As a result of the high specific strength/stiffness to mass ratio, filament wound composite pressure vessels are extensively used to contain gas or fluid under pressure. The ability to in-situ monitor the composite pressure vessels for possible damage is important for high-pressure medium storage industries. This paper describes an in-situ monitoring method to permanently monitor composite pressure vessels for their structural integrity. The sensor is made of a multi-walled carbon nanotube (MWCNT) that can be embedded in the composite skin of the pressure vessels. The sensing ability of the sensor is firstly evaluated in various mechanical tests, and in-situ monitoring experiments of a full-scale composite pressure vessel during hydraulic fatigue cycling and pressurization are performed. The monitoring results of the MWCNT sensor are compared with the strains measured by the strain gauges. The results show that the measured signal by the developed sensor matches the mechanical behavior of the composite laminates under various load conditions. In the hydraulic fatigue test, the relationship between the resistance and the strain is built, and could be used to quantitative monitor the filament wound pressure vessel. The bursting of the pressure vessel can be detected by the sharp increase of the MWCNT sensor resistance. Embedding the MWCNT sensor into the composite pressure vessel is successfully demonstrated as a promising method for structural health monitoring. Filament wound pressure vessels have been extensively used in many engineering fields such as in the nuclear energy, naval, petrochemical, and aero-space industries ,2. BecauBecause the detection of filament wound pressure vessels is of fundamental importance in order to avoid the occurrence of an abrupt and catastrophic event, studies related to the detection of damages in the pressure vessels are of notable interests ,9,10,11.Embedding a nano-material-based sensor into the filament wound pressure vessel could perform the in-situ structural health monitoring to get the damage information ,32,33,34To verify the reliability of the MWCNT sensor, we tested the sensing ability of the sensor in the short beam shear, flexural, tensile, and fatigue test of a composite laminates, before applying it in a real filament wound pressure vessel. In the mentioned mechanical tests, the MWCNT sensor was embedded into the GF/epoxy composite laminate by vacuum-assisted resin transfer molding (VARTM) processing. The details of the VARTM processing can be found in the literature ,39. The 10/(±15°)20/90°10] during the winding process, and the pre-tension of yarn was kept constant at 40 N for all of the windings.The filament wound pressure vessel was manufactured in Shanghai Ronghua High-Pressure Vessel Co, Ltd, Shanghai, China. It was made by filament winding around a 30CrMo steel inner tank. The manufacture processing of the filament wound composite pressure vessels is shown in The developed MWCNT sensors with an active length of 20 mm were embedded in the middle thickness of the composite layer, as shown in The resistance and strain of the filament wound pressure vessel hydraulic fatigue cycling and pressurization were recorded by the MWCNT and strain sensors, respectively. The hydraulic fatigue cycling parameters were set as in The filament wound pressure vessel generally works in a complex working environment ,42,43. G3 with the span of 40 mm. In the flexural test, the dimension of the specimens is 180 × 15 × 6.2 mm3 with the span of 160 mm. The experiments are carried out in the three-point-bending mode with a cross-head loading speed of 2 mm/min. The radius of the cross head is 10 mm. The composite laminates are made of a unidirectional glass fiber reinforced epoxy matrix with the stacking sequence of [0°]30. The MWCNT sensor is located between the 1/2, 15/16, and 29/30 layers in the laminates, respectively. During the test, the sensor is connected with the Keithley 2700 programmable electrometer by a conductive silver paint, as shown in the experimental setup in In the short beam shear test, the dimension of the specimens is 50 × 14 × 6.2 mmR/R0 is determined by the following:R is the test resistance during loading, while R0 is the initial resistance before the mechanical tests. As can be seen in 11, respectively. The sensing length in the longitudinal resistance test in ΔR/R0 of the longitudinal resistance is 2.24 ± 0.13, while it is 0.70 ± 0.05 for the transverse resistance. The average test results, together with their standard deviations, of the composite laminates with and without MWCNT are listed in In the tensile test, the MWCNT sensor was located in the longitudinal and transverse direction of a woven glass fabric reinforced epoxy composite laminate with stacking sequence of [0°/90°]R, is defined as the minimum load to the maximum load in the fatigue, and is kept constant at 0.1, with a loading frequency of 5 Hz. The displacement fluctuation range in the fatigue test is 1 mm, as illustrated in The composite laminates adopted in the fatigue test have the same dimension and stacking sequence as the specimens in the tensile test. In the fatigue test, the maximum and minimum load is set as 3 and 30 kN, respectively. The stress ratio, The in-situ monitoring results of the MWCNT sensor in the filament wound pressure vessel during hydraulic fatigue cycling up to 5700 cycles are shown in The filament wound pressure vessel after hydraulic fatigue for 5700 cycles was then used in the bursting test. The relative resistance, pressure, and the stain as a function of the pressure time are shown in The developed MWCNT sensor could in-situ sense the health status of the composite laminates under a short beam shear and flexural tests. The shear damage inner, the middle thickness, and the larger deformation of the bottom surface in the specimens could lead to the resistance change of the sensor, respectively. In the tensile and fatigue test, the measured resistance signal also matches the mechanical behavior of the structure well.The MWCNT sensor could monitor the filament wound pressure vessel in the hydraulic fatigue cycling, and the equivalence relationship between the relative resistance and the strain is built in the fatigue test.In the bursting test, the relative resistance remains 0 before the pressure in the vessel reaches 30 MPa, which indicates that damages do not appear in the composite skin before 30 MP for a pressure vessel with burst pressure of 48.11 MPa. The changing tendency of the resistance signal matches the strain well, and the bursting of the pressure vessel can be reflected by the sharp increase of the resistance measured by the embedded MWCNT sensor.This paper mainly aims to study the in-situ monitoring of a filament wound pressure vessel under hydraulic fatigue cycling and pressurization, by the developed MWCNT sensor. The manufacturing and sensing performance of the MWCNT sensor are firstly discussed, and then the sensor is applied in a full-scale filament wound pressure vessel. The following conclusions can be drawn in this study:


