Rain erosion damage, caused by repeated droplet impact on wind turbine blades, is a major cause for concern, even more so at offshore locations with larger blades and higher tip speeds. Due to the negative economic influence of blade erosion, all wind turbine Original Equipment Manufacturers (OEMs) are actively seeking solutions. In most cases, since the surface coating plays a decisive role in the blade manufacture and overall performance, it has been identified as an area where a solution may be obtained. In this research, two main coating technologies have been considered: In-mould coatings (Gel coating) applied during moulding on the entire blade surface and the post-mould coatings specifically developed for Leading Edge Protection (LEP). The coating adhesion and erosion is affected by the shock waves created by the collapsing water droplets on impact. The stress waves are reflected and transmitted to the laminate substrate, so microstructural discontinuities in coating layers and interfaces play a key role on its degradation and may accelerate erosion by delamination. Analytical and numerical models are commonly used to relate lifetime prediction and to identify suitable coating and composite substrate combinations based on their potential stress reduction on the interface. Nevertheless, in order to use them, it is necessary to measure the contact adhesion resistance of the multi-layered system interfaces. The rain erosion performance is assessed using an accelerated testing technique, whereby the test material is repeatedly impacted at high speed with water droplets in a Whirling Arm Rain Erosion Rig (WARER). The materials, specifically the coating–laminate interphase region and acoustic properties, are further characterised by several laboratory tests, including Differential Scanning Calorimetry (DSC), pull-off testing, peeling–adhesion testing and nanoindentation testing. This body of work includes a number of case studies. The first case study compares two of the main coating technologies used in industry ; the second case investigates the effects of the in-mould gel coating curing; and the third considers the inclusion of a primer layer on a LEP configuration system. Following these case studies, the LEP is found to be a far superior coating due to its appropriate mechanical and acoustic properties and the interface between the coating and the substrate is highlighted as a key aspect, as poor adhesion can lead to delamination and, ultimately, premature failure of the coating. The EU objective to cut greenhouse gas emissions by 80–95% by 2050 has severe implications for the energy sector . By 2050Leading edge erosion of wind turbine blades has seen an intense increase in both damage initiation and the rate at which the damage progresses see . This isIn this work, an investigation into the mechanical characterisation of the multi-layered composite system, focusing on the coating–laminate interphase, is being undertaken. Firstly, the overall coating materials and processing technologies approach employed in the blade manufacturing are introduced. Secondly, we provide an overview of the liquid impact phenomena allowing one to identify how adhesion and erosion are affected by the shock wave caused by the collapsing water droplet on impact. Mechanical testing and rain erosion durability testing of the coatings were undertaken through accelerated rain erosion testing of a range of samples with processing parameter variations. The results and conclusions are validated and endorsed to optimise manufacturing and coating processes for blades into knowledge-based guidelines for leading edge coating material development.The large and ever-growing scale of modern blades has resulted in the widespread implementation of fibre-reinforced thermosetting polymer composite technologies due to their high specific strength and stiffness properties and fatigue performance. Glass–fibre composites such as glass-reinforced plastics (GRP) and carbon-fibre-reinforced plastics (CFRP) are appropriate materials for use in such applications. Their use opened up great prospects in the design and manufacture of future wind turbine blades due to the versatility offered in the material optimisation and design. Nevertheless, composites perform poorly under transverse impact  and are sensitive to environmental factors such as heat, moisture, icing, salinity and/or UV. Blade manufacturers employ surface coatings to protect the composite structure from exposure to these factors ,14; see Composite wind turbine blades can be manufactured using numerous processing methods. The two most common approaches are through pre-preg application or liquid composite moulding techniques  ,16,17,18In-mould coatings use a similar material to the composite matrix substrate, i.e., epoxy/polyester. The in-mould coating plays a key role in the product performance of the whole blade part and is used in liquid composite moulding processes. The ease of integration into the blade manufacturing process makes it advantageous, as it simplifies and reduces the cost of applying the coating system. An appropriate in-mould gel coating needs to meet the blade processing window requirements. The finished product must be adequately bonded to the reinforcement, have an appropriate surface finish and provide long-term protection .A post-mould application, through painting or spraying, has different flexible materials to choose from, a polyurethane-based coating for example, see In wind turbine blades liquid moulding manufacturing, two common surface coating technologies can be employed :In-mouldIn all the above mentioned cases, optimal interface adhesion between the surface coating system and the composite substrate laminate is necessary for sufficient mechanical performance and to match both systems’ properties in an integral solution, as will be analysed in the next sections.Well-recognised rain erosion prediction models and case studies can be found in the literature in order to determine which coating factors affect erosion performance the most ,19,20,21The analysis of erosion damage caused by rain droplets is based essentially on the static concept of direct impact on a rigid surface, although evidence shows that the damage is in fact a dynamic event resulting in the propagation of shock waves—see C the elastic wave speed (the speed of sound of the medium). LZ, CZ, and SZ are the elastic impedances of the consecutive materials , coating (C), and substrate (S) layers). The post-impact shock wave also propagates through the multi-layer system materials and depends on the elastic and viscoelastic responses, the surface preparation, coating application and the interactions between layers. The understanding of these interactions through the mechanical modelling is limited but thought to be of key significance—see Moreover, this impact shock wave is also reflected wherever the acoustic impedance properties differ locally, so microstructural defects, such as voids, blisters and lack of adhesion, play a key role on the degradation of a particular coating. Hence, indirect damage by delamination may occur at the interface boundaries between material layers, caused by the propagation and interaction of the compressional waves from the impact of water droplets, as shown in LZ, CZ, and SZ denote the impedances of the liquid, coating and substrate, respectively. Their ability to reduce or increase the incident impact stress wave is quantified via Equations (1) and (2) and allows one to identify, as a first approach, the suitable material combinations.The capability of the coating to transfer wave energy in the multi-layered system can influence the erosion damage. Stress reflections oscillate repeatedly through the coating and substrate structure until dampened out by the materials’ properties, to reduce the energy of the initial shockwave . NumerouIn a rigid composite substrate typically used in wind turbine blades , there are two main coating technologies as introduced earlier: in-mould gel coatings and post-mould LEP coatings. The in-mould gel coatings, usually employed for the whole blade protection, are rigid, brittle and have a high modulus due to the epoxy or polyester polymer-based formulation. Owing to their high acoustic impedance, these gel coatings are able to moderate the transmitted stress to the substrate and to the coating surface. On the other hand, the post-mould coatings are usually developed for the Leading Edge Protection (LEP) where the rain droplet impact energy is greater, mainly due to the higher tip speeds. These LEP elastomer material coatings are formulated with low macroscopic elastic modulus, high ultimate strain and high resilience that will reduce the stress at the impact surface and dampen the stress waves, ensuring that the recovery time of the material is rapid and the energy is dissipated quickly (depending on the dynamic properties and the thickness). It is important to remark from The progression of erosion can be experimentally measured in a number of ways. One method is in terms of the average erosion depth versus time  or mass In order to predict the incubation time and the mass removal rate, the stress history in the coating and in the substrate has to be identified analytically or numerically. It is affected by the shockwave progression due to the vibro-acoustic properties of each layer, and by the frequency of the repeated water droplet impacts. Fatigue life of the material is calculated using an equivalent dynamic stress with a semi-empirical approach and depends on the ultimate tensile strength and other relevant properties of both the coating material and substrate. The model can be applied to estimate the stress at different locations through the thickness, i.e., the coating surface or at the coating–substrate interface. Nevertheless, it is assumed that the bond and adhesion of the boundary interface is ideally perfect, so the modelling does not account for the microstructural imperfections and lack of adhesion