Previous studies have shown that our perception of stimulus properties can be affected by the emotional nature of the stimulus. It is not clear, however, how emotions affect visually-guided actions toward objects. To address this question, we used toy rats, toy squirrels, and wooden blocks to induce negative, positive, and neutral emotions, respectively. Participants were asked to report the perceived distance and the perceived size of a target object resting on top of one of the three emotion-inducing objects; or to grasp the same target object either without visual feedback (open-loop) or with visual feedback (closed-loop) of both the target object and their grasping hand during the execution of grasping. We found that the target object was perceived closer and larger, but was grasped with a smaller grip aperture in the rat condition than in the squirrel and the wooden-block conditions when no visual feedback was available. With visual feedback present, this difference in grip aperture disappeared. These results showed that negative emotion influences both perceived size and grip aperture, but in opposite directions  and its influence on grip aperture could be corrected by visual feedback, which revealed different effects of emotion to perception and action. Our results have implications on the understanding of the relationship between perception and action in emotional condition, which showed the novel difference from previous theories. Emotion-laden stimuli can affect our perception. For example, spiders appear to move faster than non-threatening objects ; verticaAlthough a lot of research has been done on how emotion influences perception, it is still unclear how the grasping taken toward an object could be influenced by the emotional state of the environment. One possibility is that the influence of emotion on action relates to and reflects its influence on perception. For example, when an object is perceived as closer as and larger than it really is, one may also reach closer and use a wider grip aperture to grasp it. If this is the case, the bias in the perception of distance and size could have serious consequences. These consequences can be seen when interacting directly with threatening stimuli, such as removing a bomb or demolition of a delicate explosive device which contains strong negative emotions (such as fear) and fine hand movements (such as grasping), simultaneously. Although the perception could be influenced, the action could usually be finished successfully.However, since our ancestors have been dealing with threats for millions of years, it is possible that our visuomotor system has evolved and developed a way to deal with distance and size information without being influenced by any bias in perception. Indeed, it has been reported that action does not always reflect the perception of an object. For example, in the Ebbinghaus illusion, the perceived size of a target object is influenced by the size of its flankers; however, people are still able to grasp the target object according to its physical size . In addiIn this study, we conducted three experiments to test the influence of stimuli with negative and positive emotional valence on perceptual judgments and on grasping. Previous studies have used movie clips to induce emotions e.g., . But herIn experiment 1, we first replicated the previous finding that emotion affects perceived distance and perceived size, but with a different way to measure the perception – that is, we asked participants to use their finger to point to where the target object was and use their fingers to manually estimate the size of the object. We did this because participants would use their fingers to perform the grasping task in experiment 2. In experiment 2, we tested how emotions influence the reaction time (RT), movement time, and grip aperture during grasping. It has been suggested that the planning and control of an action involves separate neural systems . TherefoEighteen native students from Nanjing University , with normal or corrected-to-normal vision, took part in this experiment. The participants gave informed consent before participating. The participants had no idea of the purpose of the experiment. All the participants were right-handed, and their handedness was assessed using the Edinburgh Handedness Inventory . They ga3, large: 14×5×6cm3). The brown toy squirrels also had two different sizes . The white wooden blocks had two different sizes  too. The target objects were rectangle wooden plaques of two different sizes  affixed to the heads of the toys or the top surface of the wooden blocks. We used inducers (toys or white wooden blocks) of two sizes to reduce the possibility of judging the size of the target object relative to the size of the inducers . This was confirmed in experiment 3 which suggests that participants would not use the size of the toys as a cue for size estimation (see results for details).In this experiment, we examined how positive emotions  and gray wooden blocks (the same color with toy rats) as objects to induce emotions were also included. The sizes of these wooden blocks were the same as the white wooden blocks mentioned above.The toys and wooden blocks were placed at one of three distances  from the start button along with a line 15cm to the right of the mid-sagittal plane. Three distances were used to increase participants’ engagement in the task. The start button was located 5cm from the edge of the table facing the participants and was on the mid-line of the table. Black cubes of different heights were put under the toys and wooden blocks so that the target objects were always at the same level in all emotion conditions.Liquid crystal goggles  were used to control the visibility of the participant’s hands and the working space. The goggles could be switched from translucent to transparent in approximately 1ms and from transparent to translucent in 6ms or even less. The 3D positions of the thumb and index finger were recorded with an Optotrak Certus  system, with the infrared emitting diodes (IREDs) attached to the distal left corner of the index-finger nail and the distal right corner of the thumb nail. Two more IREDS were attached to the two corners of the table along the side nearest the participants to locate the center of the table, which is also the center of the participants’ body because participants were seated in the middle line of the table. The sampling rate of Optotrak was 200Hz.At the beginning of the experiment, the three target objects were presented with random sequence: the toy squirrels, toy rats, and wooden blocks. To confirm these targets induced the positive, negative, and neutral emotions, respectively, participants were asked to report how “threatened or frightened” and how “happy” they felt in the presence of each object using a Likert scale ranging from 1  to 7 (very much). The scores of positive emotion and negative emotion were recorded, respectively.Then, participants were asked to sit comfortably in front of the table with the mid-line of their body aligned to the middle of the table and the start button (the start button is located on the mid-line of the table). The experimenter confirmed that all participants could reach out and indicate the furthest distance of the target object comfortably without leaning forward with the thumb and index fingers of their right hand pinched together. Then participants were asked to put their chin on the chinrest throughout the testing session. They were told to fixate in a natural way and concentrated on the experimental tasks during the experiment.At the beginning of each trial, participants were asked to hold down the start button. The goggles were closed. After the experimenter placed one of the emotion inducers and the target object on the right location, the experimenter pushed the space key to open the goggles. There were two tasks. For the perceived distance task, participants were instructed to indicate the perceived distance between the target object and themselves by reaching out and touching the table with their index finger and thumb pinched together at a point along the middle-line of the table that was perceived equally far away as the target plaque . In other words, they were not able to see their hand or the target object when they were making the estimates  and the toy squirrel (expected to induce positive emotion) blocks of trials were performed in a random order across participants. The order of size estimation and distance estimation was counter-balanced across participants. These two emotional blocks of trials were interleaved with the neutral blocks. There were 24 trials separately for each block, with 12 trials for each size and eight trials for each distance. The control conditions were identical with the toy rats and toy squirrel conditions except that the toys were replaced by gray and brown wooden blocks. There were eight blocks in total [4 ×2 (size estimation and distance estimation)] with 24 trials in each. The control conditions and the experimental conditions were conducted in the same testing session with order balanced across participants.t-tests were used to evaluate whether the three objects induced different emotions.First, to verify whether the three objects  induced the expected emotional arousal for the participants, we recorded the ratings that participants gave to each kind of inducing object separately for each of the two different sizes, and then averaged the ratings across the two different sizes. One-way repeated measures ANOVA and paired To assess the effect of negative and positive emotional valence on the perception of the distance and size of objects, we extracted the estimated distance or the estimated size in each trial. The estimated distance was calculated as the distance from the midpoint between the thumb and index finger markers to the center position of the participant . The estimated size was defined as the aperture between the two IREDS that were attached to the thumb and index finger when participants were indicating the perceived size (length) of the target object. Some trials were discarded due to participant’s or experimenter’s error . The discard rate for estimated size was 12 of 864 (1.4%), and for estimated distance was 13 of 864 (1.5%).target object on top of the toys, not the toys themselves. Experiments 3 confirmed that participants would not use the relative size to judge the size of the target. Second, preliminary analysis showed that the main effect of distance was not significant.Note that although the toys had different sizes and were placed at three different distances to make the task less predictable and make the participants more engaged in the task, the data of perceived distance and estimated size were averaged over the different toy sizes and different presentation distances for each emotion condition. This was because, first, participants reported the distance and size of the To evaluate the effect of emotion (positive emotion induced by brown squirrels and negative emotion induced by toy rats) on perceived distance and estimated size, and to rule out of the possibility that the difference in the color of the toys might have affected the results, we performed a 2×2 repeated measures ANOVA. The first factor is color which could be brown or gray. The second factor is category which could be wooden blocks in the control conditions or the toys in the experimental conditions . The data in the white wooden block condition were not included for analysis because we already included the control condition with color-matched wooden blocks in the above ANVOA analysis.F =100.881, p<0.001] and the positive emotional arousal scores . Simple effect analysis based on ANOVAs revealed that, the negative emotional arousal score for the toy rats was significantly higher than those for the wooden blocks (p<0.001) and the toy squirrels . Thus, only toy rats induced negative emotion. On the other side, the positive emotional arousal score for the toy squirrel condition was significantly higher than the scores for the wooden blocks (p<0.001) and toy rats (p<0.001) conditions. Moreover, the scores for wooden blocks were also significantly higher than the ratings for toy rats (p<0.001). Thus, toy squirrels appeared to induce stronger positive emotion than both wooden blocks and toy rats =12.079, p=0.003; F =0.810, p=0.381] and category  was not significant. Simple effect analysis revealed that the estimated distance was significantly shorter for the toy rat condition than that for the toy squirrel condition (p=0.013), which is consistent with previous studies showing that people tend to feel objects associated with negative emotions closer to themselves (p=0.103) suggesting that the influence of emotion on perceived distance could not be simply attributed to the difference in color.As mentioned above, a repeated-measures ANOVA with color (brown vs. gray) and object category (wooden blocks vs. toys) was conducted to reveal the influence of color and object category on perceived distance. The interactions between color and object category . Similarly, the normalized distance estimate was defined as (distanceRats−distanceGrayBlocks)/distanceGrayBlocks. The normalized emotional scores and the normalized distance estimate was negatively correlated =5.442, p=0.032; F=0.741, p=0.401] was not significant while the category  was significant. Simple effect analysis revealed that the estimated size for the target object was significantly larger when the target object was resting on top of the toy rats than when it was resting on top of the toy squirrels (p=0.016) suggesting that negative emotions increased the perceived size of a standard target object, which is consistent with the results of previous studies (p=0.690).Similar to the results in distance estimation, a repeated-measures ANOVA with color (brown vs. gray) and object category (blocks vs. toys) was conducted. The interactions between color (brown vs. gray) and object category  with 24 trials in each.t-tests were used to examine whether the toys induced different emotions.First, we analyzed the ratings that participants gave for each kind of object for each of the two different sizes. One-way repeated measures ANOVAs and paired Then to assess the effect of negative and positive emotional valence on the grasping behavior, we extracted the RT, movement time, and peak grip aperture (PGA) from each grasping trial. The RT was defined as the time interval between the goggles were opened and the movement onset of wrist IRED. The movement onset was defined as the first frame of the 40 consecutive frames during which the wrist IRED exceeded 20mm/s, the movement offset was defined as the first frame of the 40 consecutive frames during which the wrist IRED fell below 20mm/s. The movement time was defined as the time between movement onset of wrist IRED and the movement offset of wrist IRED. Participants’ thumb and index fingers were pinched together before grasping. When they reached out to grasp an object, the aperture between the two fingers first opened, reached to peak well before they made contact with the target object, and then closed down to hold the object see . The seaSome trials were excluded due to participant or experimenter error . The discard rate for RT was 84 of 3,456 (2.4%), and for PGA was 28 of 3,456 (0.8%). Repeated-measures ANOVAs with three factors {[2 visual feedback (closed-loop vs. open-loop)×2 colors (gray vs. brown)×2 categories (toy vs. block)]} were conducted to reveal the influence of color and object category on reaction time and PGA.F =84.944, p<0.001] and positive emotional arousal scores . The negative emotional arousal score for the toy rat condition was significantly higher than those for the wooden block condition (p<0.001) and the toy squirrel condition (p<0.001). There was no significant difference in the negative arousal scores between the wooden block and toy squirrel conditions (p=0.886). The positive emotional arousal score in the toy-squirrel condition was significantly higher than that in the wooden-block condition (p<0.001) and toy-rat condition (p<0.001). Moreover, the positive emotional score for the wooden block condition was also significantly higher than the score for the toy rat condition (p<0.001). In sum, toy rats and toy squirrels induced negative emotion and positive emotion, respectively.The result is consistent with the emotional score result in experiment 1. One-way repeated measures ANOVA indicated that there were significant differences among different emotions both for the negative  when a three-way repeated-measures ANOVA [2 visual feedback (closed-loop vs. open-loop)×2 colors (gray vs. brown)×2 categories (toy vs. block)] was conducted. The interaction of three-way repeated-measures ANOVA was not significant . The interaction between colors and visual feedback was not significant , and neither was the interaction between categories and visual feedback . The main effect of categories  was significant while colors was not significant. The interaction between colors and categories  was marginally significant suggesting that it was not just the color of the toys that modulated the reaction time.As shown in p=0.116). Moreover, the small (and non-significant difference) in reaction time between the toy-rat and the toy-squirrel conditions was as small as that between the gray-wooden block and the brown-wooden block conditions, which suggests that this small difference may be explained by the difference in color.To have a close look at the influence of the toy rats and toy squirrels on the reaction time, we performed a simple effect test to reveal any difference in the effect of emotion on reaction time separately for the open- and closed-loop conditions. In the open-loop condition when participants were not able to see the target or the grasping hand during grasping, there was no significant difference in the reaction times between the toy-rat or toy-squirrel conditions (p=0.007) and brown wooden blocks (p=0.045). The reaction time had no difference in the toy rat and the gray block conditions (p=0.148) suggesting that the negative emotion induced by toy rats did not influence the reaction time. The reaction time in the toy squirrel condition was significantly smaller than that in the brown blocks condition suggesting that people tended to grasp the object on top of an object that induces positive emotion faster. Overall, the results suggest that visual feedback is helpful for the implement of the modulation of positive emotion.In contrast, in the closed-loop condition, when participants were able to see the target object and their grasping hand, the reaction time in grasping the target object was shorter when the target object was resting on top of the toy squirrels than when it was resting on top of the toy rats (Rat−ESWoodenBlocks)/ESWoodenBlocks and (RTRat−RTBrownBlocks)/RTBrownBlocks. The correlation coefficient was not significant . In the toy squirrel condition, we calculated correlation between the value of (ESSquirrel−ESWoodenBlocks)/ESWoodenBlocks and (RTSquirrel−RTBrownBlocks)/RTBrownBlocks. The correlation between the normalized emotional scores and the normalized reaction time was negative and significant  suggesting that people who had stronger positive emotion on the inducer also had shorter reaction time when reached out to grasp the object on it  and the normalized RT when the target object was on the squirrels in the closed-loop condition. In the toy rat condition, we calculated correlation between the value of =22.504, p<0.001)] when a three-way repeated-measures ANOVA [2 visual feedback (closed-loop vs. open-loop)×2 colors (gray vs. brown)×2 categories (toy vs. block)] was conducted. The larger PGA in the open-loop condition is in line with previous results =1.980, p=0.177]. The interaction between colors and visual feedback was significant , but the interaction between categories and visual feedback  was not, neither was the interaction between categories and colors . The main effect of categories  and colors  was not significant.It could be clearly seen in  results  and coulF =8.541, p=0.009] suggesting that the influence of toys on PGAs is different from the influence of the color of the blocks on PGAs. The simple main effect analysis revealed that participants opened their thumb and index finger smaller when the target object was on top of the toy rats than it was on top of the toy squirrels  or gray blocks . But the grip aperture on the toy squirrel condition did not differ from the grip aperture for grasping the same target in the brown block condition . And the grip aperture on the gray block did not differ from the grip aperture for grasping the same target on the brown block condition . In the closed-loop condition, neither the main effects of color or category , nor the interaction between color and category  was significant when the target object and grasping were visible and thus adjustment of grip aperture was available.To have a closer look at the effect of emotion when visual feedback was available or unavailable, we performed repeated measures ANOVAs [2 colors (gray vs. brown)×2 categories (toy vs. block)] for the closed-loop and open-loop conditions separately. In the open-loop condition , the interaction of color×category is significant  and the normalized PGA  when the target object was on the rat in the open-loop condition . The correlation was significant  suggesting that the stronger the induced negative emotion, the smaller the grip aperture during grasping =20.633, p=0.001]. Simple effect analysis revealed that, the PGA was significantly different from the size estimation in positive emotion condition  and also in negative emotion . It indicates that the emotions (rats vs. squirrels) influenced the size estimation and PGA differently, although PGA was much larger than the size estimation.Moreover, to directly compare whether the induced