The results showed that corn steep liquor (CSL) is an agro-industrial residue that can be advantageously used to produce microbiological chitosan with yields up to 7.8 g/kg of substrate. FT-IR spectra of the product showed typical peak distributions like those of standard chitosan which confirmed the extracted product was chitosan-like. The efficiency of removing low concentrations of AO7 by using microbiological chitosan in distilled water (up to 89.96%) and tap water (up to 80.60%) was significantly higher than the efficiency of the control (chitosan obtained from crustaceans), suggesting that this biopolymer is a better economic alternative for discoloring wastewater where a low concentration of the dye is considered toxic. The high percentage recovery of AO7 from the microbiological chitosan particles used favors this biopolymer as a possible bleaching agent which may be reusable.Due to the existence of new methodologies that have reduced the production costs of microbiological chitosan, this paper puts forward the use of agro-industrial residues in order to produce microbiological chitosan and to apply chitosan as an innovative resource for removing acid orange 7 (AO7) from wastewaters. The best culture conditions were selected by a full 2 Amongectively ,7,8,9,10re media .Currently, chitosan is produced from α-chitin, because the production values are commercially advantageous. However, obtaining chitosan from α-chitin requires some care regarding standardizing the product ,13 and iGiven this situation, obtaining chitosan by submerged culture of fungi has the advantage of manipulating and standardizing specific physicochemical characteristics, thus facilitating its incorporation into industrial production lines, besides helping to reduce the environmental waste generated when producing chitosan from the deacetylation of α-chitin ,15,16. NThe great interest in producing chitosan is justified by its potential in biotechnological applications, especially with regard to using it in medical and environmental areas ,20,21,2250.With the increase in textile consumption and interest in diversifying colors, industries have increased the use of color additives in the production of clothing, for example acid orange 7 or Orange II (AO7). AO7 is a synthetic acid dye that is toxic at a concentration of 0.011 mg/mL as expressed by the acute toxicity test EC3 Central Composite Rotational Design (CCRD), with four central points, to evaluate the simultaneous effect of chitosan concentration, dye concentration and pH on effluent decolorization by coagulation-flocculation.Thus, due to the need to reduce the costs of production and enhance the efficiency of fungi in producing chitosan, this paper assesses the interactive influence of different factors  by a full factorial design and applying chitosan as a coagulant agent of azo dye acid orange 7. Despite there already being extensive knowledge of the mechanisms of interactions between chitosan and azo dyes, this study innovates by applying a 2The simplest and most effective statistical method for analyzing different factors that can interfere in the response to a product is a full factorial design , since tIn our study, the CSL which was used as the sole source of carbon and nitrogen in batch positively influenced the microbiological production of chitosan. This fact may have occurred due to high concentrations of nitrogen 17.57%) and carbohydrate (13.03%) found in the CSL concentrate used in this research. The results corroborate those in the literature, which also describe the use of CSL as a good source of nitrogen for the production of biopolymers .57% and . The dis2 spores/mL. For these conditions, chitosan was produced at 62.44 mg per gram of dry biomass, or 7.8 g of chitosan per kilogram of CSL concentrate. This result was superior to the results of Wang et al. [Absidia coerulea. This fact corroborates the literature which describes S. racemosum as a good producer of chitosan in different nutritional media [The experimental design used to analyze the main effects between the independent factors  on the microbiological production of chitosan showed that the best assay occurred when the dilution of concentrated CSL was only 2% (v/v), with initial pH 8.0, 25 °C and an inoculum size of 10al media . et al. [3− groups of the structure of azo dyes [As described by Aranaz et al. , the appazo dyes ,31,32.In studies of crystallinity, microbiological chitosan showed a high crystallinity  and standard chitosan was seen to be amorphous, suggesting a lower amount of intermolecular structural links between the amino groups of residues in the standard chitosan when compared with microbiological chitosan ,33. DuriIn the analysis of viscosimetric molecular weight, the microbiological chitosan showed a low molecular weight, while standard chitosan showed an average viscosimetric molecular weight. The importance of molecular weight on coagulation-flocculation process is noted in the literature which states that the lower molecular weight of chitosan is related to the increased efficiency in removing azo dyes in systems where the solvent has a low ionic strength (distilled water) .After selecting the culture medium for the low-cost production of chitosan, production was scaled up to obtain satisfactory amounts of chitosan to be used to evaluate its application in removing AO7, which was used in this study as a dye model for treating from textile effluents .The literature describes the use of chitosan obtained from the exoskeleton of crustaceans, as an alternative to the chemical treatment of wastewater, and shows that some factors such as the concentration of chitosan in solution, the type of chemical pollutant, pH, the type and concentration of dye and ionic strength of the solution are significant variables in the adsorption process by chitosan ,25,37,38The coagulant-flocculant action, at first, was influenced by the origin and physico-chemical characteristics of chitosan and by the ionic strength of the water used as solvent , and obtp < 0.05) for the factors of chitosan concentration and dye concentration, which enabled the variance analysis and showed the efficiency of the decolorization by using the response surface methodology , it was observed that for the systems where the solvent was distilled water there was a significant result  for representation in a quadratic model. Using the response surface generated by the model  were observed when the ionic strengths of the solvent were compared on the removal of AO7, as observed by the Tukey test , which was suggested as influential in the process of removing the azo dye Acid Blue 92 (AB92). However, the tap water used in this experiment had a low sulfate concentration (data not shown), which can be differentiated in the results obtained. The physico-chemical properties of the chitosans are another factor suggested as important for explaining the difference in the results.The difference from the influence of the tap water used in the study by Szygula et al.  is suggeAlthough a higher removal efficiency of AO7, up to 89.91%, was observed due to the action of microbiological chitosan in distilled water, the high cost of using distilled water at industrial levels suggests the use of microbiological chitosan in systems where the solvent may have to be tap water. The suggestion arises from the fact that regardless of the ionic strength of the solvent, microbiological chitosan showed higher efficiency in removing AO7, when compared with standard chitosan (chitosan obtained from crustaceans) .The general quadratic model was used to explain the higher removal percentage of AO7 by microbiological chitosan in a solution of low ionic strength (distilled water) for the range of values selected in this study:ue of Xi .In p < 0.01 and R2 = 0.983, thus demonstrating the applicability of the model when the experiment is projected.The statistical significance of the prediction response equation was certified by the F test and by variance analysis (ANOVA). The ANOVA (data not shown) of the quadratic regression model demonstrated that the model was significant, having a value et al. [The recovery of the dye from the particles of microbiological and standard chitosan used during the experiments, in both distilled or tap water, was performed by solubilizing the flocculant agent in 30 mL of 0.1 M NaOH per sample of the agent obtained after carrying out each assay . From thet al.  where apSyncephalastrum racemosum (WFCC/UCP-0148), grown on Potato Dextrose Agar  at 28 °C for 120 h were stored and used to make the spore solutions. For biomass production, S. racemosum was grown in an aerated environment (150 rpm) for 