of such interfaces.The appropriate development of numerical modelling of rain droplet impact can also be used to compute the stress history in the material ,22—see FDue to the absence of suitable rain erosion testing standards within the wind sector, the industry looked to the aerospace sector . EvaluatThe objective of the current research is to assess the relationship between the coating–laminate interphase characterisation and the material’s resistance to erosion damage, through mass loss measurements.The rain erosion testing of this work was conducted in the University of Limerick’s whirling arm rain erosion facility  applied to two layers of biaxial epoxy–GF (1.4 mm thick). The circular coupons had a diameter of 27 mm. The two coating types were compared using the same substrate: first, an in-mould gel coating prototype , which has an epoxy-based formulation and second, a post-mould leading edge protection coating prototype , which has an elastomeric-based formulation. The testing results of the eroded samples are shown in No surface damage is assessed on the elastomeric coating samples during the testing period as was predicted based on its acoustic properties, see This type of erosion failure that yields coating delamination has premature and catastrophic consequences for the composite laminate and has to be assessed for both techniques. As a first approach, it is evident that the samples manufactured with a more rigid material performed worse in regard to erosion compared to those that had a low modulus of elasticity and high strain rate deformation capability.In this section, the in-mould curing conditions are investigated with a view to assessing how they affect erosion performance. It is very important to determine the effect of surface coating curing time on the dynamic behaviour of the resin when infusing a fabric ,34. In aTwo different curing conditions for the in-mould gel-coat EPOLIT GC are used in order to generate differences in the impregnation and flow advancement of the epoxy resin in the dry laminate preform during filling. The whole part is completely cured in both cases before demoulding. The substrate laminate is manufactured in both cases with two-layer biaxial glass fibre (1.4 mm thick) and the in-mould coating layer is defined as 0.3 mm, as in the previous case. Coat 1 and Coat 2 were previously characterised by performing a measure of the degree of conversion of the polymerisation reaction of the polymer matrix. The degree of conversion (α) is obtained by measuring the residual enthalpy ΔH (J/g) using Differential Scanning Calorimetry (DSC). Coat 1 is cured for 24 h at 25 °C, which is considered to be a full cure (89.7% cured), whereas Coat 2 is cured for 40 min at 45 °C, which is considered to be semi-cured (59.3% cured). The samples are quantified and outlined in The typical mechanical testing used in the wind turbine industry for material qualification is shown in order to assess the macroscopic behaviour of the laminates and how it is influenced by the coating curing conditions. In These results correlate well with the rain erosion tests, as shown in In In order to explore a local variation of the acoustic impedances due to the interface layer in both cases, nanoindentation testing is done. First, the bulk properties of both gel coats and composite GFRP matrix materials are obtained; see In subsequent testing, lines of indents are carried out across these interfaces through the thickness; see As can be observed in A very interesting result concerns the improved acoustic effect of the Coat 2 interphase, i.e., Semi-cured. The surface coating layer is defined by the EPOLIT GC gel coating bulk properties, which are the same for both Coat 1 and Coat 2, and were obtained far from the interface. In this case, the first subsequent substrate layer is considered to be defined by the Coat 2 interphase. It can be appreciated how the relative impedances from the Gel Coat–Coat 2 interphase layers generate and attenuate the reflected and transmitted waves from the coating to the first substrate layer and even larger from this one to the GFRP laminate. That result correlates well with the delayed incubation time obtained from the erosion testing and observed in The key points to take from this case study are that the adhesion of the coating to the substrate is of paramount importance for the rain erosion resistance of the material. The coating, which was only partially cured before the fibre reinforcement was inserted, out-performed the coating, which was fully cured, in all aspects of the test.In this section, a post-mould coating system configuration that includes a filler layer between the surface coating and the composite laminate is assessed. The performance of this configuration was compared to a comparable system that includes an additional primer layer to improve the contact adhesion of the coating to the substrate, as depicted in The two configurations make use of a similar prototype LEP material  with the substrate defined by an intermediate filler layer prototype . The substrate (from the EPOPUR MS range), and the composite laminate, in both cases, is a two-layer biaxial Glass Fibre laminate (1.4 mm. thick). The primer layer included in one of the configurations is based on a prototype material . This configuration is not optimised in terms of everlasting lifetime, so erosion rate is not an issue in this case. The objective is defined for experimental rapid testing purposes and delamination failure analysis.In These testing results correlate with the rain erosion tests, as shown in Complementary nanoindentation tests are carried out on the primer application configuration for more precise local interface discontinuities characterisation. The nanoindentation settings are as outlined in In addition, two lines of shallow (500 nm) indents across the interfaces of the three materials are implemented. Each line contained 40 indents, which were equally spaced by 5 μm, a total line distance of 200 μm. The resulting indentation moduli are shown in While a distinct change in modulus is apparent for the LEP–primer interface, the slightly lower modulus of the thin primer layer (compared with the filler) can be seen for the primer–filler interface. This result reveals a similar acoustic impedance on the primer–filler interface and also shows how the primer matches the filler acoustic impedance without pronounced discontinuities.In The key result is that the inclusion of a primer layer, in this case, does not negatively influence the rain erosion performance of the coating systems. The adhesion of the coating to the substrate has been significantly improved, which, in turn, reduces the opportunities for delamination to initiate, offering a more reliable solution. Further optimisation of the primer material could improve the rain erosion performance of the entire system.The development of new coating systems, with an aim to diminish the rain erosion damage in wind turbine blades, requires knowledge-based tools for erosion lifetime prediction and to identify suitable coating and composite substrate combinations. This research has been directed into the coating–laminate interphase adhesion characterisation in order to effectively predict rain erosion performance. The experimental work involved accelerated rain erosion testing, pull-off testing, peeling–adhesion testing and nanoindentation testing of individual coating configuration cases. The rain erosion testing results correlated well with the mechanical adhesion characterisation in all cases. In a first case, a low-modulus elastomeric material used for leading edge protection showed better response than a rigid gel coating. Their related impedances with a GFRP composite laminate were determined with a simplified approach. A second configuration case showed that samples manufactured with a higher degree of curing (as determined using DSC), were out-performed by those that had a lower degree of curing due to a more rigid and broad coating–laminate interphase during the in-mould curing. Another set of experiments, based on the typical LEP configuration, focussed on the effects of including a primer layer with a filler material within a multi-layer system. It was determined that the inclusion of a primer layer drastically improves the adhesion performance between the coating and the filler substrate and consequently avoids the erosion failure by delamination. Moreover, the incubation time of the erosion damage was not appreciably affected by the inclusion of the primer layer.In this work, referenced simplified models were used to correlate the droplet impact shockwave stress history on the coating with the relative impedance values between materials. A more precise and complete analysis which has not been implemented in this investigation, requires the use of appropriate numerical models that account for stress–strain behaviour and the accurate acoustic propagation of shock wave in the multi-layered composite. Furthermore, in order to create complete analytical or numerical models of rain droplet impact and corresponding physical rain erosion testing, it is necessary to characterise the failure resistance of the system interfaces, so that is what this work has been focussed on.In future research, it is necessary to implement ultrasonic testing to accurately measure the impedance of materials and take into account improved models for the stress–strain behaviour in order to cover for the viscoelastic properties of the LEP systems. Nanoindentation can be a very convenient testing method to characterise such a behaviour on the interface and surface boundaries at the microscopic scale. Moreover, it can allow one to create more accurate numerical models in the future. Cohesive Zone Modelling (CZM) between layers is planned to be incorporated into the numerical modelling of the droplet impact. The input parameters for the interface CZM can be defined by means of the adhesion characterisation methodology employed in this work.


