recent study using databases from two multicenter clinical trials, 725 patients were retrospectively staged through the trial course. The authors reported that no reversions to earlier disease stages occurred and that most people progressed to the consecutive stage . In ALS,Another possible limitation should be considered in the interpretation of the asymmetry of the metabolic clusters identified in the analyses, due to the lacking of full information about handedness. Indeed, such data were available only for a part of the patient sample and were unavailable for controls. A further possible limitation is the absence of partial volume effect correction for cortical atrophy. Unfortunately, MRI scans were not available for all subjects. However, studies employing voxel-based atrophy correction of resting glucose metabolism showed that metabolic measurements were relatively independent of brain atrophy .C9orf72 carriers with heterogeneous clinical presentations . Based on the limited number of mutation carriers in our series, we think that the possible impact of genetic mutations on brain metabolism should be investigated in further studies including a larger amount of carriers.On the other hand, our study increases the knowledge about the neuroimaging correlates of King’s stages, which is still limited to few MRI studies with small samples. In this field, a recent study using magnetic resonance (MR) high-angular resolution diffusion imaging (HARDI), suggested an early pattern of microstructural degeneration in ALS, mainly involving the CST and the corpus callosum . Neverth18F-FDG-PET in ALS. Recently, a panel of experts, on behalf of the European Association of Nuclear Medicine (EANM) and the European Academy of Neurology (EAN), did not recommend the clinical use of brain 18F-FDG-PET even to study ALS-related brain dysfunction [18F-FDG-PET to study ALS-related brain changes across motor and cognitive regions in a research setting. Otherwise, in agreement with the EANM-EAN recommendations, its use in the clinical setting needs further studies, including the comparison with ALS mimic disorders, to achieve a reliable accuracy at the single-patient level.Another strength of this study is the contribution to the debate about the use of brain function , 28. We 18F-FDG-PET assessment ever published. We found that, with the increase of King’s stage, there was a decrease in metabolism in motor areas, with progressive involvement of extramotor regions. Since 18F-FDG-PET is a marker of neurodegeneration in vivo [To our knowledge, this is the first study evaluating the brain metabolic correlates of regional extent expressed as disease staging in ALS and includes the largest ALS series with  in vivo  and is c in vivo , our dat in vivo , and are in vivo . LongituSupplemental Figure 1Glass brain rendering of the full factorial analysis including the following groups: King’s stage 1, King’s stage, 2, King’s stage 3, and healthy controls. The clusters showing a significant main effect of groups are projected on brain surface. (PNG 801 kb)High Resolution Image (TIF 170 kb)Supplemental Figure 2Glass brain rendering of the comparison: King’s stage 1 versus healthy controls. The clusters showing a statistically significant relative hypometabolism in the King’s stage 1 group as compared to healthy controls are projected on brain surface. (PNG 768 kb)High Resolution Image (TIF 161 kb)Supplemental Figure 3Glass brain rendering of the comparison: King’s stage 2 versus healthy controls. The clusters showing a statistically significant relative hypometabolism in the King’s stage 2 group as compared to healthy controls are projected on brain surface. (PNG 731 kb)High Resolution Image (TIF 155 kb)Supplemental Figure 4Glass brain rendering of the comparison: King’s stage 3 versus healthy controls. The clusters showing a statistically significant relative hypometabolism in the King’s stage 3 group as compared to healthy controls are projected on brain surface. (PNG 1265 kb)High Resolution Image (TIF 174 kb)


This narrative review highlights the latest achievements in the field of tele-rehabilitation: Virtual Reality (VR) and Augmented Reality (AR) serious games aimed at restoring and improving cognitive functions could be effectively used in Developmental Coordination Disorder Training. Studies investigating the effects of the abovementioned tech applications on cognitive improvement have been considered, following a comprehensive literature search in the scientific electronic databases: Pubmed, Scopus, Plos One, ScienceDirect. This review investigates the effects of VR and AR in improving space/motor skills through mental images manipulation training in children with developmental coordination disorders. The results revealed that in spite of the spreading of technology, actually only four studies investigated the effects of VR/AR tools on mental images manipulation. This study highlights new, promising VR and AR based therapeutic opportunities for digital natives now available, emphasizing the advantages of using motivational reward-oriented tools, in a playful therapeutic environment. However, more research in this filed is needed to identify the most effective virtual tool set for clinical use. In the last decades the number of tech applications for cognitive Rehabilitation in childhood has increased, thanks to technological innovation. Virtual Reality (VR) and Augmented Reality (AR) have arisen as a promising approach in the field of clinical rehabilitation. This narrative review aims at pointing out the most recent advances in the field of neuro-rehabilitation: It will focus on studies using VR and AR serious games in the treatment of Developmental Coordination Disorder (DCD) in childhood. Specifically, VR and AR training may be useful to enhance mental images manipulation such as rotation, spatial visualization, spatial orientation, and motor plan programming, offering children a constant feedback on their performance.As a matter of fact, children with DCD show a reduced ability to imagine a motor act (esp. from a first-person perspective), which has been shown in research using mental limb rotation and visually guided pointing tasks . Other wVirtual environments have been found effective in representing further contexts for children to test their adaptive strategies and to improve responses. The present work has two advantages over previous works: First, it depicts the most recent state of the art of VR and AR application in children with DCD and, second, it identifies useful differences in terms of tools and methods applied to approach digital native’s neurorehabilitation. The main goal of this work is giving a view of the studies carried out so far and encouraging both researchers and clinicians to identify what should be further investigated to increase knowledge in this field of study.As described in the American Psychiatric Association’s  latest edition of the Diagnostic and Statistical Manual of Mental Disorders DSM-5) , the chi , the chAll children with DCD show some impairment in motor learning and in new motor skill acquisition, as opposite to adult apraxia which is a disorder in the execution of already learned movements. There is no consensus on etiology of DCD. Intragroup approach through factor and cluster analysis highlighted that “motor impairment in DCD children varies both in severity and nature” . Indeed,A systematic review of 16 studies involving school-aged children, published in 2011, showed significantly greater odds of developmental coordination disorder among children who had very low birth weights (<1500 g) or were very preterm (<32 week) than among age-matched controls born at term with normal birth weights  [In a prospective, population-based cohort study in southwestern England, probable developmental coordination disorder was identified in 346 children aged 7–9 . Risk faA plausible hypothesis to explain the compromised motor ability of children with Developmental Coordination Disorder (DCD) suggests a substantial deficit in their ability to utilize internal models for motor control. A dysfunction in this mode of control is thought to compromise motor learning capabilities .Children with DCD have problems generating and/or monitoring a mental (action) representation of intended actions, termed the “internal modeling deficit” (IMD) hypothesis .Internal modeling deficits (IMDs) have been proposed as a neurological cause of DCD . AccordiTwo approaches target the Internal Modeling: Mental Imagery (MI) and Action Observation (AO). According to Adams , the aboOther studies  showed tA mental image is a product of cognitive activity which enables to represent reality through recall, manipulation, reproduction of objects and events without sensorial stimulation . People MI is not a single ability but emerges from a crossroads of singles abilities. Working memory has an important role in MI. According to Kosslyn , in ordeThe same neuronal mechanisms underpinning simulation (imagery) are involved in real execution of actions . As an eMI have been investigated to examine the cognitive aspects linked to action and movement control. The main advantage in using MI in rehabilitation trainings is the possibility to significantly increase the number of task repetitions since we use a mental recall of motor tasks. Wilson  pioneereIn the last decades, many tech tools enabling motor skills treatment in Neurodevelopmental Disorders and in the field of DCD were developed. This has been possible because of a growing interest in tailored tools, able to meet patient specific needs. In such a framework, technological tools emerge as motivating and stimulating devices, adaptable to a single child’s needs.Telemedicine is currently developing in Italy and the National Healthcare System (NHS) has not exploited all the possibilities it offers yet . In the In the last 20 years, gaming industry flourished and there was a combination between electronic games and neurorehabilitation research. “Serious Games” were born from this combination. With the term Serious Games we are referring to games whose peculiarity is not mere entertainment, but the empowerment of cognitive and motor function . Video gRegarding VR Intervention, Wilson  distinguOther studies explored the advantages of a specific design for tools in rehabilitation such as the AR Serious Game “Athynos” , an AR tAmong various technologies explored to work on DCD, one recent and largely unexplored technology is Serious Games combined with VR and AR.VR is defined as a three dimensional immersive and interactive experience occurring in real time . AR can VR has been successfully employed in the neurorehabilitation of several disease in adulthood after brain injury or stroke ,44,45,46AR has been found effective in empowering coordination skills in children. A study by Avila Pesantez  investigDespite the good chances offered by these technologies, only few studies applied VR and AR to DCDs. In 1987, Mc Clurg  proved tIn his study, Wilson  highlighThis narrative review was implemented on the basis of a research conducted on major scientific online databases . We included randomized controlled trials, reviews, systematic reviews, metanalysis, book chapters, and official guidelines from scientific associations published until December 2020. Our literature search was based on the following search terms: “Developmental Coordination Disorder” or “Coordination Disorder in children” or “motor coordination skills” or “mental rotation skills” or “mental images” or “mental images manipulation” combined with “VR treatment” or “VR/AR rehabilitation” or “VR intervention” or “Virtual remediation” or “Virtual Reality” or “Augmented Reality” or “virtual Reality training”.To be considered for this review studies had to meet the following criteria. First, the study aim had to examine the impact of a VR or AR training on DCD in children; Second, the study protocol had to implement mental images manipulation such as rotation, spatial visualization, spatial orientation, and motor plan programming. Single case studies were not included in this study because of the lack of generality of obtained effects.From the literature