emotions by toy rats and toy squirrels had different effects on size estimation (experiment 1) and PGA (experiment 2 in open-loop condition), we performed a two-way repeated-measures ANOVA with emotion (two levels: toy rats vs. toy squirrels) and task measurements (two levels: size estimation in perception task vs. PGA in grasping task) as factors. Note: only the data of participants who took part in both experiments were included. We found that the interaction between the two factors was significant . The interaction between colors and visual feedback was not significant , neither was the interaction between categories and visual feedback . In addition, the interaction between categories and colors was not significant . The main effect of visual feedback  and colors  was not significant, while the main effect of categories was significant , the movement time in toys condition  was longer than the movement time in blocks condition , but no significant effects of colors and visual feedback were found which may because the participants were required to grasp the objects in nature pace.Movement time is also an important kinematic feature of action. A three-way repeated measures ANOVA [2 categories (blocks vs. toys)×2 colors (gray vs. brown)×2 visual feedback (open-loop vs. closed-loop)] was performed. The three way interaction was not significant  for each kind of wrapped toy. For each tasks, there were four blocks of 24 trials, with six trials for each condition. Each task was carried out for two times, one for the wrapped toy rats and the other one for the wrapped toy squirrels. The order of the different target object size and different neutral stimuli size conditions was counter-balanced across participants. The order of wrapped toys type was counter-balanced across participants. Participants were required to perform their grasping movements separately for the two feedback conditions (closed-loop vs. open-loop), and the order was also counter-balanced across the participants.The same methods were used to extract the size estimation and PGA values in each trial. To exclude the effect of extra variables  on size estimation and PGA, three 3-way repeated measures ANOVAs were performed with the type of wrapped toys (wrapped toy rats and wrapped toy squirrels), toy size and target size on the size estimation, and PGA in open loop and closed loop separately.F =9.89, p=0.331], nor the interaction between toy types and toy size , toy size and target size , or toy types and target size . The main effect of toy size  and toy types  was not significant. The main effect of target object size was significant , and size estimation was larger in large target condition. As shown in F =1.478, p=0.238], nor the interaction between toy types and toy size , toy size and target size , or toy types and target size . The main effect of toy size  and toy types  was not significant. The main effect of target object size was significant , size estimation was larger in large target condition. As shown in F =2.176, p=0.155], nor the interaction between toy types and toy size , toy size and target size , or toy types and target size . The main effect of target size was significant , size estimation was larger in large target condition. The main effect of toy types was not significant , and the toy size was not significant .As shown in These results suggested that in these three conditions, the shape and size of neutral stimuli did not have an effect on the perception or the PGA, only the target object size would affect the estimation and grasping which excluded the uncertainty of previous results for the possible effect of stimuli size and shape. Therefore, we thought we offered an available verification for this study.In this study, we first carried out two experiments to investigate how emotional stimuli (toy rats and toy squirrels) affected the distance and size perception of a target object resting on them and the actions directed toward that target object. The results of Likert scales confirmed that the toy rats induced negative emotions while the toy squirrels induced positive emotions. In experiment 1, we found that participants perceived the target object on top of the toy rats (induced negative stimulus) significantly closer and larger than the same target object resting on top of the toy squirrels (induced positive stimulus) suggesting that there is perceptual bias even within the reachable personal space. In experiment 2, when no visual feedback was available , participants used a smaller grip aperture to grasp the target object when it was placed on top of the toy rats (negative emotion) than when it was placed on top of the toy squirrels (positive emotion). The different effects of negative emotion on size perception and grip aperture  suggest that there are independent neural mechanisms for the influence of negative emotion on perception and action. In addition to the influence of negative emotion on grip aperture, we also found that positive emotion sped up the onset of the grasping movement  but only when visual feedback was available . Moreover, the effects of negative emotion on the size and distance perception and grip aperture, along with the effects of positive emotions on the reaction time of grasping, as addressed above, were correlated with the strength of the corresponding emotions across individuals. It may further indicate that the induced emotion caused the observed changes in perception or action. At last, we also performed a control experiment which showed that the effects of induced emotions by toy rats and toy squirrels on the perception and grasping of targets were not affected by the shape of toy rats and toy squirrels in our study.To exclude the possibility that participants exploited the clues of their limbs and surrounding items to estimate the target distance, the target location in distance estimation task was designed to be different with the size estimation task and grasping task. With wooden blocks of the same color used as controls, we found that only the toy rat (not the toy squirrels) which induced negative emotions affected the perceived size and perceived distance of the target object. Majority of previous studies that examined the influence of emotion on perception tested whether the perception of the threatening objects themselves was biased . In our How do we then explain the influence of negative emotion on size and distance perception? One possibility is that emotional valence affects perception in ways that reflect heightened attention. For example, coins seemed to be larger than same-size cardboard disks for children from a poor family . It mighThere is evidence showing that the perceived size of an object is represented in the primary visual cortex . AdditioFirst, the reaction time  was shorter for the squirrel condition when visual feedback was available . These results are consistent with those of a large number of studies that have demonstrated differences in the reaction times for approach and avoidance when participants are confronted with stimuli of different emotional valences . For exaSecond, the PGA was smaller when the target object was on top of a toy rat than when it was on top of a toy squirrel and its corresponding controls (gray blocks) when visual feedback was not available . This suggests that participants tend to open their hand less when the target object was associated with negative emotions. The smaller grip aperture probably reflects the fact that participants were unwilling to grasp the target object that was associated with negative emotion or were trying to avoid the unpleasant toy rat during grasping. However, the influence in grip aperture disappeared in the closed-loop condition suggesting that the online visual feedback and adjustment could eliminate the influence of negative emotion on the programming stage . The different effects observed in the open and closed-loop condition provide further evidence that the planning and control of an action involves different neural network .In our study, we showed that the influence of negative emotion on perception and action is independent: when the target object was positioned on top of the rats, participants perceived the target object as larger than when it was on top of the squirrels, but used a smaller grip aperture to grasp it.Although it is unclear why the difference in the effect of emotion on perception and action was, our results seems to be consistent with the two-visual-stream theory  which stAlthough there was evidence showing that action is less susceptible to the influence of objects in the surroundings ,b, it isThe grasping in the open-loop condition depends only on the programming of grasping based on the visual information participants obtained before the hand movement. Conversely, the grasping in the closed-loop condition depends on both programming before the hand movement (planning stage of grasping) and adjustment based on visual feedback during hand movement (execution stage of grasping). Our finding that the negative emotion influences grip aperture only in the open-loop condition but positive emotion influences reaction time only in the closed-loop condition revealed a critical difference between negative and positive emotions.It appears that the influence of negative emotion is automatic and pre-attentive, and therefore appears during the programming of grasping in the open-loop condition, but could be eliminated by visual feedback in the closed-loop condition. In contrast, the influence of positive emotion on reaction time is gradually accumulated during the consecutive closed-loop trials with visual feedback. We speculate that the influence of positive emotion on reaction time occurs gradually because visual feedback on a particular trial was received after participants released the start button, i.e., after the reaction time was measured. Therefore, it must be feedback from previous trials in the same closed-loop block that influenced the reaction time of the upcoming trial(s), which resulted in a reduction in the mean reaction time of all trials.To conclude, we found that when a target object was associated with negative emotion, the target object would be perceived as larger and closer, but participants would use a smaller grip aperture to grasp the target object. In addition, the smaller grip aperture during grasping was observed when participants were not allowed to see the target or their hand during the execution of grasping but was not observed when the target and their hand were visible during grasping. Furthermore, positive emotion only influences the reaction time to object grasping when participants could see the target and their hand. Our results have implications on the understanding of the relationship between perception and action in emotional condition, which showed the novel difference from previous theories.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by Ethics Committee at Nanjing University. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.CS designed and conducted the experiment, analyzed the data, and wrote the article. JC wrote and revised the article. YC designed and conducted the experiment and analyzed the data. RT designed the experiment, wrote, and revised the article. All authors contributed to the article and approved the submitted version.This study was supported by grants from National Natural Science Foundation of China (Grant #31571131 to RT and No. 31800908 and No. 31970981 to JC), the fourth pilot research program for human spaceflight (030602) to RT, and the Key Realm R&D Program of Guangzhou (202007030005) to JC.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain. Multiscale computational methods and simulations have attracted scientists and engineers for many years, which has been documented by the comprehensive review presented in . As is eSuch multiscale homogenization methods have been worked out in solid mechanics to predict the elastic effective properties of fiber-reinforced composites , metal–cNevertheless, the problem of stochastic micro or nanostructure and the realistic impact of the random spaces on the overall characteristics of the composite material (or system) is rather infrequent, and this is why it shall be discussed in this paper.The linear mechanical behavior of single phase isotropic and anisotropic materials is well understood and has been proved by a firm theoretical background. This is also true for composites with non-complex internal composition and geometry, for which analytical solutions apply, and when geometry of the microstructure represents a certain pattern and symmetries. This allows them to be included in certain class of behaviors, e.g., cubic or orthotropic, etc. When such symmetries are not recognizable straight away, various homogenization approaches are used that usually require multi-scale considerations; some modern ones include the FE2 scheme  or neuraMechanical behavior in the non-linear regime of materials is already complex in the isotropic case, where multiple constitutive laws may be utilized for the same material. This is true for the hyper-elastic regime for instance, where these laws are usually defined assuming material isotropy, so that the potential application area is strictly limited. There also exists some hyper-elastic theories accounting for the anisotropy of material microstructures , howeverIndependently from the composites’ response under the given loads, one of the most important aspects of both deterministic and stochastic numerical modelling is the connection of their constituents. A perfect bonding is not achieved in many cases because of the chemical, thermal, electrical or mechanical properties’ incompatibilities and also due to manufacturing processes. In such cases, an interphase is inserted in-between the original constituents of the composite , which fThe interface defects are considered in this work and the influence of uncertainty in their volume fraction in the given interphase on effective mechanical properties of some particulate composite is numerically studied using the generalized stochastic perturbation-based computational analysis. We verify the impact of this input uncertainty and, independently, of the strain level on the effective probabilistic stiffness tensor components, when particles are linear-elastic and the matrix is hyper-elastic. The iterative stochastic finite element method based on higher order Taylor expansions and polynomial bases is used to determine the first four probabilistic characteristics of the effective tensor components. Computational implementation has been completed using a hybrid application of the finite element method system Abaqus Standard and computer algebra system Maple 2017.Let us consider a periodic particulate composite  j=1 … r ,35. The Next, the effective composite stiffness Energy contributions to this effective stiffness come from the hyper-elastic matrix and the interphase as well as from the elastic particles60). It was selected as the closest approximation of the matrix response coming from laboratory tests in this specific case study. A constitutive relation of the interphase The interphase and the matrix work according to the Arruda–Boyce hyper-elastic potential . This po60) occupy 5% of the RVE, 5% of the interphase, and the last 90% of this composite is filled with a matrix. The mesh of this composite (The representative volume element (RVE) of the composite used in the finite element method (FEM) computations has a single centrally located particle, which is surrounded by an interphase of constant thickness, and they are both inserted into the matrix; this composition is shown in omposite a is madeA source of randomness in this work is the statistical dispersion of the volume fraction of interface defects echnique . In thislable in .Computations of the effective properties of the composite are made in the following order: firstly, a set of computations is completed in the FEM system Abaqus according to the boundary conditions shown schematically in on (MCS)  with 50,on (MCS) ,40. CharFinal diagrams of the effective stiffness tensor  Cijeff iThe expected values and the coefficients of variation for all the components and probabilistic methods are exclusively positive, skewness is predominantly negative and kurtosis is positive for the MCS and SAM, while negative for the ISFEM. All the coefficients, despite the expected values, increase in magnitude together with an increase in input uncertainty The expected values of the effective stiffness tensor  tension a and bia tension b are dec tension c slightlThe coefficients of variation of the effective stiffness tensor Skewness of the effective stiffness Kurtosis of all the effective stiffness tensor components is presented in 60 spherical fullerenes surrounded by the interphase defects. It is conducted in a hyper-elastic regime of this material, where the constitutive relation of the matrix has been adopted after initial laboratory tests. This work reports a successful determination of the random nonlinear cubic effective stiffness tensor The resulting effective stiffness tensor is sensitive to uncertainty in the volume fraction of the interface defects and it cannot have a Gaussian distribution regardless of the strain intensity applied. It has more than twice the lower uncertainty level than the input one and, unlike for the linear elastic case, its probabilistic characteristics highly depend upon the strain imposed on the RVE; this dependence has no evident pattern for the respective components and different probabilistic characteristics but it is basically monotonic. An influence of statistical scattering of the interface defects on the expected values of the effective stiffness tensor components is relatively small (limited to A coincidence of the three probabilistic methods is relatively high for the expectations There is no doubt that experimentally-based homogenization of particulate composites with stochastic interface defects brings new interesting results, so that further SFEM computational studies will concern numerical simulation of hysteresis of such a composite in the probabilistic context.


Recently, the COVID-19 virus pandemic has led to many studies on the airborne transmission of expiratory droplets. While limited experiments and on-site measurements offer qualitative indication of potential virus spread rates and the level of transmission risk, the quantitative understanding and mechanistic insights also indispensably come from careful theoretical modeling and numerical simulation efforts around which a surge of research papers has emerged. However, due to the highly interdisciplinary nature of the topic, numerical simulations of the airborne spread of expiratory droplets face serious challenges. It is essential to examine the assumptions and simplifications made in the existing modeling and simulations, which will be reviewed carefully here to better advance the fidelity of numerical results when compared to the reality. So far, existing review papers have focused on discussing the simulation results without questioning or comparing the model assumptions. This review paper focuses instead on the details of the model simplifications used in the numerical methods and how to properly incorporate important processes associated with respiratory droplet transmission. Specifically, the critical issues reviewed here include modeling of the respiratory droplet evaporation, droplet size distribution, and time-dependent velocity profile of air exhaled from coughing and sneezing. According to the literature review, another problem in numerical simulations is that the virus decay rate and suspended viable viral dose are often not incorporated; therefore here, empirical relationships for the bioactivity of coronavirus are presented. It is hoped that this paper can assist researchers to significantly improve their model fidelity when simulating respiratory droplet transmission. I.As of August 2021, the COVID-19 virus pandemic has infected more than 216 484 958 people and caused more than 4 503 000 deaths worldwide.Sneezing, coughing, talking, and even the infected patient exhaling can spread the virus in the environment. These activities first generate virus-containing droplets of different sizes. These droplets are transported by their initial velocity at the mouth/nose release point and the environmental airflow, and they may settle to the ground or other surfaces by gravity. Depending on the environmental temperature and humidity, their sizes also change due to evaporation. In this review paper, the basic terminology and size ranges are given in Therefore, virus infection can either be transmitted by larger droplets upon direct contact over short  social distance or by smaller airborne droplets and droplet nuclei in the air over a much longer distance range (∼10 m or more).Another complexity for numerical modeling is the proper boundary conditions. The number of research that examined the dynamic flow characteristics and PSD of coughing and sneezing is considerable.