Here, we employed a temporal reproduction task with a single motor response at a point in time with and without auditory feedback. This task limits participants to reducing errors by employing auditory feedback in a post hoc manner. Additionally, the participants were asked to judge the self-produced timing in this task. The results showed that, in the presence of auditory feedback, the participants exhibited smaller variability and bias in terms of temporal reproduction and the perception of self-produced time intervals in the subsecond range but not in the suprasecond range. Furthermore, in the presence of auditory feedback, the positive serial dependency of temporal reproduction, which is the tendency of reproduced intervals to be similar to those in adjacent trials, was reduced in the subsecond range but not in the suprasecond range. These results suggest that auditory feedback assists the post hoc error correction of temporal reproduction, and the perception of self-produced time intervals in the subsecond range.We examined whether auditory feedback assists the  Timing is essential during various activities, such as performing music and playing sports. In the timing literature, bias and variance in timing tasks have been utilized to construct models of temporal behavior . Therefore, unlike the temporal reproduction task used by post hoc error correction. If auditory feedback has a role in post hoc correction, the bias and/or variability in our temporal reproduction task would be reduced by the presence of auditory feedback.The remaining questions as regards the role of auditory feedback in temporal reproduction are whether immediate auditory feedback assists post hoc error correction.We also analyzed the lag-1 autocorrelation in the temporal reproduction task. This autocorrelation is the correlation between the produced intervals of trials and those of the next trials. A negative value means that the next produced interval of a larger  produced interval tends to be smaller (larger), suggesting overcorrection of error. Conversely, a positive value means that produced intervals tend to be similar in value to those in adjacent trials, suggesting memorized error and/or small correction. Therefore, this measure provides evidence as to whether or not auditory feedback affects the relationship between adjacent trials. In studies of repetitive tapping, it has been stated that auditory feedback negatively affects the lag-1 autocorrelation of produced intervals . Unlike Moreover, we examined whether the effect of auditory feedback is dependent on target duration in the subsecond and suprasecond ranges. Based on psychophysical, pharmacological, neuroimaging investigations it has been proposed that there are distinct timing mechanisms between these ranges e.g., . One claAdditionally, we measured the variability and bias of the perception of self-produced time intervals in a temporal reproduction task. Although the perception of self-produced time intervals will always accompany temporal reproduction, its properties have only been recently and as yet sparsely explored. Sixteen individuals  participated in the experiment. All participants had normal hearing. They gave written informed consent and were paid for their participation. This study was conducted in accordance with the Declaration of Helsinki and was approved by the Ethics and Safety Committees of NTT Communication Science Laboratories . The data for 2 of the 16 participants were excluded because of their reversed psychometric function . The data obtained from the remaining 14 participants  were analyzed in terms of perception performance.The experiment was conducted in a sound-insulated booth. Stimulus presentation and data acquisition were performed by a computer  using MATLAB 8.1 (The MathWorks) and Psychophysics Toolbox Version 3 . The stiFigure 1) × 2 . Participants were asked to listen to three successive tones  with two base intervals, and then immediately press a button (shift key) to create a subjectively isochronous interval between the button-press and the last tone of the three previously presented tones. In the auditory-feedback condition, a feedback tone was presented immediately when the participant pressed the button, whereas in the no-auditory-feedback condition, the feedback tone was not presented. The property of feedback tones was identical with the three successive tones. The participants were also asked to judge whether the produced timing was earlier or later than the subjectively isochronous timing. The judgment was indicated by pressing one of the two buttons . Except for the first trial of each session, each trial started 1 s after the judgment. The first trial of each session was initiated by the experimenter. The beginning of a trial was indicated by a tone . After a 6-s silent period from the beginning of a trial, the three successive tones that indicate the base interval were presented.The experiment was conducted under four conditions: 2  per condition were analyzed. All the sessions for a given condition were completed, and then the feedback condition was alternated. The base interval condition was alternated after the completion of all the sessions for the two feedback conditions of a base interval condition. The order of the feedback and base interval conditions were counterbalanced across the participants.First, we excluded the outliers of the produced intervals for each condition and participant. We defined the outliers as below two inter-quartile ranges (IQRs) from the first quartile or above two IQRs from the third quartile.To evaluate the reproduction performance, we calculated the SD, mean, and lag-1 autocorrelation of the produced intervals for each condition and participant. The autocorrelation was computed in each session, and then averaged across all sessions.To evaluate perception performance, we estimated the probability function of ‘later’ responses to a produced interval  in each condition and participant. To estimate the psychometric function, we used a logistic regression undertaken with the maximal likelihood method for the data of pair of judgment and produced interval. The produced interval at a 50% judgment rate was defined as a point of subjective equality (PSE), which indicates the criterion of judgments. Half of the difference between the produced intervals at judgment rates of 25 and 75% was defined as a just noticeable difference (JND), which indicates the variability of judgments. Two participants were excluded from the analysis because their psychometric functions were reversed in at least one condition.Figure 2A shows the standard deviations of produced intervals divided by their base interval. The results imply that motor variability for a 0.5-s base interval was less variable in the auditory-feedback condition than in the no-auditory-feedback condition , whereas that for the 3.2-s base interval was comparable in the feedback conditions . A two-way  repeated-measures ANOVA indicated a marginally significant main effect of the base interval . This result implies that temporal reproduction in a trial is performed with a produced interval memorized in the previous trial.We investigated whether auditory feedback affects the performance of temporal reproduction with a single motor response at a point in time, and the perception of self-produced time intervals in the subsecond and suprasecond ranges. The results indicated that auditory feedback improves both temporal reproduction and the perception of self-produced time intervals in the subsecond range but not in the suprasecond range. The results also indicated that auditory feedback reduces the serial dependency  of temporal reproduction in the subsecond range but not in the suprasecond range. Furthermore, we found that the serial dependency was significantly positive in all conditions except under the auditory-feedback and 0.5-s base interval conditions. In addition, the substantial deterioration in the perception of self-produced timing caused in absence of auditory feedback was limited to the subsecond range. This result clearly indicates the invalidity of the sensory attenuation explanation for the deteriorated perception of self-produced timing in the suprasecond range.The reduced variability and bias of temporal reproduction and the perception of self-produced time intervals by auditory feedback are consistent with previous studies indicating that the perception of intermodal intervals is less stable than that of intramodal intervals (for review see This improvement caused by auditory feedback in the subsecond range must be involved in the stabilization of the internal representation of self-produced time intervals by auditory feedback. There are several possible reasons for this stabilization. One possibility is the additional noise originating from the translation of a modal representation into an amodal representation to calculate the intermodal interval, when auditory feedback is not provided. This consideration is based on the notion that modality-specific and amodal mechanisms underlie the processing of subsecond timing. Another possibility is multisensory integration, which can be considered another aspect of amodal mechanisms. It has been suggested that human beings combine information from multisensory modalities to reduce the variability of estimates based on the reliabilities of each multisensory modality in time perception (for review see The comparable variability of temporal reproduction and the perception of self-produced time intervals in the feedback conditions in the suprasecond range does not necessarily mean that auditory feedback has no effect in the suprasecond range. It can be considered that there are duration-dependent and duration-independent noises for motor and perceptual timing . If the To reduce the variability and bias of temporal reproduction, the representation of self-produced time intervals must be stabilized and the temporal reproduction must be performed using the stabilized representation. The reduced lag-1 autocorrelation with auditory feedback in the subsecond range supports this idea. When participants know that a produced interval in a trial is overproduced, they will try to make the next produced interval shorter than the previous one. Therefore, error correction must lead to the reduction of the lag-1 autocorrelation of produced intervals.In addition, the positive lag-1 autocorrelation of produced intervals was found in all conditions except the auditory-feedback and subsecond conditions. This result implies that the self-produced time interval information is used not only when auditory feedback is available but also when it is not available. This idea is plausible because computing for temporal reproduction with the memory of previous intervals will lead to a greater reduction in variability and more computational loss than that without this memory. Consistent with this idea, post hoc error correction in temporal reproduction, and reduces the variability and bias of temporal reproduction and the perception of self-produced time intervals in the subsecond range. Our findings provide an insight how sensory feedback contributes to reducing the errors of motor and perceptual timing. We consider that they will contribute to the precise modeling of temporal processing.We examined the role of auditory feedback in temporal reproduction, and in the perception of self-produced intervals. The current study demonstrated that auditory feedback assists KM and MK conceived and designed the study. KM performed testing, data collection and data analysis. KM drafted the paper. MK provided critical revisions. KM and MK approved the final version of the paper for submission.MK is an employee of Communication Science Laboratories, which is a basic-science research section of Nippon Telegraph and Telephone Corporation. The other author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The malaria-infected red blood cells experience a significant decrease in cell deformability and increase in cell membrane adhesion. Blood hemodynamics in microvessels is significantly affected by the alteration of the mechanical property as well as the aggregation of parasitized red blood cells. In this study, we aim to numerically study the connection between cell-level mechanobiological properties of human red blood cells and related malaria disease state by investigating the transport of multiple red blood cell aggregates passing