search, only four studies specifically investigated the potential of VR or AR technology in DCD rehabilitation exploring mental images manipulation improvement.In 2011, Straker  investigIn 2013, Ashkenazi  investigIn 2020, a randomized controlled study  investigAR potentialities have also been investigated in the already mentioned study by Avila Pesantez , who comThe purpose of the present narrative review was twofold. First, we aimed to provide an up-to-date overview of the findings from VR/AR studies using mental images manipulation in DCD treatment for children. Second, we wanted to recommend researchers and clinicians worthy points to be additionally investigated in future research. Today, despite of the increasing use of technology in the clinical field, only four studies have been found interested in the role of VR and AR technologies in improving mental images manipulation for DCD treatment in children. Notwithstanding the literature is at a very early stage, some preliminary qualitative data can be recollected from the reviewed studies.Results emerging from the presented studies, despite limitations, reveal a good potential in DCD treatment. Three out of the four studies presented in this review reported significant results in the outcome measures ,40,64.Straker  groundedAll the studies included in the present work diverged in many methodological aspects, such as sample size, study timeline, type of tools designed for intervention. These differences limited to some extent the chance to determine a direct link between a specific intervention and different outcomes. The limitation of the studies included in the present review are mostly the sample exiguity or methodological differences. However, the abovementioned limitations are very common in pioneering studies exploring the use of new technological tools for neurorehabilitation.To overcome this problem, the scientific community has been invited  to standTelemedicine is still under development in Italy but, since good results have been achieved from initial research, a great effort is required for researchers in this field of study. The potential of the use of VR/AR technology for children stands in the possibility of giving professional, daily treatment, intrinsically eliciting motivation and enjoyment. As a second advantage to be considered, children could be involved in well-structured game-like trainings outside of the hospital context.Unfortunately, it could not be assessed which intervention is, among the others, more effective for a specific age-range. This was due to the fact that the studies investigated the efficacy of VR ad AR applications in different populations aged between four and twelve years (a wide age span). Greater attention should be dedicated in research to define whether a window of sensitivity is available or has to be agreed for this kind of treatments, since different age ranges have been considered in clinical studies conducted so far. Additionally, some attention should be dedicated to the longitudinal effects of virtual training in terms of improvement duration and outcome measures considered through life span. As an example, social involvement in children who underwent a DCD training during adolescence could be investigated.The present review had some limitations. First, the goal of this work was to provide an up-to-date narrative overview of recent findings on the use of VR and AR Serious games training in DCD. To do this, we limited our search to a small amount of studies investigating the role of mental images on DCD rehabilitation. In addition, we considered only papers in English and we not considered single case studies because of the lack of generalizability of the outcomes. Moreover, as previously discussed, some methodological aspects of the reviewed studies also limited our findings . Lastly, as is common knowledge, retention of learning skills for a certain time is a critical issue of any treatment. Future research on VR/AR interventions on DCD should include follow-up visits to evaluate the maintenance or the evolution of the benefits achieved over time.VR and AR serious games training for DCD treatment are motivating tools, as they offer immediate feedback in very realistic game environments. Because of their features, VR and AR are among the most interesting tools researchers should look at to deliver tailored intervention for child’s needs, as required by recent scientific guidelines .The present review suggests that VR and AR interventions could have some beneficial effects in treating DCD. This work encourages future trials to consider mental images manipulation through VR/AR tool as a possible target for interventions on children with DCD.More research is needed in this field: First, to explore further chances offered by this technology as a strategic asset in the field of DCD and, second, to identify procedures and targets that best fit the needs in this specific clinical area. This approach could lead to soon determine best practices for using VR and AR technology in this field of study.


X and player Y, have different cognitions, but player X detects the misperception and it is believed to make ZD strategies by player Y. We provide a necessary and sufficient condition for the ZD strategies in IPD with misperception, where there is also a linear relationship between players’ utilities in player X’s cognition. Then we explore bounds of players’ expected utility deviation from a linear relationship in player X’s cognition with also improving its own utility.Zero-determinant (ZD) strategies have attracted wide attention in Iterated Prisoner’s Dilemma (IPD) games, since the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. On the other hand, uncertainties, which may be caused by misperception, occur in IPD inevitably in practical circumstances. To better understand the situation, we consider the influence of misperception on ZD strategies in IPD, where the two players, player  It is generated by a one-shot Prisoner’s Dilemma (PD) game between player X and player Y, where both of them choose to cooperate (c) or defect (d). Players’ utility matrix is shown in Table T, R, P, S] of the PD game are constrained by 6. Thus, mutual defection is the only Nash equilibrium, but mutual cooperation is the globally best outcome. In IPD games, the analysis of players’ utilities is quite complicated since players may promote cooperation through past actions. Fortunately, Press and Dyson7 proposed zero-determinant (ZD) strategies, where the player equipped with ZD strategies can unilaterally enforce the two players’ expected utilities subjected to a linear relation. Afterward, various ZD strategies were widely studied in public goods game (PGG), human-computer interaction (HCI), and moving target defense (MTD) problems11. For example, the equalizer strategy12 is a special ZD strategy that can unilaterally set the opponent’s utility. Besides, the player who adopts extortion strategies13 can make that its utility is not lower than the opponent’s utility. Conversely, the generous strategy15 is another special ZD strategy that ensures that the utility of the player with generous strategies is not higher than the opponent’s utility, but it is dominant in the game.Iterated Prisoner’s Dilemma (IPD) games have long been studied for understanding the evolution of cooperation and competition between players16, and there have been many models to describe uncertain circumstances in game theory, such as robust games, stochastic games, and hypergames19. Misperception is one of the most common uncertain phenomena. For example, in the Internet of Things, limited attention is a type of misperception, leading to bounded rationality and increasing cyber risks of the community20, and in cyber security problems, hackers may have a confused cognition of the system’s TCP/IP stack, which is known to the network administrator21. Moreover, players’ strategies may be influenced by uncertainty, which results in obvious deviation from opponents’ cognitions and attendant suspicion, such as the extenuating circumstances which consider intentions and outcomes in the legal system23, while players may misunderstand their opponents’ strategies, such as some companies relying on private monitoring instead of their opponents’ real actions25.Actually, uncertainty is always unavoidable in human interactions27. Particularly, misperception may spoil players’ cognition if others’ strategies are not consistent with their own anticipation, and moreover, it may even ruin the balance or even lead to collapse of the model28. For instance, in psychological experiments, participants’ doubts may affect the sponsor’s control29. Actually, due to the historical information or knowledge from others, a player may know that its opponent takes some given strategies, and moreover, the awareness of the opponent’s ZD strategies has been widely considered in many IPD games9. In the case when players prefer ZD strategies in IPD with misperception, a player may doubt its cognition if its opponent does not choose ZD strategies as it expects. Nevertheless, most existent works on ZD strategies in IPD with uncertainties, such as ZD strategies with observation errors25 or implementation errors30, have paid less attention to strategies that maintain players’ cognition.In fact, the condition for players to trust their cognition is crucial in games with misperceptionX knows the misperception about the game, and player Y believes that player X prefers to make ZD strategies according to the original model without misperception. Then player X tends to choose strategies consistent with its opponent’s anticipation, and meanwhile improve its own expected utility.Therefore, the motivation of this paper is to analyze how misperception affects a player’s ZD strategy without causing its opponent’s suspicion. Specifically, we consider the case when player X is able to achieve at least a linear relationship between players’ expected utilities without causing the opponent’s awareness of misperception. Additionally, misperception can bring a bounded deviation from the linear relationship between players’ expected utilities in player X’s cognition, which can be applied to player X’s strategy implementation. Further, player X can utilize the misperception and take some benefits, such as improving the supremum or the infimum of its expected utility.To this end, we find some conditions where player 31. Due to the misperception, the parameter in the real game changes from X notices the change. Thus, player Y’s cognition of the parameter is X’s cognition of the parameter is X chooses a strategy from its strategy set e.g., X’s probability for cooperating with given previous outcome Y’s strategy set is 7, this game can be characterized by a Markov chain with a state transition matrix Y, they are playing game X, they are playing game X knows that player Y’s cognition is Consider an IPD game with misperception such as implementation errors and observation errorsentclass1pt{minimaZD strategy7 of player X in Y’s strategy X in G can be expressed as 12: equalizer strategy13: extortion strategy15: generous strategyBased on the past experience, player Y knows that player X prefers ZD strategies, which has been widely considered in many IPD games9. To avoid that player Y notices the change, which may result in potential decrease of player X’s utility21 or collapse of the model28, player X keeps choosing ZD strategies according to Y’s anticipation. To sum up, in our formulation,the real game is Y thinks that they are playing game X thinks that they are playing game player X knows that player Y’s cognition is player Y believes that player X chooses ZD strategies;player X tends to choose a ZD strategy according to Y’s suspicion of misperception.player  In fact, player X can benefit from the misperception through the ZD strategy. For example, player X can adopt a generous strategy in Y’s cooperation behavior, but also make player X’s utility higher than that of player Y, if the generous strategy is an extortion strategy in X is able to maintain a linear relationship between players’ utilities or improve the supremum or the