μm, and different values have been reported regarding the maximum speed of coughing and sneezing.Finally, there are significant inconsistencies in the literature regarding the droplet sizes expelled during coughing, sneezing, breathing, and talking.Therefore, based on our understanding of the literature and our CFD knowledge and experience, main challenges in the numerical simulation of virus transport may be summarized in This review paper aims one to prepare a guideline for more accurately modeling of human expiratory activities such as breathing, coughing, speaking, and sneezing. The presentation of the details of the state-of-the-art literature can help formulate a more realistic simulation of disease transmission through indoor and outdoor environments. The application of more realistic boundary conditions is one of the essential steps in numerical simulations. In addition, careful evaporation rate modeling is a vital step in the numerical simulation of virus transmission by droplets.More than 300 articles were studied in preparing this review article with the keywords of numerical simulation of respiratory droplet dispersion, respiratory droplet size distribution, decay rate of the virus, and multi-component droplet evaporation modeling. These articles were categorized based on the title and abstract of the articles. A subset of about 100 articles was selected to address important issues related to the accuracy and modeling fidelity of the numerical simulation. This process led to the selection of three main issues indicated in et al.et al.et al.A few recent review papers relevant to virus airborne transmission, but with different focuses, should be noted. Some pervious review papers discussed the effect of air flow patternThe remainder of the current review paper is organized as follows. In Sec. II.As mentioned in Section et al.et al.μm and larger, while smaller droplets with diameter less than 60 μm may become airborne and lead to the potential for indirect transmission.Balachandar ., the wind speed) in the same direction and neglect any vertical motion of the background air or the effect of the boundary layer near the ground. Using the typical empirical nonlinear dragIn some studies, particle dispersion has been mathematically modeled in more details.Due to the nonlinear drag, the above two equations are coupled. To obtain approximate analytical solutions, we shall only include the nonlinear drag correction in the vertical direction so that the terminal velocity can be properly estimated. Namely, the particle Reynolds number is simplified asSince the droplet response time shown in μm is about 2 m and increases somewhat with the background airflow speed. Another interesting observation from the simple analysis is that the distance is very sensitive to the droplet size when Under all the above approximations, the equation of motion in the horizontal direction can now be written asrms denotes the root-mean-squared dispersion distance. To show the effect of a fluctuating velocity component on the distance traveled by the particle, the dispersion distance due to turbulent fluctuations alone is shown in Next, we consider the effect of turbulent dispersion on the horizontal transport of droplets. We first note that the Lagrangian integral timescale We may now combine the effects of mean air motion and fluctuating air motion, by adding the two contributions together as an estimate for the worst-case scenario to model the total horizontal displacement asFrom the above simple analysis, we conclude that the two most critical parameters affecting the distance traveled by a droplet are the mean air velocity and droplet diameter. Although the fluctuating velocity component can carry the small droplets, the effect of the mean air velocity on the droplet transport is more significant. It is cautioned that the assumption of uniform background mean airflow is often not appropriate for an enclosed space such as a hospital room, and in such a case, a 3D numerical simulation must be executed to model the dispersion process.III.Based on the discussions in Sec. et al.et al.Many experimental studies on the size of respiratory droplets of healthyIn addition to the measured PSD, parameterizing the size distribution with minimum error is essential. The lognormal distribution is one of the most popular descriptions used to parameterize the aerosol size distribution, in which the probability distribution of Although accurate determination of the size distribution of droplets released from the respiratory activity is a challenging task,μm, and some are even larger than 100 μm, whereas Lee et al.et al.μm, and the average diameter was 8.35 μm.The range of droplet's initial size varies significantly in the literature. For example, based on the results of Duguid,et al.Han μm. Morawska et al.3). The second mode was reported at 1.8 3). They mentioned that the additional particles in a diameter of 3.5–5 Papineni and Rosenthalet al.μm, respectively. Their results show that the mean diameter at a distance of 60 mm, compared to 10 mm, decreased modestly. It might be caused by evaporation of the particles or the less traveling time of small particles. Measurement of the exhaled jet shows that the initial velocity of coughing and speaking at a distance of 60 mm is 11.7 and 3.9 m/s, respectively. They have compared their results with the results of DuguidChao et al.μm. Due to the variety of sex, height, weight, and ages of the participants, they concluded that the effect of age, weight, height, and gender on the size distribution is not significant.Zayas μm. Duguidet al.et al.et al.et al.Xie In addition to the particle size range, the number of particles in each size is also important. In some references,et al.μm, 23% in droplet nuclei from 1 to 4 μm, and 35% in droplet nuclei > 4 μm.It should be noted that the diameter size of viruses has been studied in the literature. Lindsley In addition to accurately measuring the PSD of the respiratory activities, mathematical modeling of the PSD is also essential. It seems necessary to study the fitting capability of different distribution models to provide a PSD description for respiratory droplets. In most numerical studies, the Rosin–Rammler distributionIV.•mouth or nose opening area,•flow rate and duration of the respiratory event,•time-dependent velocity profile during the event, and•temperature profile during the event.Based on what discussed above, applying the correct initial and boundary conditions in a numerical simulation is very important. Boundary conditions and the initial condition far from reality lead to incorrect results. In simulating the droplets dispersion caused by the human respiratory activity, several important input parameters are needed and they include:While inhalation from both mouth and nose is aerodynamically the same, the flow patterns of the exhaled air from mouth and nose are entirely different;2 during normal breathing but exceeded 300 mm2 during coughing. These geometrical differences between different studies contributed partially to the discrepancies in the simulated transport of airborne aerosols. Here, we instead focus on the time characteristics of the exhaled jet velocity without attending to the shape of the opening area.In a numerical simulation, creating a geometric model is one essential step. If the details are considered in the geometric model, the problem will be simulated closer to reality. The geometric shape of the mouse and nose may be a cause for concern in simulating respiratory activity and attracted the researchers' attention. In their review paper, Ai and Melikovet al.et al.The created jet during breathing activities has features such as the flow direction, spread angle, and time-dependent velocity profile. Various values have been reported for the flow direction and spread angle.et al.The penetration length of the cough strongly depends on the type of the applied boundary conditions. Here, the penetration length is defined as the distance traveled by the jet when the air velocity drops below 0.01 m/s.In addition to the cough cloud characteristics, the particle size can affect the particle dispersion pattern. Compared to large droplets, smaller droplets are suspended by the buoyant cough cloud and transported over long distances.One of the important characteristics of the discharged jet by the respiratory activity is the jet's maximum velocity. Depending on the location of breathing or coughing (from the mouth or nose), the maximum velocity of the discharged jet varies. The maximum velocity of the exhaled jet through the mouth breathing was reported to be 2–3 m/s.To formulate the velocity profile of respiratory activities and make it possible to set it as a boundary condition in a numerical simulation, we reviewed some investigations in this area.et al.By using PIV and the indoor acrylic chamber, Kwon et al.et al.et al.,et al.,et al.Gupta As mentioned, for the initial velocity of the jets produced by respiratory activities, various mathematical models have been proposed based on experimental tests. Although the information presented in them, including the maximum speed and the time to reach the maximum velocity, are not well compatible with each other, all of them have shown that the velocity profile of coughing varies over time. Therefore, it is recommended that in future numerical simulations, the constant velocity model should not be applied as the boundary condition for coughing or sneezing.Finally, in V.In this section, the literature related to the numerical simulations of respiratory droplet dispersion is reviewed. Type of the respiratory activities, description of initial size distribution, evaporation rate modeling, composition of the sputum droplets, environment condition, and some overall details about the numerical methods are discussed. A summary of the recent numerical papers is presented in A.μm in diameter.The most fraction of the droplets released by coughing or sneezing is water. These droplets span over a wide size range and about half of the droplets evaporate within several seconds and become droplet nuclei.In addition to the effect of droplet diameter on the evaporation process, the composition of droplets released from human respiratory activity also affects the evaporation rate. Drops released from the respiratory activity are different from pure water droplets and contain components such as salt, protein, lipid, carbohydrates, and DNA. Vejerano and MarrThe droplet properties  significantly affect the droplet's evaporation rate. The presence of these components makes the simulation of the droplet evaporation process from human respiratory activities different from the simulation of pure water droplets and makes it more difficult to simulate. How is the evaporation rate of droplets released from human respiratory activity modeled in the literature? Has the literature paid attention to the thermophysical properties of real respiratory droplets? What relationship was often used to model the heat transfer rate for the droplets? These are the questions that will be addressed in this section.In recent decades, many experimental investigations have considered pure water droplets and human saliva droplets. Ranz and Marshall examined a distilled water droplet's evaporation rate at a low Reynolds number.Based on the experimental results,The coefficients were used in mass and heat transfer equations Each of the shells is treated as uniform concerning temperature and solute concentrations.(2)The number of shells does not vary during evaporation.(3)All shells have the same thickness proportional to the diameter of the droplet.(4)The outer shell evaporates.(5)There are mass transfer and heat transfer between the shells.