through microchannels with symmetric stenosis. Effects of stenosis magnitude, aggregation strength, and cell deformability on cell rheology and flow characteristics were studied by a two-dimensional model using the fictitious domain-immersed boundary method. The results indicated that the motion and dissociation of red blood cell aggregates were influenced by these factors and the flow resistance increases with the increase of aggregating strength and cell stiffness. Further, the roughness of the velocity profile was enhanced by cell aggregation, which considerably affected the blood flow characteristics. The study may assist us in understanding cellular-level mechanisms in disease development. Plasmodium falciparum , a protozoan parasite transmitted by mosquitos. When the RBCs are parasitized by P-falciparum, two critical effects have been observed in the infected cells, namely, the reduced deformability of the cell and increased adhesion of the RBCs to vessel endothelium and other blood cells [Malaria infects 350–500 million people and kills more than two millions every year, mostly in Africa and other underdeveloped countries. In most of the malaria cases, red blood cells (RBCs) are parasitized byod cells . Thus, tod cells ) and tenUnder healthy physiological conditions, red blood cells move individually with blood plasma or form temporal aggregates and they can undergo severe, reversible, large elastic deformation in blood flow. Although the formation of red blood cell aggregates could be due to other factors such as the decrease of the shear rate, increase of the hematocrit, and variation of the viscosity of the suspending plasma in the blood vessel, the malaria-infected RBCs tend to form firm and irreversible aggregates. Severe aggregation of RBCs may decrease the surface area of cells contacting with the blood plasma. It also causes pressure and shear stress change in the region of the aggregation. These aggregates get stuck in the small blood vessels, blocking individual RBC from passing, thus decreasing the amount of oxygen and the nutrition transferred in human body.Experimental measurements have been done on dynamic or rheological properties and behaviors of parasitized RBCs –10. In tHowever, very few investigations on malaria-infected RBCs have been conducted in stenotic vessels and their impact on hemodynamics in stenotic vessels is not well understood. In particular, there is a lack of studies considering cell-to-cell interactions at microscopic scale. This paper aims to provide a qualitative analysis on the dynamics of malaria-infected RBCs in stenotic microvessels. Since the malaria-infected RBC gradually loses its deformability and develops adhesiveness through the three stages of infection ring, trophozoite , and schizont, this study considers the ring and trophozoite stages in which the cells become stiffer and more adhesive while the shape of the RBCs is not significantly modified. The RBC was simulated by a spring model and the hardening of the parasitized cell was mimicked by varying the membrane constants. The malaria-infected RBCs were assumed existing as aggregates with firm or loose adhesion. By using fictitious domain-immersed boundary formalism in two dimensions, we simulated the transit of RBC aggregates through a prototypical channel with a contraction. By studying the motion and dissociation of RBC aggregates and flow characteristics, we delineated the contribution to hemodynamics from each of the three factors, hardening of the membrane, aggregation strength, and stenosis magnitude.We considered a two-dimensional microvessel with a symmetric stenosis and employed numerical simulations to study the rheological behavior of RBC aggregates in the blood flow. In this study, blood was assumed to be a suspension of RBCs in an incompressible, Newtonian fluid with constant density and viscosity. In order to simulate the blood flow and fluid-cell interactions in this irregular-shaped domain, the fictitious domain method was combined with the immersed boundary method and the RBCs have been modeled by the spring model.s∗ = 0.481.Two types of RBC model are widely used currently, namely, elastic membrane models , 23 and P-falciparum. However, the stickiness of the cell surface and the mechanism of the aggregation still remain disputable. Two different theoretical models, namely, the bridging model [F = −∂E/∂r with the Morse-type potential E asDe is the energy constant corresponding to the density of the aggregating particles; β is the scaling factor which relates to the thickness of the depletion layer or interactive distance; r0 is the reference distance or zero-force distance.The hardening of the RBCs is due to the parasite of the ng model , 31 and ng model , coexistng model  in whichF/De) as a function of separation distance for different parameters is shown in De or by decreasing β. On the other hand, decreasing in β and increasing in r0 may raise the depletion thickness and the equilibrium distance of the RBCs in aggregates.The scaling aggregation force  and p are the fluid velocity and pressure anywhere in the flow; ρ is the fluid density; μ is the fluid viscosity. The boundary conditions were such that, on ∂Ωf, a no-slip condition was applied and, at the inlet and outlet of the channel, a periodic flow condition was enforced. A detailed description of the solution method of (The flow region we studied was a stenotic microchannel for which the regular structured mesh was not applicable at the boundary of the region. Thus, we adopted the fictitious domain method because in this method the irregular-shaped domain is extended to regular shape so that simple structured mesh instead of unstructured mesh can be used, which substantially reduces computational complexity of the algorithm. The fictitious domain method and its applications to fluid flow problems have been extensively described , 34. To quations:ρ∂u∂t+u·∇We studied the hydrodynamic behavior of multiple red blood cell aggregates in a horizontal channel filled with Newtonian fluid with a symmetric stenosis at the central part of the vessel. The blood plasma density and plasma viscosity were presumed fixed values. We performed a series of simulations to study RBC deformation, flow field, and cell-cell interactions as the aggregates traversed the stenotic vessel. The fluid flow was generated from left to right by a constant pressure drop. A stream of flow approaching the stenosis contracted to a high speed flow at the throat of the stenosis. Afterwards, the flow was allowed to develop fully along the straight rectangular channel. At the meantime, prelocated multiple RBC aggregates flowed with the fluid in the channel. The parameters used are given in Aggregates of four cells used in the simulations were formed in static plasma before putting them in the flow channels. The red blood cells were placed face-to-face in static plasma initially. The center-to-center distance was close enough in order for the aggregation force to take effect. When the simulation starts, red blood cells approached each other and reached an equilibrium configuration. The red blood cells were modeled by two membrane constants for two different stiffness and three aggregation strengths for different adhesiveness. Therefore, six different configurations were obtained and they are shown in μm long, 30 μm wide two-dimensional channel with symmetric stenosis formed at the central location. The geometry of the fluid domain and the initial placement of the RBC aggregates are illustrated in The microvessel in this study is a 140 The motion and dissociation of 6 RBC aggregates in a 40% stenosis microvessel have been simulated. The results for two membrane bending constants and three aggregating strengths are shown in Figures Figures Simulation also has been done in the microchannel with 60% stenosis and the results are shown in Figures In general, for all three stenosis levels, healthy RBCs and aggregates with ring stage or early trophozoite-stage infection (configurations in Figures In Figures Next we investigated the effect of aggregation force on the velocity profile at the throat of stenosis . It is nThe cell membrane deformability also had an effect on the velocity of blood flow at the stenosis and the results are revealed in Figures The main objective of this work is to probe how changes in the cell membrane rigidity, the aggregating strength, and the magnitude of the stenosis affect the transit of the malaria-infected RBC aggregates through stenotic microchannels. Two types of RBCs, namely, soft and rigid, have been studied under three different levels of aggregating strength. The simulations were performed over a range of stenosis magnitudes: 40%, 50%, and 60%.It has been found in this study that soft RBCs with strong aggregating force formed the most compact aggregates. In the aggregates, the RBCs experienced large deformation. Rigid ones with weak aggregating force formed the loosest aggregates. In these aggregates, the RBCs maintained their normal biconcave shape. In blood flow, the aggregates of weak aggregating strength were more likely to dissociate to individual cells, while the aggregates with strong aggregating strength would form even larger aggregates or rouleaux. The rigidity of the cell membrane hindered passage of the cell through microchannels and this result is qualitatively in agreement with experimental findings on the rheological behaviors of malaria-infected RBCs through a narrow constriction in a microchannel. The flow velocity at the throat of the stenosis decreased with increasing membrane modulus and more deviation from the parabolic profile was observed, especially for the narrower stenosis and stronger aggregating force.The present study used a two-dimensional model to qualitatively simulate malaria-infected RBCs in stenotic microvessels. It is important to extend this algorithm to the physiologically relevant hematocrit contents in three-dimensional situation and compare the results with experimental observations quantitatively. It is also quite interesting to adapt the model for the more thorough investigation of RBC rheology at various stages of malaria infection as well as its impact on leukocyte migration. In addition, it provides a potential approach to investigate drug delivery at cellular level in microvessels involving infected RBCs.


Numerous data demonstrate that distracting emotional stimuli cause behavioral slowing  and that behavior dynamically adapts to such distractors. However, the cognitive and neural mechanisms that mediate these behavioral findings are poorly understood. Several theoretical models have been developed that attempt to explain these phenomena, but these models have not been directly tested on human behavior nor compared. A potential tool to overcome this limitation is Hidden Markov Modeling (HMM), which is a computational approach to modeling indirectly observed systems. Here, we administered an emotional Stroop task to a sample of healthy adolescent girls (N = 24) during fMRI and used HMM to implement theoretical behavioral models. We then compared the model fits and tested for neural representations of the hidden states of the most supported model. We found that a modified variant of the model posited by Mathews et al. (1998) was most concordant with observed behavior and that brain activity was related to the model-based hidden states. Particularly, while the valences of the stimuli themselves were encoded primarily in the ventral visual cortex, the model-based detection of threatening targets was associated with increased activity in the bilateral anterior insula, while task effort (i.e. adaptation) was associated with reduction in the activity of these areas. These findings suggest that emotional target detection and adaptation are accomplished partly through increases and decreases, respectively, in the perceived immediate relevance of threatening cues and also demonstrate the efficacy of using HMM to apply theoretical models to human behavior. Emotions are an important mechanism facilitating behavioral responses to salient and goal-related environmental cues , and theGross changes in emotion regulation strategy and aptitude take place over the course of development . This isEmotional conflict processing tasks have drawn heavily from earlier studies of attentional control over nonemotional or “cognitive” distractors, which reliably demonstrated that naming ink color is slowed in the presence