infimum of its utility in its own cognition. In the following, we aim to analyze player X’s implementation of a ZD strategy in IPD with misperception, and proofs are given in the Supplementary Information.Let X’s ZD strategies may be kept in IPD games with misperception from implementation errors or observation errors. In particular, player X keeps choosing a ZD strategy Y’s suspicion about possible misperception. In the view of player X, it can also enforce players’ expected utilities subjected to a linear relationship if Player X in Any ZD strategy X can ignore the misperception and choose an arbitrary ZD strategy based on its opponent’s anticipation since it also leads to a linear relationship between players’ utilities, as shown in Fig. X can not unscrupulously choose ZD strategies based on player Y’s cognition. There is a player X’s ZD strategy in player Y’s cognition which is not the ZD strategy in player X’s cognition. Further, because of the symmetry of X’s any available ZD strategy X can choose any ZD strategy based on its own cognition, which does not cause suspicion of the opponent since it is also consistent with player Y’s anticipation. Additionally, the slopes of linear relations between players’ utilities may be different, as also shown in Fig. X can benefit from the misperception by choosing a ZD strategy to improve the corresponding slope.If  holds, pmentclass2pt{minimmentclass2pt{minimX’s any ZD strategy mentclass2pt{minimX’s any ZD strategy 32. At this point, the relationship between cooperation rate and efficiency is monotonous, i.e., the higher the cooperation rate of both sides, the greater the efficiency (the sum of players’ utilities).mentclass2pt{minimFurthermore, for the three special ZD strategies, player X can also maintain a linear relationship between players’ utilities in the IPD game with misperception.In fact,  covers tY’s cognition, player X can unilaterally set player Y’s utilities, as shown in the following corollary.By choosing equalizer strategies according to player X’s any equalizer strategy Player X can unilaterally set player Y’s utility by choosing any equalizer strategy in X can not unscrupulously choose an equalizer strategy based on player Y’s cognition since it may not be an equalizer strategy in player X’s cognition. is also Y’s cognition, player X can get an extortionate share, as shown in the following corollary.By choosing extortion strategies according to player X’s extortion strategy For player mentclass2pt{minimX’s extortion strategy in X’s utility is not lower than the opponent’s utility in its own cognition. Thus, player X chooses a strategy that satisfies  strategy35, i.e., X gets the supremum of the expected utility in X’s utility is improved in the IPD game with misperception.Actually, when player Y’s cognition, player X can also improve the supremum of its expected utility.By choosing extortion strategies according to player X’s extortion strategy X’s expected utility in For player Y aims to maximize its own utility with great eagerness, player Y chooses the ALLC strategy when player X chooses extortion strategies7. In this case, by choosing the extortion strategy which satisfies  strategy35, i.e., X since it gets the minimum expected utility in X is able to improve its expected utility in the worst situation.When player Y is unaware of the different cognitions, but it believes that player X takes a ZD strategy, while player X can detect the misperception. Since each player observes the strategy in sequence, to avoid player Y’s suspicion, player X needs to keep its ZD strategies. Therefore, we have explored the ZD strategies in IPD with misperception—a linear relationship between the two players’ expected utilities. In fact, under this affine constraint, player X can ignore the misperception and choose ZD strategies freely. Specifically, we have studied the three typical ZD strategies—equalizer, extortion, and generous ones, and moreover, we have investigated the players’ expected utility deviation from misperception in player X’s cognition. For clarification, we have described the deviation not only from the corresponding linear relationship of the ZD strategy but also from another linear relationship that is not directly obtained by player X. Finally, we have revealed that the player equipped with ZD strategies may benefit from misperception to improve its own utility. Thus, player X can adopt special equalizer, extortion, or generous strategies to promote the supremum/infimum of its utility in IPD with misperception.This paper concentrates on how misperception affects ZD strategies in IPD games. In our problem, player X to choose beneficial strategies if aiming to get as close to a linear relationship as possible, but no caring about what the linear relationship is. On the other hand, Fig. X’s utility with misperception.Although both Fig. entclass1pt{minima36, or deliberately mislead their opponents with imitative strategies such as “fake news”38. In fact, players may change the parameters and utilities of IPD in others’ cognition by deceiving their opponents. Hence, how the player who adopts ZD strategies benefits from deception in IPD without the opponent’s awareness is also worth analyzing. Since the ZD strategy has also been widely applied in other complicated situations, such as non-symmetric games39, PGG10, and evolutionary situations33, the misperception influence analysis will be extended to the ZD strategies in these practical fields.Moreover, players may actively adopt misperception to deceive their opponents. For example, players may be able to control their opponents’ observation by interfering with private monitoringM is regular when all elements of M are positive, e.g., Thus, The notations in Corollary The notations in Corollary Supplementary Information.


Purpose: This study was conducted to evaluate the accommodative response in young participants with visual impairment in comparison with visually normal participants. Methods: Fifteen participants with confirmed visual impairment and 30 visually normal participants aged 12–15 years were recruited. Accommodative response was measured using autorefractor (Grand Seiko WV500) at distances of accommodative demand of 33, 25, and 20 cm. The targets were one-line-above participant threshold acuity. The participants’ accommodative responses were compared between both groups after calibration for refractive errors and the vertex distance of the glasses. Visual acuity and refractive status were also assessed. Results: The age was not significantly different between both participant groups. The visual acuity of visually impaired patients was 6/30 to 6/240, and that of visually normal participants was 6/7.5 or better. Ten of the visually impaired patients and 29 of visually normal participants were myopic. In total, 61–73% of visually impaired patients showed an accommodative lead. Five subtypes of accommodative response were observed. In general, the accommodative inaccuracy increased with increasing accommodative demand. However, the visually normal participants largely exhibited an accommodative lag. A mild-to-moderate relationship was observed between visual acuity and accommodative response . Conclusion: Accommodative response in young visually impaired patients can be variable and on an individual basis. Low vision specialists should anticipate accommodative response outside the normal range. Therefore, we shall consider evaluating each patient’s accommodative response before prescribing any near addition lenses. Accommodation inaccuracy is often more complex than predicted due to increased depth of focus caused by reduced visual acuity. The change occurring in the optical system to maintain a clear image of an object as its distance varies is termed accommodation . AbnormaAccommodative response (AR) takes place when the eye changes its fixation from a distant point in space to a nearby object ,5. The dSeveral factors can affect AR, including visual acuity (VA) , age 1919,20, rePatients with visual impairment (VI)  prominently have reduced VA that could lead to unreliable AR ,33. SomePreviously, some cross-sectional studies investigated AR in patients with VI at certain points of age but reported conflicting results ,35,36. WThe present study was conducted to investigate the AR of young adults with VI in the age range of 12–15 years, an issue that has not been fully explored previously. The potential differences in AR between young adults with VI and healthy subjects were also evaluated. Understanding the accuracy of accommodation in young patients with VI is an important factor when prescribing optical devices . Unlike The study was conducted over a period of 8 months. This study recruited 15 young participants with VI and 30 HPs without any other ophthalmic pathology (aged 12–15 years). Past history of the participants with VI was reviewed to determine the diagnosis and VA for study eligibility. Macular degeneration was identified as the cause of reduced VA in all participants with VI. VA was evaluated using the Early Treatment Diabetic Retinopathy Study (ETDRS) chart. Noncycloplegic refraction was used to confirm the participants’ habitual distance correction.L, object vergence; d, vertex distance; and SR, spectacle refraction.R, autorefractor reading; d, vertex distance; and SR, spectacle refraction.The Grand Seiko WV500  open-field autorefractor was used to measure AR at demand distances of 50 cm (2 D stimulus), 33 cm (3 D stimulus), and 20 cm (5 D stimulus) using a vertical high-contrast grating pattern that is one-line above each patient’s threshold VA and a near-point rod and custom made near-point target holder. The holder allows the near-point target to be moved closer to the eye under the instrument’s beam-splitter housing. At each test distance, the target size was maintained at one-line above the participant’s threshold. The room illumination was full to allow the participants to view the near chart clearly. For testing, the participants were seated at the instrument with their head stabilized in the chin rest and forehead strap. The test was conducted monocularly, during which the other eye was covered with the instrument’s occluder. The autorefractor measurements were repeated three times for each distance, and the average of the three readings  was recorded as the representative reading. The entire testing was conducted through the subject’s best distance refraction. This study used the formulas suggested by Atchison and Varnas (2017) to calculate the accommodative stimulus, accommodative response, and accommodative lag/lead for each participant at the three accommodative demands . The calAL) if positive and accommodative lead if negative.Giving that accommodative lag (p < 0.050). Median ± interquartile ranges were used to report the data. The Mann–Whitney test was used to examine the difference in AR between participants with VI and HPs. Differences were considered to be statistically significant when the p value was <0.05.The IBM SPSS Statistics for Windows, version 22 , were used for data analysis. Data were not normally distributed as assessed by the Kolmogorov–Smirnov test . Therefore, the AR of one eye from each participant in both groups was randomly selected, and further analysis was conducted. This was done to avoid any eventual correlation existing between the right and left eyes of a single patient [The AR was measured monocularly during the phase of data collection. The Spearman test was conducted to investigate the relationship between the outcomes of the right and left eyes in both study groups. The test showed a very strong significant relationship between both eyes in both groups  were myopic (−0.25 to −6.50 D), 8 patients had myopia less than −2.50 D, 4 patients (27%) had hyperopia (0.50–6.00 D), and a patient had emmetropia . In the In terms of AR, the majority of patients with VI had accommodative lead . In detaThe five subtypes of AR classification that were defined and used by Heyman were also applied in this study for comparison purposes . The fivIn this study, the patients’ AR fell into three subtypes of those subtypes and an additional two subtypes were observed . In detap = 0.003, r = −0.54, p < 0.001, r = −0.1, p = 0.5, respectively). However, the strength of this relation does not fully explain the AR and would suggest that the AR is more complex than VA alone.In the VI group, the relationship among participants’ age, VA, and refractive errors with AR under the three conditions demonstrated that VA was the major determinant of AR at the three demands  that has not been investigated sufficiently. Specifically, White and Wick recruited participants in the age range of 19–34 years; in the study of Leat and Mohr, only two participants were recruited (of the 21 participants aged 5–31 years) in the same age group of our study; and Heyman recruited five participants in the age range of 12–15 years out of the 10 patients recruited.Leat and Gargon recruited a group of normal children aged 4–15 years, and it was found that the older age group demonstrated underaccommodation that increased with accommodative demand . It has Our study findings are in agreement with three of the five subtypes suggested by Heyman and also found two additional subtypes. This result indicates that AR could vary markedly between individuals. Consistent with the study of White and Wick, this result also emphasizes that visually impaired patients are generally overaccommodating . These rIn the present study, AR was significantly different between the VI and HP groups. This result was similar to that suggested in previous reports. Patients with macular pathology demonstrated less accurate AR ,36. LastThe AR of the visually normal population to a specific near demand was investigated previously ,17,18,45r = 0.3–0.5). Previous studies have suggested that reduced VA is not a sufficient explanation for the reduced accommodative accuracy [The AR and VA showed a mild-to-moderate relationship (accuracy ,35,36. Aaccuracy . Legge eaccuracy . The nataccuracy . These sThe results of this study could indicate that in the clinic, young patients with reduced VA have variable AR. Patients with VI generally hold the reading material at distances less than the habitual 40 cm. Previous research suggests that under our binocular condition, patients with macular degeneration should be able to accommodate fairly accurately . It has There were some limitations in the present study. The first limitation was the small sample size, although it is challenging to recruit a large sample from this population as reported by previous studies ,35,41. H


The vascular endothelium acts as a selective barrier to regulate macromolecule exchange between the blood and tissues. However, the integrity of the endothelium barrier is compromised in an array of pathological settings, including ischemic disease and cancer, which are the leading causes of death worldwide. The resulting vascular hyperpermeability to plasma molecules as well as leukocytes then leads to tissue damaging edema formation and inflammation. The vascular endothelial growth factor A (VEGFA) is a potent permeability factor, and therefore a desirable target for impeding vascular hyperpermeability. However, VEGFA also promotes angiogenesis, the growth of new blood vessels, which is required for reperfusion of ischemic tissues. Moreover, edema increases interstitial pressure in poorly perfused tumors, thereby affecting the delivery of therapeutics, which could be counteracted by stimulating the growth of new functional blood vessels. Thus, targets must be identified to accurately modulate the barrier function of blood vessels without affecting angiogenesis, as well as to develop more effective pro- or anti-angiogenic therapies. Recent studies have shown that the VEGFA co-receptor neuropilin 1 (NRP1) could be playing a fundamental role in steering VEGFA-induced responses of vascular endothelial cells towards angiogenesis or vascular permeability. Moreover, NRP1 is involved in mediating permeability signals induced by ligands other than VEGFA. This review therefore focuses on current knowledge on the role of NRP1 in the regulation of vascular permeability signaling in the endothelium to provide an up-to-date landscape of the current knowledge in this field. The vascular system consists of a complex network of blood vessels organized as a closed circulatory system in all vertebrates as well as some invertebrates ,2. The vThe inner lining of all blood vessels is formed by a monolayer of endothelial cells (ECs) that are anchored to a basement membrane on the abluminal side and joined together by intercellular junctional complexes. The primary function of the vascular endothelium is to serve as a selective barrier between the blood and each tissue in the body, whereby the permeability of the endothelium to blood cells, plasma macromolecules and water can be adapted according to the physiological need and localization. For instance, blood vessels in the kidney and in endocrine organs show a high basal permeability to enable plasma filtration and hormone release into the bloodstream, respectively. In contrast, the blood-brain barrier forms a tight, highly impenetrable interface to maintain the central nervous system in a more protected environment .Vascular permeability, i.e., the movement of solutes and molecules from the luminal to the abluminal side of the endothelial barrier, can be modulated by the exposure to permeabilizing agents. However, certain molecules can cause the permeability of the vascular endothelium to become excessive, resulting in acute or chronic vascular leakage. Such vascular hyperpermeability contributes to the pathophysiology of several human disorders, including cancer, heart, brain and limb ischemia, neovascular eye diseases and chronic inflammatory conditions ,10,11,12Vascular permeability can be beneficial after acute tissue injury through the delivery of coagulation factors, antibodies and cytokines. However, the leakage of plasma molecules during chronic hyperpermeability can cause pathological tissue edema, which is the accumulation of fluids in the extracellular space that induces deleterious swelling and increases interstitial pressure. Moreover, vascular hyperpermeability can foster leukocyte recruitment, which favors inflammation, often promoting disease progression (reviewed by ). In addIn cancer, disruption of the vascular barrier may potentiate tumor cell intravasation and/or extravasation, leading to widespread metastatic disease, while increased interstitial pressure often prevents efficient drug delivery to cancer sites (reviewed by ). MoreovStimulating blood vessel growth through angiogenesis is considered a promising treatment for organ ischemia and may provide a useful method to increase delivery of therapeutics to poorly perfused tumors. However, any beneficial effect of supportive angiogenesis will be hampered if accompanied by edema generation. This is unfortunately the case for the most potent angiogenic factor described to date, the vascular endothelial growth factor A (VEGFA), whose expression is associated with re-vascularization of damaged tissues but also increases vascular permeability. In fact, VEGFA was originally identified because of its potent permeability-inducing properties and accordingly first named vascular permeability factor (VPF). After two decades of VEGFA research, it is still not clear how VEGFA and its receptors selectively induce vessel growth versus vascular permeability to meet specific physiological needs, and how excessive vascular permeability may be controlled to limit tissue damage caused by edema. For these reasons, any novel insight on the signaling pathways that modulate different vascular responses, for example to attenuate vascular leakage in ischemic diseases without preventing new vessel growth, will be of fundamental value for devising more efficient therapeutic interventions. This review will therefore focus on the cellular mechanisms mediating vascular permeability and, in particular, the latest updates on the molecular mechanisms by which the VEGFA co-receptor neuropilin 1 (NRP1) modulates vascular responses to regulate permeability in both physiological and pathological settings.Vascular permeability occurs via paracellular or transcellular routes ,19,20. PTranscellular permeability describes the transfer of fluid and solutes through the cell from the apical to basal side of the endothelium (or viceversa) via vesicles, e.g., caveolae or vesicles complexes fusing into transendothelial channels such as the vesiculo-vacuolar organelle (VVO) . HoweverThe NRPs are a family of single pass transmembrane proteins of about 130 kDa. In mammals and most vertebrates, two NRP family members exist, NRP1 and NRP2, which share the same overall domain structure and are, on average, 44% identical at the amino acid level . In zebrAll NRPs are composed of a relatively large extracellular portion, a short transmembrane domain and a cytoplasmic domain of 43-44 amino acids ,35,36,37NRP1 is able to form homodimers or heterodimeric complexes with NRP2 , even thNRP1 has been widely studied as a receptor for the secreted glycoprotein VEGFA. VEGFA gene contains 8 exons and, judging from transcript levels, is expressed as three main isoforms that differentially include exons 6 and 7 ,55. In hMoreover, NRP1 also interacts with other extracellular binding partners that do not belong to growth factors. In fact it was also originally discovered as an adhesion protein on the axons of the developing frog nervous system  and lateDuring development, NRP1 is highly expressed in blood vessels to promote angiogenesis . AccordiMore recently, we have shown that NRP1 expression is maintained in the adult quiescent endothelium, including postcapillary venules  45], wh, wh45], Since NRP1 is able to interact with multiple ligands and co-receptors, NRP1 can promote a wide range of functions, including the promotion of vascular permeability.While VEGFA is best known as an angiogenic growth factor, it was originally described as a vascular permeability factor because it disrupts endothelial barrier function and thereby increases vascular leakage and interstitial pressure . Most stThe tyrosine kinase receptor VEGFR2 has been implicated as the main VEGFA receptor for promoting endothelial hyperpermeability signaling in various organs, including the lung, skin and brain ,83,84,85In response to VEGFA, VEGFR2 undergoes dimerization and autophosphorylation at several sites, including the tyrosine (Y) 949 residue (Y951 in human) that is essential to transduce VEGFA signals into increased vascular leakage via sequential phosphorylation of cytoplasmic SRC family kinases (SFKs) and junctional VE-cadherin . Within In order to activate SFKs, the VEGFR2 Y949 phosphosite has been shown to recruit an adaptor molecule, T cell-specific adaptor , which can directly interact with SFKs to translate VEGFA permeability signals . Our recFollowing a distinct VEGFR2-dependent pathway, disassembly of adherens junctions in response to VEGFA can also occur via phosphorylation of AKT1 and subsequent activation of endothelial nitric oxide synthase (eNOS), whereby NO production induces S-nitrosylation of β-catenin that will cause its dissociation from VE-cadherin ,98. OtheSince it is widely accepted that VEGFA121 does not signal through NRP1 due to the isoform’s low affinity for this receptor, several reports in the last two decades focused on the role of NRP1 in vascular hyperpermeability induced by VEGFA165. Evidence to support a role for NRP1 in VEGFA165-induced vascular hyperpermeability was obtained by genetic studies in which mice lacking endothelial NRP1 expression ,99 showeRecently, we demonstrated that mice lacking the NRP1 cytoplasmic domain displayed less leakage when stimulated with VEGFA164 in the Miles assay ; an unexTo recapitulate, Like VEGF ligands, most of the known natural proteins or artificially generated peptides with NRP1-binding activity bind through a carboxy (C)-terminal R/KXXR/K minimal sequence motif (X stands for any amino acid); this requirement is called the C-end rule (CendR ). All thIn addition to binding VEGFs, NRPs are co-receptors for members of the semaphorin family. In particular, on top of its original role in axonal guidance, SEMA3A has