120 h. The culture media were formulated from corn steep liquor (CSL) as the sole source of carbon and nitrogen, in accordance with full 24 factorial designs with three central points  of chitosan was determined by infrared spectroscopy and calculated by Equation 2 . The cryThe molecular weight of chitosan was estimated by viscometry as per the methodology proposed by Terbojevich and Cosani . The mea−1) and then diluted (v/v) as per The azo dye, acid orange 7 , also known as Orange II, is a monoazo compound with a reactive sulfonic group and negative loads in aqueous solution a. It wasS. racemosum grown in the best condition selected by the full factorial design described in Commercial chitosan, described as chitosan obtained by alpha-chitin, was used during the experiments as a comparative standard (Sigma-Aldrich) and dissolved in acetic acid without purification. The microbiological chitosan used in the coagulation-flocculation experiments was obtained from 3 Central Composite Rotational Design (CCRD), with six axial points and four central points  in the process of coagulation-flocculation of the dye AO7 by standard and microbiological chitosan, a 2l points  was prop  were added  using a Genesis Spectronic UV-vis spectrophotometer, model 2 . The percentage of decolorization was calculated by Equation (4):In this study the tested concentrations of Orange AO7 ranged from 20 to 105 mg/mL. The concentrations chosen for the tests were intended to demonstrate the ability of chitosan, a non-toxic polymer that degrades easily in the environment, as a substitute for expensive processes that are potentially toxic to aquatic organisms present in the environment. Based on the results obtained, it is noticed that chitosan was capable of removing up to 80.32% of dye present in tap water in situations where a concentration of 88 mg/mL is dependent on the conditions tested in only 2 h of incubation. Additional analyses associated with the use of “acetosyringone” laccase to oxidize low concentrations of AO7 (17.52 mg/L) at non-toxic levels have been described in the literature , but theSyncephalastrum racemosum in wastewater from industrial food industries further reduces the cost of removing AO7 from wastewater from the dyeing industry.The high efficiency removal of different concentrations of AO7 tested by microbiological chitosan rather than crustacean chitosan suggests this microbiological polymer is an economic and eco-friendly alternative that can be applied to the discoloration of wastewater. The low cost of producing high quality microbiological chitosan by Despite the fact the removal of AO7 by microbiological chitosan in distilled water compared with the efficiency in tap water was more efficient, the high cost to industry of using distilled water suggests the use of microbiological chitosan in systems where tap water is a solvent. The high percentage recovery of AO7 from the microbiological chitosan particles used during the CCRD experiments favors the reuse of this biopolymer.


The slope (SII) and relative (RII) indices of inequality are commonly recommended to monitor health inequality policies. As an upwards shift of the educational level distribution (ELD) can be part of those policies, we examine how such a shift affects the SII, the RII and the population attributable fraction (PAF).p1 to p4) of each EL, with constant mortality rates (MR) and calculated the corresponding RII, SII and PAF. Second, we decomposed the effect on the three indices of a change affecting both the ELD and the MRs, into the contributions of each component.We simulated 632 distributions of 4 educational levels (ELs) by varying the share  contains supplementary material, which is available to authorized users. Reducing socio-economic (SE) health inequalities, is an overarching public health goal , 2, neceOne major issue when monitoring health inequality results from potential changes in the social composition of the population. As strategies for tackling health inequalities often include addressing the social determinants of health – for instance by promoting education, increasing poor people’s income, or improving living conditions  – shiftsA wide variety of inequality indices affected by the SE distribution – sometimes called “population-level” or “summary” inequality indices – has been described , 10, 11.In particular, two regression-based indices, the slope index of inequality (SII) and its relative counterpart, the relative index of inequality (RII), are often recommended , 12–16 aIn this work, we examine how upwards shifts of the SE composition of the population influence the SII and the RII. The answer to this question is of high importance, allowing to assess if they meet the expectations for policy monitoring. The behaviour of the SII and RII will be compared with another inequality indicator, namely the “population attributable fraction (PAF)” sometimes called “population attributable risk” .We first generated a large number of hypothetical populations by varying the SE compositions at fixed rates of health outcomes and examined the changes in a set of inequality indicators; secondly, we varied both the SE composition and health outcome rates and decomposed the total effect into its two components.We used the premature mortality rates in males  as health outcome and the educational level (EL) as indicator of socioeconomic position; we grouped the EL in 4 groups ranging from EL1 to EL4 and corresponding to the International Standard Classification of Education (ISCED) 1997 (*) categories 0–1 (EL1), 2 (EL2), 3–4 (EL3), 5–6 (EL4). The share of each group is given by p1 (proportion of people with the lowest EL) to p4 (proportion of people with the highest EL).p1 + p2 + p3). Only combinations where all EL proportions were comprised between 5 and 50% were retained, providing 632 different combinations. The sas code can be found at https://github.com/brechtdv/RII-SII.We generated with SAS 9.3 a series of distributions of 4 ELs in the population by varying the proportion of EL1 (p1), EL2 (p2) and EL3 (p3) from 5 to 50%, the proportion of EL4 (p4) being calculated as 100 %  − . Intermediate group values have a weaker influence on the magnitude of the slope, but will inflate the variance of the slope if they are not increasing gradually, rendering the slope not significantly different from 0.The magnitude of the slope is mainly affected by the value of the rates, and by the position of the extreme EL groups  positions of the x axis, i.e., 0 and 1. It is calculated as the ratio of the value at the bottom of the social hierarchy (corresponding to the intercept) to the value at the top of the hierarchy (corresponding to the intercept + slope). The RII is given by:More information about these measures can be found elsewhere , 11, 15.The PAF indicates the fraction of all deaths that could have been avoided if the mortality of the whole population was equal to the one observed in the highest EL. The PAF is calculated as , 20:3\doIn the first part of our analysis, we examine the effect of changes in the educational distribution on the RII, SII and PAF, while keeping the group-specific mortality rates fixed. Therefore, in each of the 632 hypothetical distributions of the Els, we attributed to each EL the EL-specific premature mortality rates in Belgian males calculated from the census 2001 as the health outcome, i.e., 733.8, 552.1, 450.1, and 313.9 per 100,000 person-years, respectively, for EL1, EL2, EL3, and EL4 .Among all possible changes, we focused on the situations where there was a change in p4 as this is the most common evolution.We calculated the RII, SII and PAF for each simulated EL distribution, as well as their confidence intervals . Only dievolutions with fixed p1 values, with p2 or p3 varying in complement to p4;evolutions with p1 varying in complement to p4, with p2 and p3 fixed.Finally, since