of a conflicting and task-incongruent color name , 18. In emotional distractors (hereafter referred to as the “Mathews model”)  . Not dirOne shortcoming of both of these models is their inability to explain well-established dynamic changes in behavior that occur from trial to trial: namely, conflict adaptation or the “Gratton effect” , 25, andNeuroimaging has also proven to be a valuable tool in characterizing cognitive and emotional processes. Studies of the neural correlates of cognitive conflict processing have found that the dorsal anterior cingulate cortex (dACC) detects stimulus conflict and triggers the recruitment of the dorsolateral prefrontal cortex (dlPFC), which then enables cognitive control through the amplification of the neural response to the task-relevant feature , 31–33. With respect to implicit emotion regulation, overlapping yet distinct neural systems are involved. The dACC is also responsive to emotional conflict, but adaptation occurs through inhibition of the amygdala by the pregenual ACC/ventromedial PFC (pgACC) , 5. In aDespite the insight into cognitive and emotional processes that these models have allowed and their success in reproducing human behavior, the models have only been indirectly tested on actual human data. That is, simulations have been done to test the ability of the models to recreate human behavior, but the models have not been directly fit to human data to test the degree to which the models explain observed human data. Similarly, neuroimaging studies have demonstrated that particular nodes  are implicated in cognitive processes specified in the models , but these studies only indirectly test the models through use of static contrast analyses instead of actually testing the neural correlates of the latent constructs specified in the models and derived through fitting the model to observed behavioral data. Thus, our theoretical models of how emotional conflict is detected and resolved have only been weakly tested in regards to both behavioral and neuroimaging data.One potential approach to directly testing these theoretical models and identifying the cognitive and neural mechanisms mediating emotional conflict detection and resolution comes from the field of computational modeling. Computational models have been shown to explain reinforcement learning behavior  and an aHere, as part of a larger study of the effects of assault victimization on development and psychopathology, we recruited a cohort of healthy control adolescent girls and administered a variant of the emotional Stroop task. We then use Hidden Markov Modeling to test the fit of the above models of cognitive and emotional control to behavior on the task. The models are then compared in their fits to the data and the best fitting model is used in an exploratory analysis of the neural correlates of the model. We hypothesize that the model-based subprocesses of emotional conflict processing will be associated with similar neural mechanisms as the contrast-based measures of neural activity . However, using this modeling-based approach to delineate the subprocesses of emotional conflict processing allows a greater degree of functional separation in the involvement of the implicated brain regions. While the posited models differ in their description of the behavioral phenomena, we hypothesize that activity of the dACC and anterior insula will be related to stimulus processing while activity in the dlPFC and pgACC will be associated with attentional control.The study was conducted in accordance with the Declaration of Helsinki and approved by the University of Arkansas for Medical Sciences Institutional Review Board. As part of larger study of the effect of trauma exposure on emotion regulation, 32 non-traumatized adolescent girls, 12–16 years of age, were recruited from the local area via newspaper advertisements and flyers. After the nature of the study had been fully explained to the participant and the participant’s parent or legal guardian and they both agreed to participation, written informed consent was obtained from the parent/legal guardian and written assent was obtained from the participant.In addition to screening for trauma exposure with the trauma assessment portion of the National Survey of Adolescents , 14, parOf the 32 non-traumatized adolescents assessed 2 had current diagnoses mental illnesses, 5 had excessive head-motion during the fMRI scan, and 1 was scanned with incorrect imaging parameters. All remaining subjects performed the task adequately (>75% accuracy). Therefore, all subsequent analyses were conducted on a final sample of 24 healthy adolescent girls.Participants underwent fMRI while being administered a variant of the emotional Stroop task. In this task participants were simultaneously presented with two images, one superimposed upon the other. The background image depicted a nature scene, either threat-related (e.g. snake or spider) or neutral (e.g. foliage or rocks), while the superimposed foreground image was of a person’s face making either a threat-related or neutral expression. The valences of the two images were factorially manipulated  and uncorrelated. The participants were instructed either to attend to the scene or to the face and make a button press to indicate whether that stimulus (the ‘target’ stimulus) was threat-related or neutral. Responses were made using the first two buttons of the Current Designs 4 Button Curved (HHSC-1x4-CR). Neurobehavioral Systems Presentation software was used for stimulus presentation and timing recording.The task was administered using a mixed block- event-related design in which each run was comprised of two blocks, one block in which the participant was instructed to attend to the face and the other to the scene. Within the blocks an event-related design was used with a jittered interstimulus interval of 3–7 seconds. The sequence of trial types  was psuedo-randomized and identical across participants. In order to reduce contributions of lower-level priming effects, stimulus features were not repeated on successive trials. Three runs of 64 trials each  were administered with each run lasting approximately 8 minutes.In order to test the validity of our task as a probe of implicit emotion regulation we performed standard contrast-based analyses of task performance. Each subject’s reaction time bias was calculated by taking the difference between the median reaction times of the task conditions comprising the contrast, using only trials in which the participant responded correctly. Then, a robust one-tailed t-test was used to test for consistent effects of the task manipulation across the group. Specifically, we tested for: a main effect of conflict, a specific effect of conflict with a threatening stimulus as the distractor, a specific effect of conflict with a threatening stimulus as the target, an effect of adaptation to conflict, and the effect of non-conflict threat-related stimuli on subsequent responses to non-conflict neutral stimuli .A Philips 3T Achieva X-series MRI system with an 8-channel head coil  was used to acquire imaging data. Anatomic images were acquired with an MPRAGE sequence . Echo planar imaging sequences were used to collect the functional images using the following sequence parameters: TR/TE/FA = 2000ms/30ms/90°, FOV = 240x240mm, matrix = 80x80, 37 oblique slices , slice thickness = 3 mm, final resolution 3x3x3 mm3.Prior to analysis, standard image preprocessing was performed with AFNI . The folA Hidden Markov Model is comprised of nodes and the conditional probabilities connecting the nodes. Although the above simulation studies , 29, 30 The models were implemented as depicted in The Cohen model  is a genAs described above, one limitation of the Cohen model is that it does not capture dynamic temporal effects across trials (the Gratton effect and the slow component of interference). To account for these effects, Botnivick et al. applied a conflict monitoring feedback node which connects competition between response tendencies to the task demand node of the subsequent trial . Here, wThe model of implicit emotion regulation described by Mathews et al.  hypothesIn order to model the Gratton effect and the slow component of emotional and cognitive interference, we separately tested a model in which we applied a modification similar to the one applied by Botvinick et al.. This moThe model of implicit emotion regulation posited by Wyble et al.  is the mTo find the set of parameters that provided the best fit of the data to a given model, we applied the Baum-Welch algorithm , which iGiven that this procedure is sensitive to the initial parameter estimates, or “priors”, we solved each model using many different initial priors in order to more fully search the parameter space. After using 3000 different priors it became very unlikely to find a more optimal solution, so all models were solved using 3000 priors. After the Baum-Welch algorithm had been performed 3000 times with different priors, the solutions were then ranked by their final negative log-likelihood in order to find the most optimal solutions.However, the unobserved nature of hidden nodes allows for symmetries to exist in the parameter space. Such symmetries occur because a node’s CPTs can be flipped, resulting in an equivalent solution as measured by the negative log-likelihood. In other words, the algorithm calculates a node be either 0 or 1, but we wish to impose the interpretation that 0 = “off/suppressed” and 1 = “on/enhanced”, rather than the alternative of 0 = “on/enhanced” and 1 = “off/suppressed”. Although symmetries aid in the finding of optimal solutions because they effectively shrink the parameter space, they become problematic when one wishes to interpret the solution. Therefore, we restricted the possible priors used to initialize the Baum-Welch algorithm in order to ensure the 0 = off/1 = on interpretation. For example, in the Cohen et al. model the detection of the scene being either neutral or threat-related should be positively correlated with whether the scene was actually neutral or threat-related. According to the negative log-likelihood, a solution in which these two are negatively correlated explains the data equally as well, but the solution in which these two are anticorrelated is nonsensical. Therefore, we only initialized using priors that are within the interpretable portion of the parameter space to ensure that a hidden state being either 0/1 confers the off/on interpretation. We also verified after the Baum-Welch procedure that the solution still represented the off/on interpretation and that the solution did not produce a trivial solution with highly correlated (r > 0.80) hidden nodes. These constraints were applied to each model and, therefore, do not alter the model comparisons, however, the constraints bias the final parameter values limiting inferences regarding particular parameters. For example, the target detector in the Mathews models is constrained to be positively correlated with the target itself, in order to insure the 0/1, off/on interpretation. Therefore, these parameters are biased by the constraints and should be subject to statistical tests of their reliability. However, the parameters governing responses are left unconstrained so stronger inferences regarding the quality of the model can be drawn when examining these parameters.min is the AICc of the optimal model and AICci is AICc of the next best model. This quantity expressed the likelihood that the next best model actually explains the data as well as the best model. Again, this value does not provide a statistical comparison between the model fits but provides a quantitative degree of certainty.Given that a more complex model should always provide a superior fit, and that the models under comparison varied in their complexity, we used four criteria to assess model fit: the Akaike Information Criterion (AIC) , AIC corAdditionally, we performed tests of the interpretability of the final model by testing for positive correlations between the actual target valence and the detected target valence and also the actual distractor valence and the detected distractor valence. To do so, for each participant separately we tested for correlation between these nodes and then used a simple one-tailed t-test across the group to test whether these correlations were significantly greater than 0. Having established this basic level of interpretability we referred