been widely reported to affect endothelial behavior, including the regulation of vascular barrier, with NRP1 being a key player in the regulation of this pathway. Thus, SEMA3A induces vascular hyperpermeability in a NRP1-dependent mechanism in the mouse Miles assay ,99 and SThe VEGFA and SEMA3A permeability pathways have been proposed to diverge, despite their shared NRP1 dependence. The difference between these two pathways involves ligand binding to different extracellular domains of NRP1. Indeed, crystallographic evidence revealed that VEGFA165 and SEMA3A do not directly compete for NRP1, but rather can simultaneously bind to NRP1 at distinct, nonoverlapping sites  Figure B. The NRNrp2 show increased vascular permeability in inflamed ears, the authors suggest that SEMA3F inhibition of vascular permeability might be mediated by its co-receptor NRP2 [In complete antithesis with the literature reviewed above, one study reported that SEMA3A can also induce permeability signals by acting via NRP2 and VEGFR1, independently of NRP1, in cultured brain endothelial cells . Even thtor NRP2 . FurtherThe expression of ANGPTL4, a HIF1-regulated gene product, is increased in the eyes of diabetic mice and patients with DME. ANGPTL4 is a multifunctional circulating protein that undergoes proteolytic processing by membrane proprotein convertases upon secretion. The resulting C-terminal domain (cANGPTL4) appears to have an important role in vascular hyperpermeability ,119,120.A non-physiological increase in vascular permeability is a common denominator of several diseases. However, since the role of NRP1 in pathological vascular permeability has been mainly studied in preclinical models of neovascular eye diseases and cancer, we will now focus on NRP1 regulation of vascular permeability in these two sets of diseases.The aberrant expression of proangiogenic factors such as VEGFA and other vasoactive mediators can lead to the deterioration of the blood-retinal barrier culminating in the accumulation of interstitial fluid in the macula, which can lead to macular edema, the major cause of severe vision loss in the Western world working population . DiabeteEdema in DME and AMD can be significantly reduced with anti-VEGFA therapies ; howeverInstead of targeting the extracellular binding of NRP1 ligands, targeting the NRP1 cytoplasmic domain-mediated signaling pathway was recently suggested. Thus, in a mouse model of choroidal neovascularisation with pathological vascular changes akin to those observed in exudative AMD , mice laTumor vasculature usually displays hierarchical disorganization, increased tortuosity, poor perfusion and instability, as well as increased vascular leakage. Since anti-angiogenic strategies have shown some beneficial effects in cancer treatment but to a minor extent than what was expected from earlier preclinical studies, a current trend in the field is to focus instead on the normalization of the tumor vessels, in particular to attenuate their exaggerated permeability. Therapies aimed at targeting NRP1-dependent permeability signals could therefore find an application for this purpose.Interestingly, Treps and colleagues reported that extracellular vesicles released by glioblastoma cancer cells transport SEMA3A, which enhances vascular permeability through NRP1 independently of VEGFA . DespiteOpposite to eye diseases, whereby vascular permeability is considered a valid therapeutic target only when inhibited, a few teams have proposed to exploit NRP1 pro-permeability properties to promote penetration of co-injected anti-cancer drugs and develop more efficient delivery systems ,132. ThuNRP1 ability of binding different types of extracellular ligands as well as its involvement in multiple signaling pathways makes it a fascinating pharmacological target, whose blockade or exploitation may be beneficial in diseases associated with vascular leakage or that require improved tissue penetration, respectively. While the existing data already provide extensive insights, further studies are clearly needed to better define the precise effector mechanisms that enable NRP1 to convey disparate signals into the induction of vascular permeability.The interest in NRP1 targeting further increased following the COVID-19 outbreak. In fact, NRP1 has very recently been shown to serve as an entry factor and potentiate SARS Coronavirus 2 (SARS-CoV-2) infectivity in vitro . By modu


Auditory Foot (AF), on the change in the frontal whole body angular momentum (WBAM) range, before and after a two-week walking rehabilitation. We conducted a pilot randomized controlled trial (RCT). We employed statistical Bayesian modeling to understand the mechanism of the rehabilitation effect and predict the expected effect in new patients. The best-performing model indicated that the frontal WBAM range was reduced in the AF group by 12.9–28.7%. This suggests that the use of kinesthetic biofeedback in gait rehabilitation contributes to the suppression of frontal WBAM, resulting in an improved walking balance function in stroke patients.Walking rehabilitation is challenging in stroke patients with sensory impairments. In this study, we examined the two-week effect of an auditory biofeedback prosthesis,  The main symptom of stroke due to brain damage is motor paralysis, e.g., gait disorder, which is the main cause of disability . Patientkinesthesia, that is, motion perception, that “how I am moving now”, which is generated through the interaction dynamics between motor and sensory systems, plays a crucial role in long-term motor learning as well as short-term motion generation. Thus, achieving kinesthesia is essential for the rehabilitation of physical impairments and disabilities. However, sensory impairments caused by neurological or physical disorders hamper kinesthesia, making walking rehabilitation difficult. Most studies have reported the effect of impaired plantar sensation on gait plasticity due to aging , respectively. ith segment. ith segment, respectively. Positive and negative values of the WBAM indicated the direction toward non-paretic and paretic sides, respectively. WBAM was normalized by the body mass (kg), height (m), and walking speed (m/sec), as these parameters affect the range of WBAM [To examine the effects of two-week rehabilitation, we focused on balance assessment in stroke patients, especially by using the whole body angular momentum (WBAM) . WBAM si of WBAM . The ranindividuality, that is, the individual differences among patients, to properly evaluate the rehabilitation effect. To investigate two-week effect of auditory feedback during rehabilitation by explicitly considering the individuality on patients, we used Bayesian statistical analysis and modeling. Bayesian model is a probabilistic model; thus, it is a good mathematical tool to model uncertainty on data, e.g., individual difference on patients. Bayesian analysis can estimate a probabilistic distribution (model) that encodes an unknown observation target by using observed data and updating the distribution in the model. Furthermore, a hierarchical (or multi-layer) model with a hyperparameter, which is a parameter for parameter, has a high affinity with Bayesian analysis and is a powerful tool to analyze data including individual differences. Thus, it is reasonable to apply Bayesian statistical modeling in the evaluation of rehabilitation for stroke patients, where individual differences can have a significant impact on the effectiveness.In rehabilitation of stroke patients, it is essential to consider Here, we modeled the relationship of the WBAM range on the pre and post two-week walking rehabilitation using four models (see the details in the next paragraph). We specified the models in probabilistic programming language Stan . Here, wR^ , where Ri and j represent the numbers of trials and patients, respectively.model 1: Non-hierarchical modelmodel 2: Hierarchical model for model 3: Hierarchical model for We assumed the distribution of model 4: Hierarchical model for We compared the predictive performance of the constructed models by using a mathematical index, namely, the WAIC ,22,23. WNineteen patients after stroke participated in this study and eighteen patients completed the rehabilitation period. A patient dropped out for onset of cerebral infarction . Two addEquation ) for eacEquation ) on the quations –8)), as), asLWBAAuditory Foot (AF) [In this study, we examined the two-week effects of auditory biofeedback on gait rehabilitation in stroke patients. During a two-week gait rehabilitation training, we used oot (AF)  which trWe employed WBAM as an evaluation criterion for two-week rehabilitation effects. Human upright bipedal walking is generated from whole body dynamic motion, suggesting that the coordination of movements between body segments significantly contributes toward maintaining dynamic walking stability. Gait asymmetry due to stroke, especially hemiplegia, has a significant impact on dynamic balance during walking, resulting in a 73% incidence rate of falls in post-stroke patients ; hence, Furthermore, recent studies have examined the effects of powered prosthesis or visual biofeedback on WBAM during walking in patients. A study that examined changes in WBAM in patients with a prosthetic powered lower-limb  reportedData-driven evaluation of rehabilitation effects is useful to understand the mechanisms behind the rehabilitation performed and, at the same time, to predict what kind of rehabilitation effects can bring in new patients. From this point of view, Bayesian statistical modeling is a highly effective approach to understand and predict the mechanisms behind complex phenomena by fitting data to a probability model. In addition, hierarchical Bayesian models can include individual differences in the hyperparameters, making it possible to predict the rehabilitation effect on a new patient with unknown gait characteristics. Recent studies examining the effects of the treadmill training have reported improvements in walking speed, endurance , walkingd value to examine the effect of sample size [d-value was also obtained as a probability distribution. The mean value of d on this distribution was Bayesian model-based rehabilitation that provides optimal and predictable interventions for each individual patient.There are several limitations to the present study. First, we have not considered the carry-over effect of the treadmill and AF rehabilitation. Maintaining the training effect is an essential aspect of long-term rehabilitation for more effective rehabilitation. A report about a rhythmic motor learning task with visual and auditory signals  indicateple size . The varus study , no evidOur statistical analysis using a Bayesian model showed that the WBAM range was reduced in the AF group by 12.9–28.7%  compared with the CT group. Furthermore, comparison with hierarchical models, including individual differences for the parameters of the rehabilitation effects, showed that the model that predicted the posterior predictive distribution most accurately was the model that did not include individual differences, suggesting that the AF and treadmill training had little effect on individual differences in terms of the gait performance. Furthermore, a comparison between model 2 (considering individuality on The clinical significance of our results confirmed the two-week effect of auditory biofeedback on the frontal WBAM in stroke patients with hemiplegia and a sufficient post-stroke period, which was determined by the formation of an “abnormal” but stable gait pattern. These results are due to brain plasticity during rehabilitation. In this study, we showed that the reconstruction of kinesthesia resulted in the plastic stabilization of gait in patients with weakened sensory function due to stroke. These patients underwent a two-week walking rehabilitation program to compensate for plantar pressure sensation based on auditory biofeedback using our AF. This study provides valuable and important results for neurorehabilitation based on sensory compensation. However, the detailed mechanism of this rehabilitation effect based on brain plasticity requires further research.