our research question was how those indices behave when the share of EL4 increases, we plotted each index against p4, for two types of evolutions in p1:In the manuscript, the behaviour of the SII, RII and PAF is described in detail for 3 examples from evolutions a) and 3 examples from evolutions b). The full set of results for all combinations of p1 to p4 values is shown in appendices.In the second part of our work, we explore what happens both to pairwise indicators and to population-level indices when varying two dimensions, i.e., the EL distribution (ELD) and the mortality rates. We built six fictive scenarios (A to F), by combining 3 sets of EL-specific mortality rates with 2 ELDs Table , and comWe further decomposed, for the 3 population-level indices, the total change from baseline into both components Table , i.e. thAll analyses were performed using SAS 9.3In this first part of the results, we kept the mortality rates constant and varied the share of p4, first for different fixed p1 and p3 values, then for fixed p2 and p3 values. Figure Figure When p1 is fixed, an increase of p4 results in a constant increase of the absolute value of the SIIs Fig.  and a stWhen the value of p1 varies in complement to the one of p4, with fixed values of p2 and p3, the SIIs follow a concave curve, increasing first at low p4 values, reaching a maximum then decreasing Fig. . The lowTable For each set of rates, when moving from ELD1 to ELD2 , pairwise rate differences do not change, as their calculation does not depend on the EL sizes. At the contrary, population-level indices are affected by the EL distribution, and this in a completely different way for each of them. In scenario B, where only the ELD (and not the rates) has changed from baseline, we observe a 31% increase of the RII, an almost stable SII and a 19% decrease of the PAF as compared to baseline. In scenarios C and D (second set of rates combined with respectively ELD1 and ELD2), absolute and relative pairwise rate differences are smaller than in the baseline scenario (A). The mortality decline in the low ELs exceeds the one of the high ELs in such an important way that it even results in a higher proportional decline in the low than in high ELs, leading to a decline in both types of rate differentials . The simScenarios E and F (3rd set of rates) show an increase of both absolute and relative mortality differentials with respect to scenario A. In scenario E (with ELD1), the population-based indices increased compared to scenario A, consistent with the evolution of the pairwise rates differentials. When moving from scenario E to scenario F, it could be expected that the upwards shift of the EL distribution would partially compensate the increase in differentials. Yet on the contrary, the RII further increased with 56% from scenario E to F, resulting in a 73% increase from scenario A. The SII increased by 11% , while the PAF decreased by 8% in total from scenario A: the 13% increase due to the rates differentials was exceeded by a 21% decrease due to the EL-shift, which is in line with a “compensation” of the inequalities brought by an upwards shift of EL.The SII and the RII are often claimed to be good indicators for monitoring health inequalities, as they include information from all ELs, and they account for changes in the SE distribution , 16, 24.At fixed mortality rates, the SIIs and the RIIs increase with the increase of the share of EL4 (p4) when the share of EL1 (p1) is fixed. When p1 varies in complement to p4, the evolution of the SIIs and the RIIs follows a reverse U-curve with an initial increase, the reach of a maximum then a decrease; for the RIIs the increasing part of the curve is much longer than for the SIIs; the maximum is only reached when the sum of p2, p3 and p4 is large, then slowly decreases. On the contrary, the PAFs monotonically decrease when p4 increases.When the mortality rates vary together with a change in the EL distribution, population-level indicators are affected by both components. For each given set of mortality rates, a p4 increase strongly modifies the partial effect on the RII evolution of the mortality differential component, in a paradoxical way: the effect of a decrease in the mortality differential component (resulting in a decrease of the RII) is diminished or even cancelled by the effect of the upward shift of the ELD. In other words, when a good scenario  moves to an even better scenario  the improvement is translated by the RII as a worsening. Also, an increase of the mortality differentials is not compensated by an improvement of the ELD. In our examples, the SIIs hardly change consequently to a p4 increase (1 to 3%). The PAFs substantially decrease (by about 20%).When rates are maintained constant, changes in the SII or in the RII are exclusively attributable to the change in the EL distribution.The SII, being the ratio of the weighted sum of the XY covariances  to the squared X variances Eq. , will inThe RII Eq.  is the rOn the contrary, the PAFs express the difference between the average rate and the rate of the highest EL, related to the average rate. When the share of the highest EL increases, the average mortality rate decreases, and so does the difference between the average and highest rates, resulting in a smaller PAF.We only performed simulations using EL as socio-economic indicator, and not, for instance, income or occupation. We chose for EL because a scenario in which the EL increases is a very realistic one, since developed countries’ governments have made large efforts to increase the educational attainment of their populations. The general conclusions about the behaviour of the two regression-based indicators, the SII and RII, are however independent of the nature of the socio-economic indicator. Our approach can indeed easily be extended to other socio-economic indicators, but this was beyond the scope of the current study.Although this study is based on empirical findings, the large variety of ELDs included in the simulations allows to be quite confident to the conclusions drawn from the studied evolutions of ELDs. This study mainly focused on the change of the indicators in function of the share of the highest EL. Our conclusions can thus not be generalized to scenarios where the p4 is fixed. An example of the variation of other ELs with a fixed p4 was published by Keppler  and althOur results warn against the use of the RII in monitoring health inequalities in the context of a change in the distribution of the SE groups in the population.Policies intended to reduce health inequalities have to address the social conditions contributing to unequal chance in health , 25. In As stated by the WHO “The results of monitoring indicate whether policies, programmes and practices are accomplishing what they are designed to achieve.” However, in most situations studied here, a positive evolution consisting in an increasing proportion of the population moving to the highest educational level, translates in a deterioration of the RII. The SII, to a lesser extent than the RII, also translates many patterns of p4 increases as worsening of inequalities. Only the PAF, albeit a simpler population-level inequality indicator, translates an improvement of the EL distribution as a progress through a decrease of the indicator value. Although the PAF does not capture the gradient of the rates across the ELs, it provides policy-makers with operational information.For monitoring purposes, we recommend to limit the use of gradient-based indicators RII and SII to situations where the EL composition does not change, for instance for comparing inequalities between populations with a same EL composition, or inequalities in different health outcomes in a given population and time. When the ELD changes, we rather recommend to compete the analysis of changes in absolute and relative rates