directly to the conditional probability tables for further examination of the model.Having applied the Baum-Welch algorithm to calculate the optimal parameters explaining the group’s data, we then applied the Viterbi algorithm to each individual’s set of data to obtain subject specific timecourses of the hidden states. The Viterbi algorithm uses the results of the Baum-Welch algorithm—the optimal model parameters (i.e. the arrows connecting the model nodes)—and the observed evidence (the stimulus features and reaction times) to explicitly solve for the most likely configuration of the hidden states for each trial (i.e. the nodes themselves) and the observed evidence (the stimulus features and the responses) . In otheContrast-based task performance measures demonstrated the task to be a valid measure of implicit emotion regulation. Conflict, when considering all conflict conditions, regardless of whether threat was the target or distractor, did not significantly slow response times, although a trend was present for conflict related slowing . However, examining more specific contrasts reveals that this interference effect was driven by trials in which the distractor stimulus was threatening vs neutral . Whereas conflict trials in which the threatening stimulus was the target were actually related to faster reaction times . Comparing conflict trials preceded by a nonconflict trial to those preceded by a conflict trial (i.e. Gratton effect) revealed significant adaptation to conflict . This adaptation effect was strongest following trials in which the distractor was threat-related , and was not present following trials in which the target was threat-related . We also tested for a slow emotional interference effect by examining whether threat-related stimuli altered responses on subsequent nonconflict neutral/neutral trials. Responses to neutral/neutral trials that were preceded by nonconflict threat/threat stimuli were significantly faster than those preceded by neutral/neutral stimuli . Tabulated results can be found in p value) was 1.8 x 10−64, which is extremely significant and driven by the large number of observations .According to all four fit criteria, the relative ranking of how well the data fit each model from best to worst was: Modified Mathews model > Mathews model > Cohen model > Modified Cohen model > Wyble model . Even acWhen examining the interpretability of the resulting modified Mathews model we found that the target valence and target detector were positively correlated across the group  and the distractor valence and distractor detector valence were also positively correlated across the group , suggesting interpretability of the model.When examining the conditional probability tables of the model  we foundAdditionally, to assess the reliability of this solution we tested whether the negative log-likelihoods of the other 2999 solutions were related to their difference from the optimal solution . There was a significant negative relationship  between negative log-likelihoods and distance from the optimal model indicating large scale stability of the solutions, such that solutions which fit the data better, according to the negative log-likelihood, were more similar to the optimal solution than solutions which fit the data worse.The following is a description of the neural regions associated with each node of the model. A multiple regression was used in the deconvolution of the data, so that each effect listed below is significant when controlling for the other nodes in the model . Regions of interests are described in the following text and a full elaboration of significant clusters is provided in Longer reaction time was positively related to broad areas of activity in the bilateral anterior insula cortex, the dACC/pre-SMA, and bilateral caudate. It was negatively related to activity in bilateral posterior insula .The model-based detection of a threat-related target stimulus was associated with increased activity in the bilateral anterior insula and decreased activity in the left motor cortex .The model-based detection of a threat-related stimulus in the distractor was not related to activity in any nodes in the salience network but only a small cluster of decreased activity in the inferior visual cortex .Model-based high task effort (high compared to low) was associated with decreases in the nodes comprises the salience network—the dACC and the bilateral anterior insula .Model-based threat evaluation (high compared to low) was associated with greater activity in the right anterior insula and the right parietal cortex .Threatening target stimuli  evoked exaggerated processing in the ventral visual cortex and decreases in the medial visual cortex extending into the parahippocampus. Additionally, threatening targets were associated with increased activity in a small cluster in the left anterior insula .The presence of threat in the distractor stimulus  was associated with a similar pattern of activation in the ventral visual and medial cortices, but also associated with deactivation in the posterior and insula .The baseline intercept of the regression accounts for neural activity related to the occurrence of all trials, regardless of type. This baseline of activity contained both positive and negative areas of activation broadly throughout the entire brain.The study of automatic biases in cognitive and emotional processing has a long history of using models to formulate and test hypotheses , 29, 30.According to all four goodness-of-fit criteria, the model that best fit the data was the modified Mathews model, and both the modified and the unmodified Mathews models greatly outperformed the other models. The Mathews models differ from the other models in two respects. They do not require knowledge as to which stimulus feature is the target and which is the distractor, and are therefore able to specify an attention-biasing system that is specific to the distractor stimuli, referred to as the threat evaluation system.The additional complexity of the Cohen model and Wyble model used to specify which feature is the target and which is the distractor is likely not necessary in this task; the valence of the target and distractor is sufficient to capture the relevant features of the stimuli. However, this framework is likely only applicable to tasks in which both features of the stimuli cause a similar interference effect. For example, in the classic Stroop task participants demonstrate an interference effect when naming the ink color, but there is no interference when reading the word, which is presumably due to the fact that word-read has higher automaticity than color naming . ApplyinThe modification to the Mathews et al. model provided even greater performance in explaining the behavioral data. This modification adds a temporal effect to the model, allowing detectors of the current trial to inform the task effort and threat evaluation system of the subsequent trial. Given the well-established observations of conflict adaptation , 25 and We also observed large scale stability in the fit of the modified Mathews to the data. The optimal parameters were chosen by ranking the solutions according to their negative log-likelihoods and finding the best solution in which the hidden states were not highly correlated and the detectors correlated positively with their stimuli, which ensured the 0/1, off/on, interpretation. Having determined the optimal solution, we found that the negative log-likelihoods of the remaining solutions were correlated with the degree to which the solutions differed from the optimal solution. This suggests that there is high-level structure in the solutions of the model and that with increasing model fit, the solutions converge toward what we have found to be the optimal solution. The parameters of this model also confirm and account for previously observed implicit emotion regulation processes, further indicating the validity of the found solution. Although most of these parameters are biased by the initialization constraints used to insure interpretability of the model, the response parameters were not constrained but they still converged to parameters which are concordant with the contrast based analyses, such that the largest impairments in reaction times were due to stimuli in which the target was neutral and the distractor was threat-related. This provides further evidence of the ability of the model to accurately capture implicit emotion regulation processes.The test for neural correlates of the optimal solution to the modified Mathews model revealed that activity in regions previously implicated in implicit emotion regulation were associated with the hidden nodes of the model. Importantly, these neural correlates of the hidden states are significant when controlling for variance attributable to reaction time as well as the actual valence of the stimuli. Therefore, these effects are not related simply to the presence of threat or the overt behavioral response to it, but to how that threat is processed according to the model.Longer reaction time was associated with large areas of activity in the cingulate and insula, consistent with previous findings that activity in these areas scales positively with reaction time, suggesting their role in sustained attention and awareness , 60. TheWhen examining the neural correlates of the modified Mathews model we found that several nodes of the model were associated with activity in the anterior insula and dACC. In particular, the detection of threat, compared to neutral in the target stimulus was associated with increased activity in the anterior insula bilaterally, while high task effort, which improves the accuracy of the target detector, was associated in inhibition of activity in these same areas as well as inhibition of the dACC. Given also that activity in these areas was related to longer reaction times, this suggests that the threatening target stimuli represented salient environmental cues and that this salience distracted attention away from the task making the motor response identifying the valence. Additionally, high task effort, which increased the accuracy of the target detector, was associated with reduction in the activity of these areas, suggesting that identification of the valence of the targets was facilitated by reduction in the perceived salience of the images. That is, the participants may have abstracted the emotional content of the images in order to identify the valence without being distracted by it.With regard to the distractor detector and threat evaluation nodes of the model, the detection of threatening distractor stimuli was not associated with greater activity in any brain region of interest. The task was counterbalanced with respect to which stimulus feature, the face or the scene, was the target so this is not explainable by imbalance in task design or feature valence. It may suggest that since the distracting stimuli were irrelevant they engendered less of an emotional response. The present analyses did not investigate neural changes associated with specific interactions between the target and distractor, e.g. detecting a threatening distractor when detecting the target as threatening vs. neutral, and future studies could analyze whether such interactions may better explain neural activity related to the distracting stimuli. We did find, however, that high threat evaluation was associated with greater activity in a small region in the right superior anterior insula. The location, size, and laterality of the finding preclude strong interpretation but may suggest that greater detection of threat is associated with a baseline higher arousal level.Although previous research strongly implicates the amygdala as an important node in the emotion processing neurocircuitry, this region was not related to any of the hidden nodes of the emotion regulation model. This is most likely due to habituation effects in the amygdala, whereby amygdala responses diminish with repeated exposure to similar threat-related stimuli . TherefoAmong this group of developing adolescents we have found evidence that the model of emotion regulation most supported by human data is the modified Mathews model. These findings confirm previous evidence that emotion regulation is a dynamic process of continual adaptation to relevant and irrelevant threatening signals. Additionally, they suggest that the direction of attention toward goal-relevant threat is independent of the direction of attention away from a goal-irrelevant threat, but that these two processes drawn upon a common neural system, the salience network, which acts to balance goal-directed behavior with automatic responses to biologically-relevant cues.Being the first study to apply and test previously hypothesized models of implicit emotion regulation to actual human data using a Hidden Markov modeling framework, the work presented is not without limitations. The use of a sample of adolescent girls impairs generalizability to adults and further studies among healthy adult populations are needed to further validate the approach described here. However, a recent study of emotional conflict in adolescents age 10–15 found that age correlated with conflict-related activity in the middle frontal gyri, and not the regions found in the present study , suggestS1 FigShown are areas that were differentially responsive to the actual presence of threatening versus neutral target stimuli (not the detection of the stimuli). Positive values (orange) indicate that a region was activated in response to threatening target stimuli and/or deactivated by neutral target stimuli. Likewise, the negative values (blue) follow the inverse of this relationship.(TIF)Click here for additional data file.S2 FigShown are areas that were differentially responsive to the actual presence of threatening versus neutral distractor stimuli (not the detection of the stimuli). Positive values (orange) indicate that a region was activated in response to threatening target stimuli and/or deactivated by neutral target stimuli. Likewise, the negative values (blue) follow the inverse of this relationship.(TIF)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