(6)The net mass transfer through each shell is proportional to the mass loss due to evaporation, while the flux of each species is determined by diffusion.Parienta The transient mass and temperature diffusion rates are calculated byThe net mass flux of component i from shell x to shell x + 1 defined as follows:The diffusion flux The boundary conditions for the net flux are as follows:h, the Nusselt number is defined as In the modeling, the convective mass transfer coefficients for the mass flux inside the droplet were calculated by the Stokes–Einstein relation and assuming Nu = 2. [Based on Eq. 90et al.,They have used the following equations to model the heat transfer between layers and surface droplets:Based on our knowledge and the literature review, in the published numerical investigations, the effect of component concentration on the multi-component respiratory droplet evaporation has not been considered, whereas considering the impact of the composition of the real respiratory droplets can enhance the accuracy of numerical results. High-accuracy numerical results are necessary, because they can help policy setting and governmental actions in the next waves of COVID-19 or pandemic.et al.Redrow The relative humidity (RH) is calculated as follows:The rate of multi-component droplet temperature variation considering the effect of surface tension is as follows:Based on the above discussions, the droplets released from the human respiratory activity have different components that significantly affect the droplet evaporation rate. Therefore, to perform an accurate simulation, it is necessary to model the multi-component droplet. In addition to the evaporating rate of the real respiratory droplets, the virus dose and decay rate of the virus in the droplet is an important factor and should be considered, which is the topic of Sec. VI.In the previous numerical simulations, the droplet trajectories and the traveled distance were predicted without considering the bioactivity of virus-containing aerosols, which makes it difficult to assess the actual effect of virus transport by droplets and aerosols. Our aim of this section is to help provide a more direct indication of the actual virus transport due to droplets and aerosols, by considering the survival rate of the virus. This fills a gap in the current literature, where the numerical simulation of respiratory droplet dispersion does not translate into the risk assessment of virus transport by droplets/aerosols.In reality, not all of the aerosolized virus remains biologically active, which is a critical factor of viral transmission. The survival ability is virus resistance to physical and biological stresses imposed by the environment.The most critical aspects affecting virus survival are biological factors like the envelope layer and the virus type. The envelope layer is the outermost layer of many viruses that primarily affect a virus's persistence in the environment. Also, the presence of blood, feces, mucus, and saliva as the surrounding organic material tends one to insulate the virus against extreme environmental changes.The second factor that affects the decay rate of virus is the physical factors that include the ambient temperature, relative humidity, and sunlight.Information regarding the environment's influence on all virus decay rates and stability in an external condition is not complete and clear. Depending on the virus type, the effect of the relative humidity varies. Also, the effect of the relative humidity may be different at different temperatures.et al.Specifically, we mention the experimental results of Pyankov et al.As mentioned in Secs. A.While it remains difficult to provide a general mathematical model for the survival rates of different types of viruses in different environmental conditions, approximate models based on experimental observations would still be much desired. Given the current epidemic around the world, this section mentions some of the studies that examined coronaviruses' survival rate. Only when a survival model is incorporated, numerical simulation results can be connected to risk estimation of the spread of infection in the environment.et al.Abundant studies have examined how long the coronaviruses remain infectious in aerosols under the different environmental conditions in recent years. Recent studies show that in climate-controlled indoor environments, SARS-CoV-2 SARS (Severe Acute Respiratory Syndrome) - CoV (Corona Virus -2) is relatively stable in aerosols with a decay rate of less than 3% per minute.et al.2), virus inactivation took 4.7 min when the temperature and relative humidity were 40 °C and 20%, respectively; whereas 10.9 min was needed when the temperature decreased to 10 °C. Examination of the effect of simulated sunlight intensity has shown that as it increases, the decay rate of virus increases. They have presented a standard regression model for the three factors affecting the decay rate of virus. The complete regression models using relative humidity are presented in Eq. Dabisch Based on the equation, the simulated sunlight intensity has the greatest influence on the decay rate. Also, the coefficient of relative humidity is much lower than the coefficient of temperature. So, it can be concluded that, the intensity of simulated sunlight and temperature are more important than relative humidity. Based on their results, as the temperature rises, the decay rate of SARS-CoV-2 virus in aerosols has increased, a behavior that has already been reported for other coronaviruses such as 229E and MERS (Middle East Respiratory Syndrome )-CoV in aerosols.et al.et al.et al.Recently, a comprehensive investigation based on the Lagrangian framework has been conducted by de Oliveira et al.et al.De Oliveira In summary, the decay rate and inactivation time of a virus are a complex problem. They depended on many parameters . Incorporation of virus decay into numerical simulation of virus aerosol transport requires cross-disciplinary knowledge transfer between fluid mechanics and virology. Based on the discussion in the current section, there is an important open question: if the COVID-19 virus was non-enveloped virus, would the assumption and results change in the numerical investigation that were published recently? Unfortunately, the answer is no, in the majority studies, because respiratory droplets are considered as pure water in the conducted simulation and the factors that affected the virus decay rate have not been considered. Based on what was reviewed, we think coupling the presented models of decay rate and the suspended viable viral dose in a 3D CFD simulation can eventually allow us to develop a reliable quantitative simulation tool for aerosol virus infection.VII.This review addresses critical questions and challenges in the accurate numerical simulation of virus transmission due to human respiratory activities. Although lot of studies have been conducted to address these questions, we point out that many sources of uncertainties remain to be addressed, and how we might handle them.Specifically, realistic boundary conditions are essential to the accuracy of numerical simulation results. We have discussed some state-of-the-art studies, which provide the necessary information to properly set up the boundary conditions, including the drop size distribution, time-dependent jet inlet velocity profile, etc. Second, droplets from coughing or sneezing have unique composition, mucus and protein, making modeling of their evaporation dynamics particularly challenging. We have provided the state-of-the-art descriptions to help CFD modelers improve their evaporation modeling in the future. Finally, some recommendations are presented to allow researchers to incorporate the decay rate and viable viral dose contained in droplets and airborne virus aerosols, so that their numerical simulations can begin to be used to quantitatively assess the risk associated with the aerosol transmission route in various settings.•The duration of coughing and the time-dependent inlet velocity profile significantly affect the penetration depth of coughing.•More accurate experimental measurements of the coughing droplet size distribution are needed to resolve the reported inconsistencies in the literature and to properly set up future simulations.•The effect of the composition of real cough droplets on the evaporation rate should be considered in the modeling.•Two developed and improved models for evaporation rate considering surface tension and the effect of real drop composition are available.•Preliminary formulation of the virus decay rate and virus dose is also available to use in the future numerical simulations.By reading this review article, the reader would appreciate and begin to pay attention the following important aspects:Based on the information presented in this review, it is suggested that improved CFD simulations should be conducted to bring CFD results closer to the condition in reality and to better compare with the clinical observation results.


The Swedish risk management case of Baltic fatty fishes, in which dioxin levels may be too high, is a typical multidimensional food safety decision problem involving public health, economic, environmental and socio-cultural aspects. To effectively address the dioxin food safety problem, the multiple dimensions and conflicting interests of stakeholders have to be considered systematically when evaluating competing risk management options. The objectives of this study were to illustrate the applicability of the Multi-Criteria Decision Analysis (MCDA) method for multidimensional food safety risk management problems, and to evaluate the Swedish dioxin risk management using MCDA. The results show that the MCDA method is indeed a relevant tool for modelling the multifactorial Swedish dioxin problem and for initiating discussions amongst stakeholders to increase the acceptance of chosen strategies. Abolishing the derogation from the European Commission’s maximum limits for the presence of dioxins in Swedish fish is the dominant strategy for risk assessors, whereas the preferences provided by the other stakeholders would suggest a continuation of the derogation without providing consumer information. However, the preferences of female consumers match with the 2011 decision of the Swedish government to ask for a derogation in combination with consumer information. The conclusion drawn from our MCDA analysis is comparable to the government’s decision that—given the gradual reduction in dioxin concentrations in Baltic fish—the decision to continue providing consumer information or not mainly depends on how risk managers balance the preferences of the different stakeholders. Food safety has increasingly become a public concern due to the occurrence of various food safety incidents in recent decades ,2,3 and An illustrative example is the case of the RM of dioxins in Baltic fatty fish species in Sweden. Although wild-caught fatty fishes are  important sources of food in Sweden, the high dioxin concentration in these species has remained a public