The nipagin-derived component acts as the renewable surrogate of petroleum-based dimethyl terephthalate (DMT), while the eugenol-derived component acts as the cooperative property modifier of parent homopoly(ether ester) PHN1. 1,6-Hexanediol was chosen as the spacer because of its renewability, high boiling point, and short chain to enhance the glass transition temperatures (Tgs) of materials. The molecular weights and chemical structures were confirmed by gel permeation chromatograph (GPC), NMR and FTIR spectroscopies. Thermal and crystalline properties were studied by thermal gravimetric analysis (TGA), differential scanning calorimetric (DSC) and wide-angle X-ray diffraction (WXRD). The tensile assays were conducted to evaluate the mechanical properties. The results suggested that properties of this kind of poly(ether ester)s could be finely tuned by the relative content of two components for the desired applications  suitable for different scenarios from polyethylene glycol terephthalate (PET) and polybutylene terephthalate (PBT).Naturally occurring nipagin and eugenol were used as the collaborative starting materials for poly(ether ester) polymers. In this study, two series of nipagin and eugenol-derived copoly(ether ester)s, PHN1 The reality prompts us to find bio-based substitutes to petroleum-based resources from the view of sustainable development11. PET and PBT are representative examples of widely used engineering plastics, but they are mainly produced from petroleum-based dimethyl terephthalate (DMT). Due to the huge consumption, finding the renewable surrogates for DMT without sacrificing the thermal stability and mechanical strength of materials is urgent.Currently, great majority of plastic consumed globally is produced from fossil resources. This situation brings about the gradual depletion of non-renewable materials, as well as increasingly severe environmental concerns13. These two starting materials have been found widespread applications in fields of liquid crystalline material15, epoxy resin18, benzoxazine20, coating22, and Li–S battery23. Because of the multifunctionality (phenol and vinyl) and renewability of nipagin and eugenol, based on them our group has been dedicated to polyester materials, whose thermal, crystalline, mechanical and degradable properties have been comprehensively investigated25. The influence of monomer structure on final properties was also studied26. However, the comprehensive performance of obtained polyesters can still be improvable, regardless of the renewability of starting materials. Either the glass transition temperatures (Tgs) were not high enough, or the mechanical tough and strength was not perfect. Consequently, further optimizing the performance of nipagin and eugenol-based polymer materials is particularly important for the development and utilization of such materials.Nipagin and eugenol are two naturally occurring building blocks, which exist in campanulaceae plant and clove, respectively28. In contrast, eugenol-derived unit is highly asymmetrical one, which endows the polymers low crystallinity and poor mechanical strength, while their flexibility and ductility are good24. Taking advantages of the complementary features of these two building blocks through rational molecular design may give the polymeric materials synergistic effect and desired final properties.Considering the structural difference of nipagin and eugenol, the symmetrical nipagin units can endow the polymers with high crystallinity and mechanical strength, but poor flexibility and ductility32, the low boiling points of which can lead to volatilize easily during the polycondensation stage and be difficult to control the stoichiometric ratio between diester and diol precisely, and thus caused low molecular weights. Meanwhile, due to the chain length of 1,6-hexanediol is shorter than that of 1,10-decanediol, the Tgs of obtained polymers were enhanced obviously compared with our previously synthesized polyesters with 1,10-decanediol as the spacer26. The high Tg values can make polymer materials applied in a wide temperature range. Synergistic effect between these two structurally distinctive components (nipagin and eugenol) endows the materials with desired performance, which can be modulated for a broad range of applications  suitable for a variety of scenarios.In this work, three nipagin and eugenol-derived diester monomers were firstly synthesized s were synthesized by a melt polycondensation method according to the predetermined composition ratios of nipagin and eugenol-derived dimethyl ester monomers. The polymerization routes are shown in Fig. PHN1Mn above 104 were successfully obtained, and polydispersity (Ɖ = Mn/ Mw) values are found to be fixed at about 1.7 regardless of the feed ratios, which also suggest the similar reactivity of diester monomers, where Mn and Mw are the number- and weight-average molecular weights, respectively. The apparent appearance of final products is closely related with the feed ratios. That is, with the gradual increase of eugenol-based units, the physical form of final product changes from white powder for PHN1, transforms into yellow powder for PHN195%E1(2)5%, PHN190%E1(2)10%, and PHN185%E115%, finally becomes light yellow semi-solid for PHN180%E120%, PHN185%E215% and PHN180%E220%. This phenomenon indicates that eugenol-derived units are easier to be oxidized than nipagin-derived units.The high yields suggest the high reactivity of the two kinds of monomers. The consistency of nipagin and eugenol-derived units in the feed and final product demonstrates that nipagin and eugenol-based diester monomers have similar reactivity and excellent compatibility. Copoly(ether ester)s with 1H NMR s were confirmed by 1−xE1x and PHN11−xE2x exhibited comparable thermal stability with the parent PHN1. Despite the content of eugenol-derived composition reached 20%, the temperature at which 5% weight loss (T5%) decreased just about 12 °C for both PHN11−xE1x and PHN11−xE2x relative to PHN1 s. Based on the above results we conclude that the incorporation of eugenol-derived units had little influence on thermal stability of the final product. T5% values were above 363 °C for all the samples, which is comparable with that of the petroleum-based poly (PBT) (T5% = 371 °C) with appropriate molecular weights  reported by others34. The temperature for maximum degradation rate (Td) values were almost identical for both PHN1 and PHN11−xE1(2)x, whose Td values were fixed at about 410 °C and found to be insusceptible to the changes of content in eugenol-derived composition. Furthermore, PHN11−xE1x with eugenol-derived composition below or equal to 10% featured a two-step degradation mechanism. However, for PHN11−xE1x with eugenol-derived composition above 10% and the whole series of PHN11−xE2x, single-step degradation was observed. This phenomenon could be explained by the mismatch of conformation of polymer chains at such specific compositions. Conclusion could be drawn from TGA analysis was that the copoly(ether ester)s featured excellent thermal stabilities, and the incorporation of eugenol-derived component actually had good compatibility with the parent PHN1. In a word, these bio-derived materials have excellent thermal stability.Thermal stability is an important parameter of polymer materials in practical applications, and determines the long-term usability. In this study, thermal stabilities of the copoly(ether ester)s were investigated by thermogravimetric analysis (TGA). Weight-loss curves and the corresponding derivative curves were depicted in Fig. Tg), melting and crystallization temperatures , together with their corresponding melting and crystallization enthalpies  are critical factors for the shape retention under normal practical use, as well as during molding process. Here these properties were studied by differential scanning calorimetric analysis (DSC). The DSC heating traces (2nd) are shown in Fig. Other thermal properties like glass transition s suggested that these samples could not crystallize from the melt during the first cooling run at the given cooling rate of 10 °C/min. The locally ordered packing of chain segments was not favoured. Although the Tg values gradually decreased with the incorporation of eugenol-derived units, the values changed not so much and were still in the scope of practical applications. Compared with our previous reported 1,10-decanediol-based copoly(ether ester)s (Tg <  − 8 °C)26, the Tg values (> 4.5 °C) of 1,6-hexanediol-based materials in this study has obvious improvement, which is beneficial for applying in a broad range of temperature.Both PHN136. Almost the same diffraction pattern was observed for all the poly(ether ester) materials when the diffraction angles and relative intensities were considered, indicating the crystalline mode of PHN1 was maintained in the copoly(ether ester)s. The crystallinity values can be calculated as the quotient between crystalline area and total area of the diffraction traces. The copoly(ether ester)s were found to be semi-crystalline and the crystallinities (Xc) decreased with the increase of eugenol-derived composition. The discrepancy of material attribute from DSC and WXRD analysis could be ascribed to the difference of treatment method. The samples for WXRD were directly from precipitation in methanol, resulting in a certain degree of crystallization. The X-ray diffraction results confirmed