HIGHLIGHTSWe test whether symbolic number comparison is handled by an analog noisy system.Analog system model has systematic biases in describing symbolic number comparison.This suggests that symbolic and non-symbolic numbers are processed by different systems.Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation. In their seminal work Moyer and Landauer  describeK × log ) function correlates well with the measured reaction time, r = 0.75. Later, more precise mathematical descriptions were offered . Therefore, it is not enough to show that the ANS model's prediction is similar to the observed data, but a more extensive test is needed.The aim of the present study is to test the appropriateness of the ANS model in comparison tasks more extensively. The appropriateness of the ANS model for both symbolic and non-symbolic notations have been investigated several times, finding that the prediction of the ANS model is similar to the observed performance  whether the error rates can be described equally well by the functions derived from the ANS model, (2) whether the reaction time pattern of the two notations fit each other linearly, and (3) whether the diffusion model drift rates of the two notations can be described by the same analog representation. According to the widely accepted version of the ANS model, the model should predict any comparison equally well, because the same ANS-type mechanism processes any numbers independent of their notations. On the other hand, the alternative views might suggest that the ANS should work relatively well only for the non-symbolic notation, but it should work relatively poorly for symbolic notation, because symbolic precise numbers are processed by other mechanisms. Finally, from a methodological point of view, it is also possible that the difference between the ANS and the alternative models is much smaller than the typical noise in the measured data, thus, even if there are differences between the symbolic and non-symbolic comparisons, the signal-to-noise ratio is not high enough to reveal the difference. For this reason only different behavioral patterns of symbolic and non-symbolic comparisons can be conclusive, supporting the alternative accounts, while lack of difference between the symbolic and non-symbolic comparisons could be either due to the correct ANS description or due to the lack of statistical power.Participants compared Indo-Arabic numbers in one condition, and they compared dot arrays in another condition. In both conditions error rate and reaction time were measured.In a trial two numbers were visible on the left and on the right sides of the screen, and participants had to choose the larger one by pressing one of the two response keys. The stimuli were visible until key press. The response was followed by an empty screen for 500 ms, then the next trial started.In the Indo-Arabic condition the numbers were between 1 and 9, to avoid multi-digit numbers (see footnote 1 for more details). All possible pairings of those values were presented, except ties, resulting in 72 possible pairs. All pairs were presented 10 times, resulting 720 trials in the condition. The order of the trials was randomized.In the dots condition it is not appropriate to use the same 1–9 range as in the Indo-Arabic condition, because sets with less than five objects can be enumerated fast, which fast enumeration is termed subitizing  any effects that are slightly deviating from the traditional distance and size effects are more visible, and (2) due to the large number of cells systematic patterns can be identified as reliable effects instead of being a random noise, thus, a continuous change in the pattern might signal a specific effect even without statistical hypothesis tests, and random irregularities can be identified as noise.In psychophysics, specific functions can be found that describe the error rates in a comparison task based on the stimulus intensities and the Weber ratio  became a successful and an increasingly popular tool to describe the reaction time of simple decision processes, including psychophysics comparison tasks. However, earlier works used some simpler models to describe the comparison tasks  functionIn these early models, there was no clear consensus about the exact function that could describe the reaction time pattern. Psychophysics was more interested in error rates close to the threshold, and much less work investigated the reaction time far from the threshold , however, to our knowledge there is no clear consensus among others about the functional relationship between the drift rate and the representational overlap, consequently, the reaction time performance could not be specified easily.Because the reaction time analysis applied here follows the reasoning of the early analysis, the current results cannot be considered as a reliable test of the ANS model, but we examine whether evidence offered formerly really support the common mechanism for symbolic and non-symbolic number processing.In the recent decades, the diffusion model and related models became increasingly popular to describe simple decision processes  whether the recovered drift rates are proportional to task difficulty and whether drift rates tend to 0 as the task difficulty increases, and (b) whether drift rates depend purely on the supposed representational overlap, as supposed by the ANS model. As in the case of the error rates, according to the ANS model, these properties should be present in both symbolic and non-symbolic comparisons Dehaene, .Mean error rates and mean reaction times for correct responses were calculated for all number pairs for all participants in the two notations, then mean values across participants were computed Figure . In bothThe error rate results also revealed that the dot comparison is more erroneous than the Indo-Arabic comparison (the mean of the cells are 6.7% for dot notation and 2.0% for Indo-Arabic notation). On one hand, this result is hardly surprising: even common sense would suggest that the exact symbolic comparison is more precise than an imprecise dot array estimation. On the other hand it raises some nontrivial questions. If both types of comparisons are supported by the same representation, how is it possible that the two types of comparisons show radically different error rates and reaction times?Because the ANS model suggests that the underlying representation works according to Weber's law, a reasonable idea is that the two notations are supported by different Weber ratios: for the Indo-Arabic comparison a more precise, low value is used, while for the dot array comparison a more imprecise, high value is applied. Dehaene  also sugAlthough we have not been able to find convincing answers to the questions mentioned so far, in the rest of our analysis we still suppose that the two Weber ratios model is correct, and investigate whether the ANS model with two ratios can explain the Indo-Arabic and dots comparisons equally well. This supposition is in line with the different mean error rate of the two notations, and it reflects the views of the proposers of the ANS model  for the dot comparison and the Indo-Arabic comparison as a function of the Weber ratio (x axis).In the present section we investigate whether the ANS model predicts the error rate patterns in both notations equally well. We calculated the error rate prediction pattern in our stimulus space for several Weber ratios. Two examples can be seen in Figure R2 value difference between the two notations is not appropriate to evaluate the ANS model. While the dot comparison reaches its R2 maximum at around 0.95, the Indo-Arabic comparison R2 is not higher than 0.6. The different maximum R2 values can not only be the result of worse overall fit of the ANS model to the Indo-Arabic comparison, but it can also be the result of the smaller error rate in Indo-Arabic comparison. It is reasonable to suppose that the amount of noise is the same in both notations. However, because of the smaller error rate in Indo-Arabic comparison, the number pairs related variability is also smaller. Thus, the Indo-Arabic comparison has a lower signal-to-noise ratio. R2 shows the percentage of the variance the model can explain of the data, but because of the lower signal-to-noise ratio, the percentage of the variance a perfect model could explain is smaller, thus, the maximum R2 a perfect model could reach is also lower. Although the R2 should be lower for a less appropriate model, here the variance of the R2 is directed more strongly by the signal-to-noise ratio. This is another reason why the overall R2 cannot be used to contrast the model's prediction in the two notations, but a more indirect analysis is required.First, it is important to clarify that the overall Several properties of the ANS model are important, which properties can be used to assess how correct the model is for the two notations. These properties can also show why a more traditional model comparison method is not sufficient.R2 values)Consistent predicted mean error rates and predicted performance patterns  depends on the Weber-fraction of the representationR2 value) reflecting that the model finds the shape of the performance across the stimulus space.To determine the Weber ratios for the two notations, we looked for the mean error rates of Weber ratios that are equal with the measured mean error rates of the two notations. Figure R2 values. As discussed above, because the goodness of fit should be highest when the Weber ratio is specified correctly , the model predicts that the best fit  can be obtained with the Weber ratio that is in line with the mean error rate of the notation. With all other Weber ratios the goodness of the fit should be worse. In the dot comparison task the R2 indeed reaches its maximum around 0.19 Weber ratio, which Weber ratio was predicted based on the measured mean error rate. Thus, the ANS model predicts correctly that the Weber ratio of the best fitting pattern and the Weber ratio based on the mean error rates are approximately the same values. However, in the Indo-Arabic comparison the best R2 value is around 0.2 Weber ratio, which is much larger than the 0.09 ratio specified with the mean error rate. This suggests that the ANS model cannot predict correctly the shape of the error rate pattern and the mean error rate at the same time in this symbolic comparison.After specifying the Weber ratios of the comparisons for the two notations, one can check if those Weber ratios also show the highest Predicted error rate patterns. Based on the specified Weber ratios we can compare the predicted and the measured error rate patterns for the whole stimulus space, which can