differences and in EL-specific health outcomes, with changes in PAF and ELD, as done in recent trends analyses , 27. FurIn contrast to what is commonly proposed, we warn against the use of the RII and SII for monitoring health inequalities or comparing populations with different educational distributions, because they do not translate upwards shifts of the educational distribution into a value indicating progress. The RII, and to a lesser extent the SII, increase in most patterns including an increase of the share of the highest EL. We recommend to use pairwise inequality indicators and PAFs to monitor health inequalities, in combination with a description of the shifts in the ELs.Additional file 1:Full set of figures representing the evolution of the SII in function of P4 at fixed p1 and p2 (PDF 637 kb)Additional file 2:Full set of figures representing the evolution of the SII in function of P4 at fixed p1 and p3 (PDF 616 kb)Additional file 3:Full set of figures representing the evolution of the RII in function of P4 at fixed p1 and p2 (PDF 555 kb)Additional file 4:Full set of figures representing the evolution of the RII in function of P4 at fixed p1 and p3 (PDF 524 kb)Additional file 5:Full set of figures representing the evolution of the PAF in function of P4 at fixed p1 and p2 (PDF 476 kb)Additional file 6:Full set of figures representing the evolution of the PAF in function of P4 at fixed p1 and p3 (PDF 478 kb)Additional file 7:Full set of figures representing the evolution of the SII in function of P4 at fixed p2 and p3 (PDF 605 kb)Additional file 8:Full set of figures representing the evolution of the RII in function of P4 at fixed p2 and p3 (PDF 517 kb)Additional file 9:Full set of figures representing the evolution of the PAF in function of P4 at fixed p2 and p3 (PDF 484 kb)


Rapid and efficient demulsification (destabilizing of an emulsion) processes of a water in oil (W/O) emulsion were carried out in a three-dimensional electric spiral plate-type microchannel (3D-ESPM). In this experiment, the demulsifying efficiency of emulsions by 3D-ESPM was compared with that by gravity settling, the factors influencing demulsifying efficiency were investigated, and the induction period, cut size and residence time in the demulsification process were studied. The results showed that in contrast to the gravity settling method, 3D-ESPM can directly separate the disperse phase (water) instead of the continuous phase (oil). The maximum demulsifying efficiency of W/O emulsion in a single pass through the 3D-ESPM reached 90.3%, with a microchannel height of 200 μm, electric field intensity of 250 V /cm, microchannel angle of 180°, microchannel with 18 plates and a flow rate of 2 mL /min. An induction period of 0.6 s during the demulsification process was simulated with experimental data fitting. When the residence time of emulsion in 3D-ESPM was longer than the induction period, its demulsifying efficiency increased as the increase of the flow velocity due to the droplet coalescence effects of Dean vortices in the spiral microchannel. For this device a cut size of droplets of 4.5 μm was deduced. Our results showed that the demulsification process of W/O emulsion was intensified by 3D-ESPM based on the coupling effect between electric field-induced droplets migration and microfluidic hydrodynamic trapping. Emulsions are widely used and play a vital role in industrial processes, agricultural industry and daily life. However, used emulsions are usually an environmental hazard , such asThis was especially the case when demulsifying water in oil (W/O) emulsions with micrometer-sized droplets; the traditional technique was complained of low efficiency or no effect, and new methods of microwave heating ,13 and mNowadays, electric demulsification, commonly known as electrocoalescence, is usually used to separate W/O emulsions in industry. The technology of electrocoalescence employs electrostatic forces to separate water droplets in the W/O emulsions without any chemical additions, and can be used conveniently for large-scale industrial production, and has evolved as the most efficient and economical way for demulsifying W/O emulsions . HoweverSince 2004, plate-type microchannels were used to for the demulsification of O/W emulsions, and these reached very high demulsifying efficiencies through the surface force among oil droplets and asymmetric hydrophobic/hydrophilic walls. Okubo applied a 10 mm-in-length glass- Polytetrafluoroethylene (PTFE) microchannel to investigate the separation of the oil and water mixture and achieved almost 100% liquid-liquid separation in 0.01 s . KolehmaDroplet coalescence is divided into passive droplet coalescence and active droplet coalescence . The pasDue to the unique micro-scale characteristics of microchannels, the manipulation of particles has become more flexible and controllable. The broadening and converging microchannels are commonly used microstructures for getting droplets close each other and appearing as coalescence. Peter Thurgood et al. studied the law of vortex generated by microstructures on particle migration and aggregation by adding U-shaped and spherical microstructures in microchannels ,30. WhenThe 3D-ESPM employs a special spiral inner microstructure and a DC electric field at the same time, and also shows an efficient demulsification action on W/O emulsions ; howeverKerosene was purchased from China Petrochemical Group Co., Ltd. ; Sulfuric Acid, Span80 and Anhydrous Ethanol were all purchased from Kelong Chemicals Co., Ltd. . Sulfuric Acid, Span80 and Anhydrous Ethanol were all of the analytical grades and used as received.The experimental apparatus is shown in The structure of 3D-ESPM was shown in 2SO4) solution (0.25 mol/L) and the Span80 emulsifier (100 g/L) were pre-prepared. Secondly, 3 mL Span80 emulsifier, 47 mL kerosene and 40 mL H2SO4 solution will be added in sequence and then mixed. Thirdly, the mixed solution was stirred for two min at 14,000 RPM speed. After settling for 2 min, the stability of emulsion was evaluated according to Equation (1):J is the stability of the emulsion, Vemulsion is the volume of the static residual emulsion; Vtotal is the total volume of the collected emulsion before the settlement; Vwater is the volume of the separated water in the emulsion; Vkerosene is the volume of separated kerosene in the oil phase. The emulsion itself is a thermodynamically unstable system, and the stability of the emulsion decreases over time [The method of preparing the target emulsion  was as fver time ,36. The η is the emulsion of the demulsification rate, Vwater′ is the volume of water separating out after demulsification, Vtotal′ is the total volume of the collected liquid from the tail liquid tube, φ is the rate of water content in the emulsion.Firstly, the prepared target emulsion was sent into the three-dimensional microchannel by using a medium pressure piston pump, while the DC power supply was used to apply the electric field of the required rate in the microchannel ends. Thus, the emulsion was demulsified in the microchannel. Finally, the tail liquid after the demulsification was collected. The result was recorded to calculate the demulsification rate according to Equation (2):In order to explore the role of the spiral plate microchannel, we replaced the 3D-ESPM with a straight PTFE tube with a diameter of 3 mm and a length of 30 cm, and placed it in an electric field with the strength of 400 V/cm. The control was experimented by pumping the target emulsion through the PTFE tube and keeping the other experimental parameters the same as 2.4.1.One of two samples of freshly prepared water in kerosene emulsions was settled with gravity for 24 h, and the other one was pumped through 3D-ESPM directly with an electric field intensity of 250 V/cm at the same time. In From We have analyzed the principle of electric field