that such materials still have slightly crystalline properties, rather than completely amorphous materials. The crystallinities gradually decrease with the insertion of eugenol-derived units.In order to verify and reinforce the above DSC results and further study their crystalline ability of this kind of materials, powder wide-angle X-ray diffraction analysis (WXRD) was performed. The WXRD traces were depicted in Fig. 1−xE1x and PHN11−xE2x copoly(ether ester)s were performed on dumb-bell shaped specimens (12 × 2 × 0.5 mm3), which were prepared by casting the chloroform solution (0.1 g/mL). The stress-stain curves were depicted in Fig. 1−xE1x was slightly higher than those of PHN11−xE2x when the content of eugenol-derived composition was the same. However, the elongations at break firstly decrease and then increase with the content of eugenol-derived composition increasing. For example, elongations at break decreased from 14.5% for PHN1 37 to 7.0% for PHN190%E110%, and then increased to 10.0% for PHN180%E120%. The elongation at break didn't exhibit the same trends as the Young’s modulus and tensile strength do. This may be ascribed to the asymmetrical nature of eugenol-derived composition, leading to the difficult stacking and loose entanglement of polymer chains. Consequently, Young’s modulus and tensile strength decreases with the insertion of eugenol-derived composition, while the elongation at break did not feature the same variation tendency. Although PHN1 seems to feature the best mechanical properties  than those of copolymerized products, the necessity of copolymerization of nipagin and eugenol-derived monomers is also significant. Nipagin and eugenol are two structurally different building blocks, which will have significant influence on thermal , crystalline , and mechanical properties , which can be tailored for a broad range of applications, such as rubbery and elastomers, etc. depending on the application scenarios.Mechanical properties  are primary parameters to be considered for practical applications. To further study the synergistic effect of nipagin and eugenol-based components on mechanical properties, tensile assays of PHN134, the polymer materials in this study presented inferior tensile strength and Young’s modulus. This was largely attributed to the insertion of eugenol-derived composition impeding the crystallization of copoly(ether ester)s significantly, together with tunable elongation at break. Although we initially targeted the substitutes of petroleum-based dimethyl terephthalate (DMT) and its derived PBT-like materials, the properties presented in this study were opposite. PBT are often used as food packaging materials, which require high Tg, young modulus, and strength values, as well as specific barrier properties, but the polymer materials in this work are appropriate for other application scenarios (elastomer and rubbery), thanks to their modulated mechanical properties by insertion of disparate components. From the point of renewability, this is significant to broaden the types of polymer materials and application fields from bio-based starting materials. The harmony synergistic effect of nipagin and eugenol-derived composition could modulate the properties of such polymer materials in desired application fields.When compared with the widely-used petroleum-based poly (PBT)  materials were synthesized via the melt polycondensation method. The effect of introduction of eugenol-derived units on thermal, crystalline, and mechanical properties was emphatically studied. TGA results revealed that the copoly(ether ester)s featured fairly high thermal stability despite the content of eugenol-derived composition reached 20%. DSC and WXRD data suggested the amorphous nature for both homopoly(ether ester) and copoly(ether ester)s, regardless of the content of highly asymmetrical eugenol-based composition. Young’s modulus and tensile strengths were also found a decreasing tendency with the insertion of eugenol-based composition. More importantly, elongation at break can be tunable via the different content of eugenol-based composition. The cooperative interaction of renewable nipagin and eugenol-derived building blocks provides a practical and suitable way to obtain polymeric materials with desired performance and suitable for various application scenarios.J&K Scientific, Beijing, China), and 1,6-hexanediol  were used as received. All solvents  were analytical grade and used as received without further purification. Silica-gel slices used for thin-layer chromatography (TLC) were purchased from Qingdao Haiyang Chemical Co. Ltd .Nipagin , eugenol , methyl thioglycolate , methyl chloroacetate , 2,2-dimethoxy-2-phenylacetophenone (DMPA)  and tetrabutyl titanate (TBT) , 1,4-dibromobutane  were recorded on a Bio-Rad FTS6000 spectrophotometer at 25 °C. Polymer samples were prepared by grinding the polymeric materials adequately with KBr powder, followed by compressing the mixture to form a pellet. The molecular weights and polydispersity (Ð) values of the samples were determined by gel permeation chromatography  at 35 °C. Tetrahydrofuran (THF) was used as the eluent at a flow rate of 1.0 mL/min. The average molecular weights were calibrated against monodisperse polystyrene (PS) standards. Thermogravimetric analysis (TGA) was carried out using a NETZSCH TG209 instrument. In a typical run, polymer sample was heated from 25 to 800 °C under a nitrogen atmosphere at a rate of 10 °C/min. The temperature leading to 5% weight loss (T5%), temperature for maximum degradation rate (Tmax), and residue weight (%) at 800 °C were recorded. Differential scanning calorimetric (DSC) analysis was carried out by a Mettler-Toledo DSC Q100 calorimeter from TA Instruments. Polymer sample after drying was first heated from room temperature to 150 °C and hold at this temperature for 10 min to eliminate thermal history, then cooled to − 30 °C. Glass transition temperature (Tg) was observed from the second heating run. All runs were carried out at a rate of 10 °C min−1. Indium was used as the calibration standards for temperature. Wide X-ray diffraction (WXRD) patterns were recorded on a D/max-2500 diffractometer using CuKα radiation with a wavelength of 0.1542 nm for dried powder samples. Crystallinity (Xc) was calculated as the quotient between crystalline area and total area. Crystalline and amorphous areas in the X-ray diffraction pattern were quantified by the PeakFit v4.12 software (SeaSolve Software Inc.) with multi-functions , deduction of reductant peaks, AutoFit , AutoScan, etc.). Tensile assays were performed at a stretching rate of 50 mm/min at 25 °C on a Testometric AX Universal Strength Testing Machine.1−xE1x, and PHN11−xE2x  copoly(ether ester)s were prepared from the mixtures of N1, E1 or E2, and 1,6-hexanediol with the pre-calculated stoichiometric composition. The polymerization was performed in a 25 mL Schleck round-bottom flask equipped with a nitrogen inlet, a vacuum distillation outlet, and a magnetic stirrer bar. The polymerization scheme is illustrated in Fig. PHN1 homopoly(ether ester), PHN11H NMR : δ = 7.99–7.97 , 6.91–6.89 , 4.66 , 4.27–4.17 , 1.76–1.62 , 1.49–1.25  ppm; 13C NMR : δ = 168.02 (-OCH2-CO-), 165.68 (Ar-CO-), 161.13 (Ar–C), 131.23 (Ar–C), 123.47 (Ar–C), 113.91 (Ar–C), 64.98–64.78 , 64.34–64.23 , 28.34–28.00 , 25.45–24.98  ppm; FTIR: 2949, 1781 (C=O), 1711 (C=O), 1606, 1510, 1253, 1170, 1105, 977, 848, 770, 697 cm−1.1H NMR : δ = 7.95–7.93 {m, (1-x)∙2H; Ar–H}, 6.88–6.86 {m, (1-x)∙2H; Ar–H}, 6.72–6.68 , 6.63–6.61 , 4.63 {s, (1-x)∙2H; ArO-CH2-CO-}, 4.60 , 4.30–4.09 {m, (1-x)∙4H; -COO-CH2-}, 4.15–4.02 , 3.81 , 3.16 , 2.62–2.57 , 1.88–1.81 {q, 3J = 8.0 Hz, x∙2H; ArCH2-CH2-CH2S-}, 1.79–1.65 {m, (1-x)∙2H; ArCOOCH2-CH2-}, 1.65–1.52 {m, (1-x)∙2H + x∙4H; -COOCH2-CH2-}, 1.50–1.17 {m, (1-x)∙4H + x∙4H; -COOCH2CH2-CH2-} ppm; 13C NMR : δ = 170.48 (-SCH2-CO-), 169.18 (ArOCH2-CO-), 168.29 (ArOCH2-CO-), 166.02 (Ar-CO-), 161.38 (Ar–C), 149.54 (Ar–C), 145.59 (Ar–C), 135.74 (Ar–C), 131.51 (Ar–C), 123.82 (Ar–C), 120.23 (Ar–C), 114.63 (Ar–C), 114.17 (Ar–C), 112.60 (Ar–C), 66.68 and 65.11 (ArO-CH2-CO-), 65.38–64.50 (-COO-CH2-), 55.87 (ArO-CH3), 34.15 (-S-CH2-CO-), 33.59 (Ar-CH2-CH2CH2S-), 31.99 (-S-CH2-CH2CH2Ar), 30.50 (ArCH2-CH2-SCH2-), 28.67–28.54 , 28.40–28.27  ppm; FTIR: 2934, 2860, 1756 (C = O), 1703 (C = O), 1603, 1510, 1422, 1265, 1166, 1105, 1070, 974, 846, 765, 693 cm−1.1H NMR : δ = 7.92–7.90 {m, (1-x)∙2H; Ar–H}, 6.85–6.83 {m, (1-x)∙2H; Ar–H}, 6.73–6.71 , 6.63–6.59 , 4.59 {s, (1-x)∙2H; ArO-CH2-CO-}, 4.19–4.10 {m, (1-x)∙4H; -COO-CH2-}, 4.03–3.97 {m, (1-x)∙4H + x∙4H; ArO-CH2-CH2- and -COO-CH2-}, 3.75 , 3.13 , 2.67–2.46 , 2.02–1.88 , 1.88–1.76 {q, 3J = 8.0 Hz, x∙4H; ArCH2-CH2-CH2S-}, 1.75–1.63 {m, (1-x)∙2H; ArCOOCH2-CH2-}, 1.62–1.47 {m, (1-x)∙2H + x∙4H; -COOCH2-CH2-), 1.46–1.12 {m, (1-x)∙4H + x∙4H; -COOCH2CH2-CH2-} ppm; 13C NMR : δ = 170.29 (-SCH2-CO-), 168.09 (ArOCH2-CO-), 165.78 (Ar-CO-), 161.22 (Ar–C), 149.20 (Ar–C), 146.57 (Ar–C), 133.87 (Ar–C), 131.31 (Ar–C), 123.62 (Ar–C), 120.13 (Ar–C), 114.00 (Ar–C), 113.21 (Ar–C), 112.20 (Ar–C), 68.58 (ArO-CH2-CH2-), 64.90 (ArO-CH2-CO-), 64.42–64.31 (-COO-CH2-), 55.71 (ArO-CH3), 33.95 (-S-CH2-CO-), 33.39 (Ar-CH2-CH2CH2S-), 31.81 (-S-CH2-CH2CH2Ar), 30.42 (ArCH2-CH2-SCH2-), 28.43–28.15 , 25.84 (ArOCH2-CH2-), 25.53–25.06  ppm; FTIR: 2935, 2860, 1756 (C=O), 1708 (C=O), 1603, 1510, 1459, 1264, 1166, 1107, 1071, 976, 847, 809, 765, 693 cm−1.Supplementary Information.