reveal further details how the ANS model prediction deviates from the measured symbolic comparison data. Figure Linear regression parameters of the model. The found parameters of the fitting procedure shed additional light on how the ANS model fails to explain symbolic comparison data. The ANS error function predicts the error rate directly, therefore, with the appropriate Weber ratio the equation of the fit should be measured_error = 1 × predicted_error + 0. How do the parameters change across different Weber values? In the dot comparison task, for example for an incorrectly small 0.07 Weber ratio the fitted function is 2.83 × model + 0.04. This high slope is reasonable, because the small Weber ratio predicts too small error rates that should be increased to fit the measured data. For larger Weber ratio the slope gradually decreases, and with the 0.19 Weber ratio (that was specified with the mean error rate) the function is 0.91 × model + 0.01, in which the slope is rather close to the expected 1 value that the ANS predicts. In the Indo-Arabic comparison for a 0.07 Weber ratio the estimated function is 0.56 × model + 0.01, which is decreasing further as the Weber increases, and for 0.09 Weber ratio the function is 0.37 × model + 0.01. These much lower than 1 slopes reflect that the model predicts too sudden increase with small ratios (as observed in the direct comparison of the measured data and the model), and the fit is better when the model is flattened. Again, linear fit of the different Weber ratio models shows that while the ANS predicts correctly the dot comparison error rates, the model cannot predict the Indo-Arabic comparison.To summarize, in a more extensive analysis, we found that on one hand the ANS model's prediction is coherent in the dot condition: a 0.19 Weber ratio correctly predicts the mean error rate, the relative shape of the error rates and the specific error rates for the number pairs. On the other hand, in the Indo-Arabic comparison the ANS model predicts a too steeply increasing error rate for small ratios, reflected in incoherent fit results. Again, the ANS model proposes that beyond the Weber fraction differences between the two notations, the same error function should hold for both notations Dehaene, , therefoIndo-Arabic_RT = 0.17 × dot_RT + 474.8, R2 = 0.684. Residuals of the fit , while the distance effect was not . The statistical lack of the distance effect contradicts the observable pattern, although visual inspection could be unreliable. One source of this contradiction could be the insufficient signal-to-noise ratio, and outliers might decrease the statistical power. After excluding two outlier cells (4-3 and 5-6) the correlation between the linear distance effect and the residuals when both numbers are in the 2–8 range  becomes significant, r(38) = 0.28, p = 0.015.Group mean of dot comparison time for the whole stimulus space was fit to the group mean of Indo-Arabic comparison time for the whole stimulus space  In an analog representation when the two signals almost completely overlap  the system is hardly able to compare the two properties, which should result in a close to 0 drift rate in the diffusion model . On Figure distance/large_number, and an indistinguishable pair has a 0/large_number value, which is 0. Thus, when difficulty tends to zero, drift rate should tend to zero, too, therefore, the intercept of the curves should be zero  k is related to the Weber ratio: smaller Weber ratio (higher sensitivity) causes higher slope. Indeed, in the linear model the Weber ratio can be present only in that parameter. Now if we have a kdot slope observed in the dot comparison task, the kIndo−Arabic slope in the more sensitive Indo-Arabic subsystem should be higher. If those parameters are combined, then again one option is to add the slopes, or another option is to use the larger slope. Both options predict a slope that is larger than the kdot, however, the result shows a smaller value. In a more conceptual rephrase of this problem, the lower slope of the Indo-Arabic comparison suggests a higher (less sensitive) Weber ratio, which contradict the idea that the Indo-Arabic comparison must be more sensitive than the dot comparison. Overall, we cannot see how the ANS model could explain a drift rate curve with high intercept and low slope, and we propose that the analysis of the Indo-Arabic comparison drift rate data as a function of task difficulty is not in line with the ANS or any other representation working according to Weber's law.Dehaene  analyzedWhile in the previous analysis the task difficulty was expressed by the relation of the two numbers, one can also incorporate the Weber ratio. The overlap of the representations of the two numbers can be calculated, that depends on the two values and the Weber ratio. The ANS model has another prediction that can be tested here: according to the model, the representational overlap predicts the drift rates in a comparison task. In contrast with the previous task difficulty vs. drift rate analysis, this relation of the drift rates and representational overlap is independent of the notation, because the different Weber ratios of the two notations are already incorporated in the overlap values.To test whether drift rates depend purely on the representational overlap we calculated the representational overlap for all number pairs in our stimulus space for the two Weber ratios specified earlier. To calculate the overlap of two numbers, two Gaussian distributions were created on a linear scale, with the mean of the two numbers to be compared, and standard deviation was the product of the numbers and the Weber ratio  These data, again, show that the ANS model cannot describe the appropriate representations for both notations.We also note that while there could be uncertainties whether EZ-diffusion model works correctly, in the current analysis all predictions of the ANS model in the dot comparison task proved to be correct, validating the EZ-diffusion model at the same time. This validation confirms that this simple to use diffusion parameter recovery method can be applied appropriately in the current comparison task.The present work investigated whether symbolic Indo-Arabic number comparison and non-symbolic dot comparison can be described by the same model, as predicted by the widely accepted ANS model, or whether the two notations show systematic differences as suggested by the increasing body of evidence and some alternative accounts of symbolic number processing. Although formerly the ANS description for different notation comparisons has been tested, and the fit was found to be satisfactory, the similarity between the ANS and the recently proposed DSS model predictions required a more rigorous and extensive test.Our results investigating several properties of the ANS model consistently showed that while the ANS model describe several behavioral aspects of the non-symbolic dot comparison relatively well, the symbolic Indo-Arabic comparison deviated from the ANS description at several points. More specifically, (1) while the ANS model predicts the error rate pattern correctly and consistently for non-symbolic dot comparison, it predicts too high error rates in Indo-Arabic comparison for the small ratio pairs, and too low error rates for medium ratio pairs. (2) The reaction time patterns of the two notations have different shapes which cannot be fitted linearly without systematic residuals, although early description of the comparison task reaction time would suggest a stricter similarity between the two patterns. (3a) In the diffusion model framework, while the dot drift rates are more clearly proportional to the difficulty of the task as defined in the ANS model, the relation between the Indo-Arabic drift rates and the ANS derived task difficulty is noisier. (3b) While the dot drift rates tend to zero when the number pairs become indistinguishable, the Indo-Arabic drift rates remain relatively high, contradicting the supposed functioning of a noisy analog representation. (3c) Across the notations, the drift rates do not show the same values depending on the representational overlap as suggested by the ANS model, showing that the two notation comparisons cannot be described by the same mechanism. All of these results show that (a) non-symbolic dot comparison and symbolic Indo-Arabic comparison do not rely purely on the same type of mechanism, and (b) while the ANS model can describe the non-symbolic dot comparison, it cannot describe the symbolic Indo-Arabic notation.One might wonder whether alternative forms of the ANS model could give an account for our findings, either by modifying the specific functions utilized in the present analyses or by conceptually modifying the model. At least one aspect of our results questions whether this is possible. In Indo-Arabic number comparison the drift rate does not tend to zero when the stimuli become almost indistinguishable, which result cannot be explained by any analog representation working according to the Weber's law. This is an analogous form of the problem that it is difficult to explain how the imprecise ANS could be responsible for precise number processing. If the EZ diffusion model recovered appropriately the drift rates , then the symbolic number comparison cannot be processed by any analog representation working according to the Weber's law, which is a defining feature of the ANS model. Thus, we argue that the ANS model cannot be modified to account for the present findings.One might also wonder whether shorter presentation of the dot stimuli could modify the results, because that could ensure that the diffusion model analysis handles a single step decision process instead of a multi-step counting process. However, the relatively precise prediction of the ANS model in dot comparison reflects that the current stimuli are successful enough to show the appropriateness of the ANS model, and further refinements can only improve this appropriateness. More generally, because the current design and stimuli were already appropriate to show that the ANS model describes non-symbolic comparison correctly, there is no need to further improve the current methods using the non-symbolic stimuli.Beyond the current empirical results, suggesting that only non-symbolic comparison seems to be supported by an analog representation, but not symbolic comparison, we briefly summarize some non-trivial key problems of the ANS model explaining symbolic number processing. (1) As we have mentioned, how could an imprecise system, as the ANS, solve precise symbolic comparison? Even a smaller Weber ratio (more sensitive system) is inappropriate to solve this issue. (2) If a supplementary precise system helps to solve precise symbolic comparison, why is this system invisible in a sense that dominant part of the variance in the comparison performance is purely influenced by the ANS? Additionally, why is the ANS thought to dominantly influence performance in cases when it cannot solve the problem at all? (3) If the supplementary precise system has an effect on the performance, how do we know by looking at the performance that the ANS is also activated in a comparison task? If performance is partly comprised of a hypothetical precise system, then without specifying that precise component, one can not find the rest of the performance that could support the ANS processing either.To summarize, all of our results show that symbolic and non-symbolic comparisons show several critical differences, and while the ANS model can successfully describe the non-symbolic dot comparison, it cannot account for many features of the symbolic Indo-Arabic comparison. Therefore, we argue that while non-symbolic comparison is supported by the ANS, symbolic comparison and number processing is supported by an alternative system. Further research can confirm whether the increasing amount of data suggest correctly that symbolic and non-symbolic numbers are processed by different types of systems, and if so, what representation is utilized to process symbolic numbers.All studies reported here were carried out in accordance with the recommendations of the Department of Cognitive Psychology ethics committee with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki.All authors listed, have made substantial, direct and intellectual contribution to the work, and approved it for publication.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.