and hydrodynamic forces in this device and the results were shown in As the flow rate increases, the vortices generated in the microchannels increase, causing the droplets to accumulate at equilibrium positions and the aggregation of droplets of different sizes. Different speeds lead to an instability of the emulsion system and increase the probability of droplets gathering. To a certain extent, an increase in flow rate will enhance the effect of droplet coalescence. In order to further verify the demulsification mechanism of 3D-ESPM, the effects of emulsion flow rate and plate number were studied.Effect of the plate number of 3D-ESPM and the flow rate of W/O emulsion on demulsifying efficiency were studied under the condition of a microchannel height of 200 μm, arc radian of 180° and electric field intensity of 250 V/cm. The plate numbers of 1–20 and flow rates of 2, 4, 6, 8 and 10 mL/min were experimented by the 3D-ESPM in a single-pass demulsification. The results are shown in η increases with the increasing of the plate number P for all five flow rates, and the η-P scatter plots prolong into an “S” shaped curve of its increasing trend [ng trend . For floThe “S” curve connection between demulsification efficiency and plate number is similar to the S-type growth curve of typical microorganisms , therefoη and resident time is common for the experimental range of the flow rate. The tangent line at the inflection point of the S-logistic spline was drawn as a red straight line, and for all flow rates the intersection of tangent extension and time axis are positive, which is shown in According to the above results, it is obvious that the demulsification efficiency of 3D-ESPM was influenced by the residence time, and the longer the residence time, the higher the demulsification efficiency. In order to further clarify this relationship, the resident time of emulsions in 3D-ESPM at five flow rates  was calculated by varying the plate number, and was plotted with the demulsifcaiton efficiency in Similar to the growth curve of a microorganism, the intercepts in In order to clarify the influence of the residence time on the demulsifying efficiency, the five data curves of De according to Equations (3) and (4).id is the hydraulic equivalent diameter of the microchannel, cd is the spiral diameter, Re is the Reynolds number, ρ is the density of emulsion, v is the flow rate of emulsion, and µ is the dynamic viscosity of the emulsion.From From the Equations (3) and (4), the Dean number is proportional to the flow rate of the emulsion. The number of this Dean number is 1.80–9.02 when the flow rate is 2–10 mL/min. With the increase of the emulsion flow rate, the Dean vortices in the 3D-ESPM gradually form and strengthen the coalescence of droplets in the emulsion fluid which can intensify the demulsification process. The above experimental results show that the Dean vortex dominates the demulsification process of the 3D-ESPM when the residence time is longer than the induction period.Droplet size distributions of emulsions before and after becoming demulsified with 3D-ESPM were measured by using an optical microscope  with an image processing software. The results are shown in D, decreases from 19.34 μm to 4.54 μm after demulsification by 3D-ESPM with a demulsifying efficiency of 90.3%. This result indicated that 3D-ESPM preferentially separates the large droplets with a diameter of more than 7 μm, which coalesce to form a water phase, and are absent in the droplet size distribution after having been demulsified. For the small droplets with a diameter of fewer than 7 μm, the percentage of droplets with a diameter from 3.5 to 6 μm in As shown in The rapid and efficient separation of the dispersed phase (water) in W/O emulsions was achieved in 0.6–10 s by flowing through the 3D-ESPM under an electric field. Because of the dual coupling effect of the electric field and the microchannel, the demulsification rate reached the highest percentage, 90.3%, by increasing the residence time (as increasing the number of micro-channel plates). The experimental results show that, under the influence of the Dean vortex, 3D-ESPM can effectively intensify the demulsification process of water in oil emulsions.


Research in type 1 diabetes management has increased exponentially since the irruption of mobile health apps for its remote and self-management. Despite this fact, the features affect in the disease management and patient empowerment are adopted by app makers and provided to the general population remain unexplored.To study the gap between literature and available apps for type 1 diabetes self-management and patient empowerment and to discover the features that an ideal app should provide to people with diabetes.The methodology comprises systematic reviews in the scientific literature and app marketplaces. We included articles describing interventions that demonstrated an effect on diabetes management with particular clinical endpoints through the use of mobile technologies. The features of these apps were gathered in a taxonomy of what an ideal app should look like to then assess which of these features are available in the market.P=.42, F=.81) nor the type of feature . Apps were classified according to the number of level 1 features and sorted into quartiles. First quartile apps had a regular distribution of the ten features in the taxonomy whereas the other 3 quartiles had an irregular distribution.The literature search resulted in 231 matches. Of these, 55 met the inclusion criteria. A taxonomy featuring 3 levels of characteristics was designed based on 5 papers which were selected for the synthesis. Level 1 includes 10 general features  Level 2 and Level 3 included features providing a descriptive detail of Level 1 features. Eighty apps matching the inclusion criteria were analyzed. None of the assessed apps fulfilled the features of the taxonomy of an ideal app. Personalization  and Data record  were the 2 top prevalent features, whereas Agenda  and Rewards  where the less predominant. The operating system was not associated with the number of features (There are significant gaps between research and the market in mobile health for type 1 diabetes management. While the literature focuses on aspects related to gamification, rewarding, and social communities, the available apps are focused on disease management aspects such as data record and appointments. Personalized and tailored empowerment features should be included in commercial apps for large-scale assessment of potential in the self-management of the disease. Diabetes mellitus is a metabolic syndrome, which comprises an impaired insulin production and action . Type 1 1c (HbA1c) among others) and other health-related outcomes are supervised by general practitioners, endocrinologists, and nurses. This type of care has shown limited effects on empowering patients to control blood sugar levels [Despite the promise of mobile health  in the specific field of diabetes ,6 and thr levels .In their review from 2011, Chomutare et al  comparedSince then, several studies have been conducted to test the effectiveness of apps in reduced samples of patients. In such studies, researchers evaluate apps with different approaches and patient groups, yielding conflicting conclusions due to the different methodology of the interventions .This study aimed to assess whether app manufacturers adopted the findings from mHealth evidence-based interventions in diabetes. The rationale is to mind the gap between research and the market to identify the features that are not available in commercial apps. The methodology comprises 2 systematic reviews using the PRISMA methodology, one in the scientific literature  and the other in app marketplaces. The systematic review of scientific literature is focused on interventions with apps on patients with T1DM into randomized