The molecular mechanism of β3-AR regulating oxidative stress, especially NADPH oxidase, remains to be determined.  Excessive myocardial oxidative stress could lead to the congestive heart failure. NADPH oxidase is involved in the pathological process of left ventricular (LV) remodeling and dysfunction. β3-AR agonist (BRL) or inhibitor (SR) administration in cardiac hypertrophy. Moreover, the cardiac function, fibrosis, heart size, oxidative stress, and cardiomyocytes apoptosis were also detected.  Cardiac hypertrophy was constructed by the transverse aortic constriction (TAC) model. ROS and NADPH oxidase subunits expression were assessed after β3-AR activation significantly alleviated cardiac hypertrophy and remodeling in pressure-overloaded mice. β3-AR stimulation also improved heart function and reduced cardiomyocytes apoptosis, oxidative stress, and fibrosis. Meanwhile, β3-AR stimulation inhibited superoxide anion production and decreased NADPH oxidase activity. Furthermore, BRL treatment increased the neuronal NOS (nNOS) expression in cardiac hypertrophy. β3-AR stimulation alleviated cardiac dysfunction and reduced cardiomyocytes apoptosis, oxidative stress, and fibrosis by inhibiting NADPH oxidases. In addition, the protective effect of β3-AR is largely attributed to nNOS activation in cardiac hypertrophy. Despite the progress of therapeutic approaches, congestive heart failure (CHF) remains to be a high morbidity and mortality , 2. ConsROS is mainly originated from the NADPH oxidases in cardiovascular system . The typβ-ARs regulate the cardiac function when exposed to stress  sham group (Sham); [2] transverse aortic constriction group (TAC); [3] TAC + BRL37344 group (TAC+BRL); and [4] TAC + SR59230A group (TAC+SR). The experiments were approved by the Fourth Military Medical University Committee on Animal Care.Transverse aortic constriction (TAC) was constructed as previously described. Briefly, mice were anesthetized with 2% isoflurane, endotracheally intubated with a 20G catheter, and ventilated. The transverse aortic arch was surgically accessed. Then, a 25G needle was placed on the transverse aorta, which was secured. Finally, the chest was closed after removing the needle, leaving a stenosis. Mice were administrated with BRL37344  or SR59230A, respectively, at 0.1 mg/kg/hour via osmotic minipumps.Primary cardiomyocytes were isolated from the neonatal mouse (1 to 3 days old) hearts as previously described. The cardiomyocytes were treated with hypertrophic agonists, phenylephrine (PE). Then, after 24 hours, the cardiomyocytes were treated with BRL37344 or SR59230A. The groups are as follows: [1] saline; [2] PE; [3] PE+BRL; and [4] PE+ SR.α-actinin ; Alexa-594 secondary antibodies .Primary cardiomyocytes were subjected to immunostaining. Antibody sources were as follows: phox were performed as previously described. The primary antibodies are NOX2 , NOX4 , and p22phox .Three weeks after TAC operation, mice were sacrificed. Tissue sections of hearts were stained with Masson's trichrome (Sigma) for detection of fibrosis. The fibrosis-related genes Col1a1, Col3a1, and fibrillin 1 (FBN1) were detected by q-PCR. Meanwhile, wheat germ agglutinin  was used to outline cardiomyocytes. Mean cardiomyocyte cross-sectional area was determined from digitized images and analyzed using the ImageJ program. ANP and BNP were detected by q-PCR. For analyzing the expressions of myocardial NAD(P)H oxidase subunit, immunohistochemical stainings of NOX2, NOX4, and p22Echocardiography studies were conducted weekly to monitor heart function as previously described . We follApoptosis in heart tissue was determined based on TUNEL and caspase-3 activity assay as previously described .2•- in the LV was measured as previously described. Meanwhile, in situ formation of tissue ROS was detected by staining with DHE and DCF as described recently. Briefly, fresh frozen left ventricular sections were incubated with DHE  or DCF , respectively. The activities of SOD and GSH were detected according to the Beyotime Kits.The production of Ophox, p47phox, p67phox, Rac-1 ; eNOS, p-eNOSSer1177, p-eNOSThr495, p-eNOSSer114, iNOS, nNOS , β3-adrenergic receptor , and β-actin .Membrane proteins or total cell proteins were extracted from homogenized LV tissue. The primary antibodies included NOX2, NOX4, p22t test for two groups' comparison. P values < 0.05 were considered statistically significant.The results are presented as mean ± SEM. All experiment data were analyzed by the GraphPad Prism8 software. Statistical comparisons for different group were performed using one-way ANOVA followed by Student's paired, two-tailed P < 0.05), indicating that pressure overload successfully induced cardiac pathological remodeling. Moreover, cross-sectional area, LV mass, and wall thickness all increased after TAC operation  and TAC+SR group  (P < 0.05) and TAC+SR group  (β3-AR stimulation decreased apoptosis in the pressure-overloaded heart. < 0.05) . Meanwhi < 0.05) . These dP < 0.05) and TAC+SR group . NADPH oxidase activity was lower in the TAC+BRL group compared to the TAC group (173.5 ± 17.4 units/min/mg vs. 301.5 ± 19.1 units/min/mg; P < 0.05, 2•- production was lower in the TAC+BRL group compared with that in the TAC group (52.2 ± 8.4 nmol/mg vs. 104.5 ± 13.2 nmol/mg; P < 0.05; β3-AR stimulation decreased oxidative stress induced by pressure overload.The production of ROS, measured by DHE and DCF staining, was significantly increased in the TAC group and TAC+SR group. However, BRL treatment significantly decreased ROS generation in pressure-overloaded mice . MeanwhiWe assessed the intracellular expressions of NADPH oxidase subunits by Western bolt assay. The expression of membrane-bound subunits, p22phox and NOX2, significantly increased in the TAC group, which was abolished by BRL treatment Figures . Howeverβ3-AR expression in all groups. The decreased β3-AR was observed in the TAC and TAC+SR groups (Figures β3-AR increased after BRL treatment. We further evaluated the expression of NOS isoforms in all groups. First, the expression of total eNOS and phosphorylated eNOSSer114 was unchanged. However, TAC operation significantly decreased the phosphorylation of eNOSThr495 but increased expression of phospho-eNOSSer1177, which were abolished by the BRL treatment. Furthermore, we examined the expression of iNOS and nNOS. There was no difference in iNOS expression in all groups (Figures Western blotting assays were performed to evaluate  Figures . Convers Figures . In cont Figures .β3-AR stimulation, which was in line with our previous study [Cardiac remodeling, a major determinant of CHF, is associated with pathological cardiac hypertrophy . Initialus study .β3-AR stimulation alleviated the oxidative stress by inhibiting NADPH oxidases. Moreover, the cardiac protective effect of BRL is mediated through NO generating via the nNOS pathway.Oxidative stress is involved in cardiomyocyte apoptosis, cardiac remodeling, cardiac dysfunction, and heart failure –28. OxidThe NOX subunit forms a stable heterodimer with the p22phox subunit. Among all NOX submits, NOX2 and NOX4 are mainly enriched in cardiomyocytes. Previous studies revealed that NOX2 deficiency inhibited cardiac hypertrophy . Interesβ-ARs may modulate cardiac function. Among them, β1-AR and β2-ARs mediate positive chronotropic and inotropic effects [β3-AR is reported to mediate lipolysis and thermogenesis in adipocytes [β3-AR is also involved in cardiovascular system regulation, which may antagonize the effects of β1/2-ARs. Moreover, β3-AR is increased in failing hearts [β3-AR overexpression attenuated cardiac hypertrophy [β3 knockout exacerbated cardiac hypertrophy induced by pressure overload [β3-AR stimulation reduced hypertrophy, prevented fibrosis, and preserved cardiac function induced by pressure overload. Furthermore, β3-AR stimulation reduced the superoxide generation in TAC mice. Meanwhile, NADPH oxidase activity was also decreased after β3-AR stimulation, indicating that the protective effect of β3-AR is mediated, at least by part, through inhibiting NADPH oxidases, which contributes to the cardiac oxidative stress induced by pressure overload (It have been demonstrated that 3 subtypes of  effects , 21. β3-ipocytes . Howeverg hearts . Meanwhiertrophy . Furtheroverload . In curroverload .β3-AR stimulation could increase NO release by NOS activity [β3-AR knockout exacerbates NOS uncoupling, suggesting that β3-AR regulates cardiac oxidase stress by regulating NO generation through NOS activity [β3-AR signaling still remains unclear. The activity of eNOS is mainly affected by eNOS-PSer1177, eNOS-PThr495, and eNOS-PSer114. Phosphorylation at Ser1177 activates eNOS, whereas phosphorylations at Ser114 and Thr497 inhibit eNOS activity [Thr495 and increased p-eNOSSer1177 were observed in chronic pressure overload after BRL treatment. Therefore, β3-AR stimulation leads to eNOS deactivation rather than activation. In contrary, β3-AR stimulation increased the expression of nNOS. Moreover, both nNOS expression and nNOS-derived NO production regulate cardiac function [β3-AR were actually abolished in nNOS–/– mice [β3-AR (activity .Moreoveractivity . Three Nactivity . In the function . The car–/– mice . Based oe [β3-AR .β3-AR stimulation regulates the oxidative stress by inhibiting NADPH oxidases, which impaired cardiac function. In addition, these cardioprotective effects of β3-AR are largely attributed to nNOS activation. These inspiring observations provide novel insight into β3-AR as a new target for treating cardiac hypertrophy.In conclusion, we provide evidence that