health concern. Dioxins and dioxin-like polychlorinated biphenyls (PCBs) are persistent environmental pollutants that are highly toxic and may cause cancer, reproductive and developmental problems, damage the immune system, and interfere with hormones . ThermalIn 2001, the European Commission (EC) set a maximum limit for the presence of dioxins in fish, with Commission Regulation No 2375/2001. The regulation was later replaced by Commission Regulation No 1881/2006, which set a maximum dioxins concentration limit of 8 pg/g for fish products . In SwedThe RA of the NFA  concludeThe decision to make the derogation permanent, in combination with consumer information, was described in a speech by the “State Secretary” (Ur N2016_05005), as a trade-off between the wish to maintain a sustainable fishing industry along the eastern coast and in the great lakes, and the public health risk. The expected consequences on fishing and local businesses, if the derogation would end, were considered to outweigh the public health risk. The decision of the government—which was against the RA recommendation—has been debated, specifically by scientists from the NFA . Although several other aspects  have also been considered in the final decision, the lack of a formal RM report makes the decision non-transparent and, therefore, it is difficult to justify on what bases the decision has been made. Food safety RM problems are multidimensional in nature, as shown by the dioxin case. Risk managers have to consider these multiple dimensions and the conflicting interests of stakeholders when evaluating RM options to address the dioxin problem. Multi-Criteria Decision Analysis (MCDA) is a powerful methodology for evaluating and ranking competing options on multiple, often conflicting, criteria . It is aThe objective of this study was to retrospectively evaluate the Swedish dioxin RM decision by applying MCDA. As a second objective, we illustrate the applicability of the MCDA method for multifactorial real-life food safety RM. The results of the MCDA procedure applied to the Swedish RM case of dioxin in Baltic fish confirm the multidimensional nature of the dioxin food safety RM problem, and the conflicting interests of stakeholders. The MCDA method is shown to be a suitable tool for balancing the multiple food safety dimensions, while considering stakeholders’ preferences in a transparent manner, by initiating discussions amongst stakeholders with conflicting interests.Several MCDA methods have been proposed for selecting the best compromising options in multidimensional decision problems . These m(1)Decision problem definition and stakeholder identification;(2)Identification of RM options;(3)Definition of criteria;(4)Construction of performance matrix; and(5)Producing the overall ranking.In this study the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) method was used . PROMETHThe above five steps were followed for evaluation of the Swedish historical food safety RM problem of dioxins in Baltic fatty fish.Fish is expected to be an integral part of a sustainable diet for ensuring food security in the face of climate change and the growing demand for animal food sources, since it is rich in protein, fatty acids, vitamins and minerals . It is aDespite the fact that the health benefits of consuming Baltic fatty fish outweigh the risks , the heaIn 2009, the Swedish government discussed making the derogation permanent or abolishing it, by considering the public health risk of consuming wild-caught fishes that exceed the ML and the socio-economic values of fishing in the region. Here, the problem is multidimensional, and several stakeholders with conflicting interests are involved. The selection of stakeholders is an essential step in MCDA. For the dioxin case, six stakeholder groups were identified: the Board of Agriculture, regional authorities, the NFA, fishermen, local businesses and consumers. Board of Agriculture: this board represents risk managers at the state level, who are responsible for making decisions on measures to manage food safety  and for making the final decision regarding the derogation by considering the different criteria, and the political implications of the competing RM options.Regional authorities: these are also risk managers, independent of the government, at regional level. In Sweden, regional authorities are responsible for the management of the great lakes  and are involved in activities for improving the ecosystem of the great lakes.NFA: risk assessors  are responsible for the scientific RA of the human health risk related to the intake of dioxins with consuming Baltic fatty fishes, especially for high-risk groups (children and childbearing women) and frequent consumers .Fishermen: this group represents the interests of professional, anglers and other recreational, and landowner fishers. Following the confiscation of the right to sport fishing in the Baltic Sea and the great lakes in 1993 by the government, sport fishing has been free for everyone (without compensation to landowners). Household fishing with nets is also free on a limited scale. In rivers such as Torne Älv, “landowner fishing” is practiced. Both continuing and abolishing the derogation, and their associated governance practices, have consequences for the businesses of fishers.Local businesses: this group represents businesses along the fish value chain . Restriction on fishing (following the EU ML) may reduce the supply of raw fish for processing and affect tourist fishing. It may affect the turnover of businesses and may result in the loss of jobs. Moreover, fish is part of traditional dishes, which are also served to tourists. The availability of local food is one of the important factors for attracting tourists and for increasing experiential loyalty . Smoked Consumers: RM decisions affect consumers’ health, product choice, product quality and price. Some consumers might be concerned with the high dioxin levels in Baltic fatty fishes. However, they might not be willing to substitute them with other fish products or imported fish because of tradition, sustainability or culinary reasons.In food safety, this PROMETHEE step refers to generating a list of potential RM options that can be applied to reduce the health risk related to consuming unsafe food, while also considering the socio-economic, cultural and ecological consequences of the proposed options. Broadly, there have been two approaches for managing the dioxin problem in the Baltic Sea region. The first approach aims at reducing the public health risks of dioxins and dioxin-like PCBs by setting an ML for the presence of these compounds in food and feed products . The second approach aims at controlling the release of dioxins and dioxin-like PCBs into the environment by setting stricter industry emission standards . We have defined the following three RM options for the Swedish dioxin case. Option A: No Derogation. This RM option refers to the abolishment of the derogation. Hence, Sweden follows the ML as set by the EC. Fishermen should subsequently sort Baltic herring by size, since large herrings (>17 cm) are not allowed for food anymore with this RM option. Moreover, authorities should recommend consumers to eat less Baltic fish in order not to exceed the TWI. As imported and farmed fish are the main sources of fish consumption in Sweden, Option A would likely further reduce the current limited use of Baltic fishes for food. Option B: Derogation in combination with consumer information. This option refers to a permanent derogation from the EC MLs in combination with consumer information . A proactive governance is required to raise the use of Baltic fish for food through providing consumers with sufficient information about the fish species, sustainability, health risks and benefits, and recipes [ recipes . Option Option C: Derogation. This option refers to a permanent derogation from the EC MLs, but without providing consumer information . Authorities do not recommend eating less or more Baltic fishes. Continuous monitoring of dioxin levels is not required. Both small and large herrings are allowed for direct human consumption within Sweden. Management measures that aim at reducing the release of pollutants into the environment and improve the ecosystem of the Baltic Sea influence the relative performance of RM options. Thus, the three RM options were evaluated under two management scenarios. The first scenario (2021 case) refers to a business-as-usual (BAU) scenario, representing the situation today, where the level of pollutants stays constant, given the current management practices. According to Goherr , the curThe definition of criteria, within the MCDA terminology, refers to the list of attributes that decision makers use for discriminating the various alternatives, as well as the scale of measurement for each criterion. Although the criteria defined highly depend on the problem and the values of decision makers, the list should be exhaustive, consistent, non-redundant, concise, complete and clear . FollowiPublic health risk and benefit. The high dioxin levels in Baltic fishes pose health risks to consumers, especially for high-risk groups such as children and childbearing women. For example, a 2007 risk assessment result showed that about 5% of 17–40 years old women exceeded the then tolerable intake of 2 pg/kg body weight/DAY [ight/DAY . Here itight/DAY . The heaOperation of businesses. Food safety RM decisions may affect the operations of businesses , for example, by imposing additional administrative, adjustment, compliance or transaction costs. The different RM options may affect the conduct and competitiveness of businesses. This criterion consists of the following indicators: administrative burdens on businesses; additional adjustment, compliance and transaction costs; cost or availability of essential inputs; creation of barriers for new suppliers and service providers; trade barriers; facilitation of anti-competitive behavior or the emergence of monopolies; market segmentation; global competitive position of EU firms; access to finance; investment cycle; stricter regulation of the conduct of a particular business; new or closing down of businesses; and products or businesses treated differently. For the Swedish dioxin case, the restriction on fishing in the Baltic Sea and the great lakes (Option A) may impact the businesses of fishermen and other local businesses along the fish value chain. Consumer acceptance. Food safety RM decisions affect consumers’ health, product choice, product quality and price. The success of any RM option depends on the perception of and its acceptance by consumers. This criterion consists of indicators such as prices; organoleptic characteristics ; consumer choice; consumer preferences; and the provision of affiliated public goods. In the Swedish dioxin case, consumers might be concerned with the high dioxin concentration in Baltic fatty fishes. However, they might not be willing