controlled trials (RCTs). In the first stage, we built the schema of what could be an ideal diabetes app  and to then analyze the characteristics of available apps and their distance to the ideal app.1c, in-range time or self-monitoring blood glucose). Exclusion criteria included (1) gray literature, (2) studies not reporting RCTs on T1DM , and (3) studies not using an app  or not describing the app’s functionality. The secondary objective was to compare the evidence-based features with the characteristics of the available apps.The primary objective of this study was to review scientific literature using the PRISMA methodology to enumerate evidence-based features that have demonstrated a positive effect in the management of T1DM in RCTs. Inclusion criteria were defined as (1) a mHealth intervention on T1DM patients using an app for remote and self-management of the disease and (2) the intervention was performed in an RCT and reports on clinical outcomes . We searched a combination of keywords including type 1 diabetes mellitus, mobile health, RCTs and self-management. The complete search strategy, combination of keywords in the queries and results for PubMed are described in Subsequently, the approach for recruiting apps was twofold. First, a web search was conducted by using keywords of 3 different groups: (1) “diabetes mellitus 1 AND apps AND (android OR iPhone) AND self-management,” (2) “diabetes mellitus,” and (3) “diabetes apps AND self-management.” A second search was conducted in Google Play and the App Store to recruit a greater number of apps. In this case, we introduced 2 keywords: “diabetes AND management.” After collecting all the available apps, the screening and selection were done in the same way as with the publications (using a PRISMA flow diagram). Subsequently, the selected apps were downloaded and tested to know which of the characteristics obtained with the systematic literature review were available in the apps.Data from the literature review and the apps assessment was extracted by 2 of the authors (AMM and EJP) using a structured data form. For the literature review, we extracted data related to the study . Studies were assessed using the Cochrane Collaboration’s tool to assess the risk of bias of included  . For theP value and the F statistic. Association of the number of features and the operative system was assessed using Kruskal-Wallis tests at 95% CI, in which we calculated the P value and the chi-square value. A value of P<.05 was considered as significant The Feature Factor (FF) was defined as the polynomial formula (Equation 1) FF= NL13+NL22+NL3 where NLx is the number of features in level 1, level 2, and level 3 respectively. We used MATLAB 2017Ra framework under Academic License to conduct the statistical analysis.A descriptive analysis of the features in the apps was done before association analytics. Association of the type of features and the type of operative system was evaluated with a two-way analysis of variance, in which we assessed the 1c improvement, self-monitoring blood glucose (SMBG) daily rate).These 6 studies reported on the results evaluating the benefits of apps in the management of T1DM . These sOverall, the included trials adequately achieved a low level of risk of bias . Three oThe majority of these studies assessed the features of the app which had a higher perceived usefulness or a good adoption among study subjects. Castensøe-Seidenfaden et al  found th1c or mean glucose values. Beyond data synchronization, no more app features were provided by authors in this paper. Finally, Ryan et al [Clemens and Staggs  reportedan et al  developeThree of these studies evaluated the user satisfaction in terms of willingness to use the app after the trial and willingness to recommend its use to peers. Each showed a high percentage of subjects willing to continue using the app and willing to recommend the app to peers -14. In oThe qualitative study of the apps used in the studies allowed us to extract the characteristics of the apps that users rated as key and researchers considered of value. These features were sorted into functional areas beyond the traditional 4 clinical areas of diabetes management taxonomy  . The newFamily support was a feature in which relatives can perform a follow-up of the data introduced by the patient in which we have identified read access and read-and-write access. This feature also contains literature support for relatives in the management of T1DM through web links and books. The Agenda feature was a common factor in the apps analyzed in the review, and it was mainly devoted for scheduling medical and personal appointments. Another recurrent feature was the storage of measurements and reports related to food intake, insulin intake, and physical activity, which are under the Data record feature. In this feature, we made a distinction between the apps that had manual data entry  and the automatic entry of data using wireless sensors, mobile phone sensors  and smartwatches and wearables. The last feature  and Google Play (Android) for diabetes management and support. Following the PRISMA methodology approach , we obtaAndroid and iOS apps were tested during a month since many apps needed control over a longer period to provide data  to the user. A mHealth expert analyzed the apps and collected all the features which matched the taxonomy of the ideal diabetes management app. Features were flagged with a Boolean value depending on whether the app provided the analyzed feature. Occasionally, the mHealth expert was provided with clarification to ensure that the analysis was more precise.P=.42, F=.81). In the same way, the level 1 type of feature was not associated with the operative system .None from the 80 analyzed apps fulfilled the criteria of the taxonomy of an ideal app. Only BlueLoop had 9 out of the 10 ideal features in level 1. Level 2 features in Personalization were dominated by the Blood glucose diary , whereas Tailored advice was only present in 11.4% (8/70). If we look into level 3 Measurements in Personalization, only 0.1% (1/70) of the apps included Tobacco and Alcohol, and 17.1% (12/70) included a field for Years of diagnosis. With regards to Family support, 100.0% (30/30) featured Read access, and 26.7% (8/30) included Writing access to relatives.Fifty-one of 60 apps (85.0%) featuring Data management had the possibility of drawing charts with the stored measurements, and more than a half , offered the possibility of data exportation in several formats. Nearly a half  offered the possibility of storing data in the Cloud, and only 30.0% (18/60) had the option of calculating statistics.Level 2 features of Tips and support showed that not all the apps have a user manual , less than a half  provided Diet/food information, only 11.67% (7/60) had 24/7 Medical support specific for diabetes, and 18.3% (11/60) had Emergency support.All the Reminders  were for blood glucose and insulin schedule. A majority were for purchasing fungibles  and Appointments . Three of 3 (100%) provided Rewards inside the app, and only 1/3 (33.3%) gave Rewards in online markets.Apps were classified according to the number of level 1 features they offered. We conducted a systematic review to discover the features of the apps that had shown an effect in T1DM management. We found a big gap between research and market in the apps for supporting and empowering T1DM patients. While research is currently testing the effectiveness of mHealth in the improvement of clinical outcomes related to T1DM and therapy adherence, the characteristics of such apps are heterogeneous and not consistently justified. The systematic search discovered 6 studies consisting of mHealth interventions on 266 participants with a study duration ranging from 3 to 12 months. Studies described the app and assessed the user perceived usefulness of the app characteristics. Three