to substitute these fishes  with imported fish or other products. Burden on public authorities. This refers to budgetary consequences and administrative burden on public authorities, associated with RM decisions. Different food safety RM decisions may result in different administrative burdens and may have different budgetary consequences for  public authorities. For the Swedish dioxin case, the level of authorities’ involvement varies among the three RM options, which has different implications for the budget and administrative burden on authorities. The provision of consumer information (Option B) may require extra budget and exert more administrative burden than the “derogation” (Option C).Employment. Food safety RM decisions may directly and/or indirectly facilitate the creation of new jobs or may result in a loss of jobs. This criterion captures impacts on job creation/loss of jobs and particular professions, groups of workers or self-employed persons. For the Swedish dioxin case, for example, the use of Baltic herring for food (Option B and C) would create new jobs along the fish value chain [ue chain . On the Environment/sustainability. Protein production, mainly from animal sources, is known for causing environmental impacts through the release of pollutants, and the use of scarce resources such as fossil fuel and arable land. The use of Baltic herring and salmon for direct human consumption is more environmentally sustainable than farmed and imported fish, and other climate-unfriendly food sources such as beef [ as beef . The use as beef . EmissioCulture. Food safety RM decisions may have an impact on the preservation of cultural heritage, cultural diversity, and citizens’ access to cultural resources and participation in cultural manifestations. Baltic herring and salmon have been an integral part of coastal culture and food traditions in the region [e region . The preU-shape preference function, the preference for option X over Y can be given by:X against option Y on criteria j; X and option Y on criteria j, respectively; and the parameter q refers to an indifference threshold. The indifference threshold q describes the point up to which a difference in performance between the two options does not make any difference to the decision maker. It indicates the minimum required difference between two options on a specific criterion in order for the better performing option to be regarded as being preferred over its alternative. In the present study, we assumed a “U-shape” preference function for all stakeholder groups, with an indifference threshold of zero. The matrix captures the performance of each RM option over each criterion, as well as the decision maker’s preference for how an alternative should perform in order for it to be preferred over its alternative, and the preference/criteria weights. In PROMETHEE, preference functions are used for conducting a pairwise comparison , and theExpert A), (ii) four experts from the Fishery Unit of the Board of Agriculture (Expert B), (iii) one expert from the Ecosystems and Environment Research Programme of the University of Helsinki (Expert C), and (iv) four experts from the County Administration Board  who have experience and expertise in the management and ecosystem of lake Vättern (Expert D). The (four) experts from the Board of Agriculture scored the RM options together as a group , referred to as Expert B. This also applies for the experts from the regional authorities, referred to as Expert D. For the criteria that were scored by more than one expert, the averages of the scores were used  high negative impact on culture/tradition and environment/sustainability, while Option C is not expected to cause any negative impact on these criteria. Although PROMETHEE allows the integration of both quantitative and qualitative data, this case study relied on only qualitative data for measuring the performance of the RM options over the eight criteria, due to a lack of quantitative data. During the finalization of this paper, Tuomisto et al.  publisheere used . For exaExpert A, Expert B (as a group) and Expert D (as a group), respectively. For Fishermen and Local Businesses, they were obtained, respectively, from a representative for a fishermen’s organization and a small business operating in Bothnian Bay. Each representative was requested to provide preference weights by dividing 100 points among the eight criteria. For consumers, the weights were obtained from Swedish fish consumers using an online survey. The consent form regarding the ethical aspects of the survey  was approved by the Social Sciences Ethics Committee of Wageningen University. The survey was advertised on Facebook with a paid post. Responses were obtained from a total of 307 respondents, of whom 185 were actual and potential wild-caught fatty fish consumers. The average of the weights elicited from these 185 consumers is used for the analysis. The preference weight of the consumers is disaggregated per consumer group: urban vs rural, and female vs male. The preference weights (criteria weights representing the relative importance of each criterion to the different stakeholder groups) are obtained from representatives of each stakeholder group using a questionnaire. For the NFA and the Board of Agriculture and Regional authorities, preference weights were elicited from X against option Y can be calculated as:X over option Y, X over option Y on criteria j. The final step in the MCDA process is ranking the RM options. Decision makers aim at minimizing risks and impacts, while benefits and positive scores are maximized . In the terion j  and Pj and the degree to which an RM option is outranked by other RM options (negative flows). Positive flow quantifies the degree to which an option is preferred over all other options  and is calculated as the sum of all pairwise comparisons in favor of an option (Equation (3)). Negative flow quantifies the degree to which all other options are preferred over the option of interest (Equation (4)) and is calculated as the sum of all pairwise comparisons, where the option under consideration is the less preferred of the other options. The net flow (Equation (5)) is used to provide an approximate measure of the overall preference. The higher the net flow, the more preferred the RM option is. The calculation of flows for RM option Visual Stability Interval of the PROMETHEE-GAIA software.The Visual PROMETHEE-GAIA software  was used to calculate the positive, negative and net flows of the six RM options. The sensitivity of the rankings of the RM options to changes in the (average) preference weights of the four main criteria are reported using the The results of the rankings of the RM options, based on the net flows, are presented in Under the BAU scenario, Option A (abolishing the derogation) is the best strategy, given the preference weights set by the NFA. This reflects that the NFA is very concerned with public health risk (80%), and the other criteria are not (or less) important in the evaluation of dioxin RM options for the NFA . Given tThe group  ranking is presented in The results of the sensitivity analyses are presented in The results of the MCDA procedure applied to the Swedish RM case of dioxin in Baltic fish confirm the multidimensional nature of the dioxin food safety RM problem and the conflicting interests of stakeholders. The MCDA method is shown to be a suitable tool for balancing the multiple food safety dimensions while considering stakeholders’ preferences in a transparent manner. Although the MCDA method is officially recognized by the FAO and WHO for food safety RM, to date, it has not been applied to real food safety RM procedures. It has only been applied in several hypothetical food safety RM cases ,19,20.Tuomisto et al.  conducteWe have used the average of the preference weights of the six stakeholder groups  when derSince all the stakeholder groups get the same weight and five of the six stakeholders prefer the continuity of the derogation , Option The similarity of the rankings of the RM options for all the stakeholder groups under the two scenarios . Second, some of the criteria were  scored by only one expert , which might involve some degree of bias/subjectivity. Third, some of the stakeholder groups were represented by only one expert  when eliciting the preference weights for the different criteria. However, it should be noted that it would not be relevant to ask for several answers from the NFA, as the ‘official’ answers may not be independent (as they work as a team). On the other hand, the number of small-scale business operators along the Baltic Sea coast is very low, and it may be very challenging to get respondents. For the fishermen, it might be relatively easy to get a response from a spokesperson, “interpreting” what s/he feels about the members’ thoughts. Hence, the use of a spokesperson’s response in the model may also introduce a bias. Despite these limitations related to the data used, the MCDA method is shown to be a relevant and transparent tool for modelling multifactorial food safety RM decision problems, while considering the interests of stakeholders.In this study, we showed how stakeholders could participate in the decision-making process, at the later stage of the process for stating their preferences . However, the results of the MCDA might differ if stakeholders are involved in all the phases of the decision-making process . Participatory approaches that are used to draw stakeholders into the process of deciding between different alternatives, but not in the formulation of those alternatives, might not achieve the intended target of the policy. Therefore, a meaningful participation requires stakeholders’ engagement in all the phases of the process . It woulWe illustrated the applicability of the MCDA method for balancing multiple dimensions in food safety RM decisions, while considering the conflicting interests of stakeholders, using the Swedish case of dioxins in Baltic fatty fish. The results show that the MCDA method is indeed a relevant and transparent tool for modelling the multifactorial dioxin problem and for initiating discussions amongst stakeholders with conflicting interests. The results also indicate that abolishing the derogation is the best RM option for the NFA, whereas the preferences provided by the other stakeholders would suggest making the derogation permanent without providing consumer information. The 2011 Swedish government’s decision to ask for a derogation with consumer information as an RM strategy agreed with the preferences of the most cautious and high-risk stakeholder group, the female consumers. Therefore, the conclusions drawn from this MCDA analysis are in line with the government’s decision that—given the gradual reduction in dioxin concentrations in Baltic fish—the decision to continue providing consumer information or not mainly depends on how risk managers balance the preferences of the different stakeholders.