of the 6 (50%) studies also reported on user satisfaction. Features of the apps were categorized and merged into a taxonomy of what would be an ideal app for T1DM management and patient empowerment .The newly proposed taxonomy featured 3 hierarchical levels, the first of which has 10 areas. Subsequent level 2 and level 3 features are embedded into level 1 features, enabling us to detail what type of feature is offered to the app user . Regarding the interaction of patients and health care professionals, we discovered apps including contact to and support from endocrinologists and diabetes educators . We thinP=.42, F=.81) nor the type of feature  with the app operative system. Level 2 features were highly heterogeneous, but we highlight the Blood glucose diary featured in 91.4% (64/70) of apps and the low rate of Tailored advice only present in 11.4% (8/70). Level 2 features of Tips and support showed that not all the apps included a user manual , less than a half  provided Diet/food information. Only 11.67% (7/60) offered 24/7 medical support specific for diabetes, and 18.3% (11/60) offered Emergency support. To our knowledge, this is the first comprehensive taxonomy specific definition of features and the first review exploring the availability of such features in commercial apps for mHealth interventions in T1DM.Moreover, this study explored systematically the features that are present in apps available at zero cost for users on the internet and mobile apps markets. Following the PRISMA approach, we found 80 apps which were analyzed in detail for 30 days. None of the assessed apps fulfilled the features of the taxonomy of an ideal app, but 1 featured 9 characteristics (BlueLoop). Personalization  and Data record  were the 2 top prevalent features, whereas Rewards  was the less predominant. We did not find an association on the number of features  relationship to technology, (2) how this relationship might make a difference to users, and (3) considering when it might not be a suitable mechanism to use . There iThe taxonomy of features was designed based on previous clinical interventions -17 whichIn 2017, Holtz et al  reportedGamification and coaching techniques are also a promising feature of mobile health apps for diabetes management. Sannino et al  introducThe review of apps allowed us to conclude that level 1 features in apps have a balanced distribution . HoweverIn this study, we have discovered Data record and Personalization as the most prevalent features in mHealth diabetes apps. This finding should be further explored to know how many of these apps that also offer a dashboard for professional management. A recent study has discovered a decrease of the consultation time in type 2 diabetes management by using artificial intelligence and predictive modeling ,28, and Finally, for the main purpose of disease management apps, rather than investigating the number of app features, we should investigate what kind of features could achieve the goal effectively. In our study, we were not able to distinguish which feature (or combination of features) was helping patients to achieve their goals. Acceptability and usability studies may help to identify the features that have a higher impact on the self-management of the disease, but further research should be conducted to critically identify the sets of features valuable for patients.A limitation of this study is the set of papers and apps selected for the literature review and the app review. The authors may have omitted significant contributions for both searches due to the incompleteness of the query commands and mismatch in the searches. We have focused our research on apps tested in RCTs with significant clinical end-points. Authors are aware of the relevant research done in the past and conducted in the present in the design of T1DM apps, which do not involve clinical endpoints nor RCTs, which may also contribute to the taxonomy of an ideal app defined in this paper. Another limitation is that the graphical user interface (GUI) of the apps are not evaluated or studied. If the GUI is not appropriate, many features might be less accessible and thus less used.This study assessed the existing gap between research and market in mobile health apps for the management of T1DM and the empowerment of patients. The mHealth has potential to support the management of T1DM, to catalyze the information exchange between patients, parents, and caregivers, and to empower and educate patients in the management of T1DM. The current landscape of apps for T1DM does not seem to be close to what researchers promote from RCTs and user-centered design. A majority of the apps mainly support the collection of measurements, and only a few of them offer a wide range of features for a personalize self-management. Rewards and social communities are not yet well adopted in market environments.


The present retrospective study evaluated the progression of osteoarthritis in stifle joints based on the radiographic grade of osteoarthritis (OA) scored in dogs with cranial cruciate ligament rupture. The aim of the study was to search for a correlation between the stage of radiographic osteoarthritis prior to surgery and the osteoarthritis progression occurring after the tibial tuberosity advancement (TTA) procedure. It was hypothesized that the procedure carried out in dogs in the early stages of OA could reduce the OA changes. A total of 190 X-ray images obtained from the medical records of 38 dogs were evaluated. The radiographic signs of osteoarthritis of 38 stifle joints were scored from 0 to 3 in 10 specific anatomic locations. The radiographs were divided into 4 groups based on the global scores: A) no-OA, B) mild-OA, C) moderate-OA, D) severe-OA; they were assessed prior to surgery, and 1, 2, 3 and 6 months post-operatively . There were no differences in osteoarthritis progression in Groups A and C at any time. Osteoarthritis changes from T0 to T6 were statistically significant in Group B. The OA changes in the anatomic locations were investigated. The most common anatomic sites for OA changes were the patella apex, the proximal and distal trochlear ridges, and the caudal aspect of the tibial plateau assessed before surgery. After surgery, the score increased in the first three locations in 10, 9 and 11 joints, respectively; instead, the progression of osteoarthritis in the caudal aspect of the tibial plateau occurred in 23 out of 38 stifle joints. The results indicated that the TTA procedure could be effective in slowing down the OA progression when carried out in the absence of or in the early stages of disease. Therefore, an early intervention may be suggested in clinical practice to obtain minimal or no progression 6 months postoperatively. Cranial cruciate ligament (CCL) rupture is one of the most common causes of hind lameness and secondary osteoarthritis (OA) in the stifle joints of dogs due to the instability of the joint –3. Many The progression of OA in CCL rupture has been assessed after conservative treatment, after extracapsular and intracapsular substitution techniques, and after osteotomy –12. The To the best of the authors’ knowledge, few studies have described the OA changes after TTA –19. In tThe aim of this retrospective study was to evaluate whether the stage of radiographic OA assessed prior to surgery could influence the OA progression occurring after the TTA procedure in dogs with spontaneous CCL rupture. It was hypothesized that TTA can lead to different results based on the degree of severity of the OA present before surgery. In particular, TTA carried out in dogs in the absence of or in the early stages of OA could slow the OA changes; early intervention would be ideal and suggested in clinical practice. Furthermore, the authors investigated the anatomic locations in the stifle joints in which the greatest radiographic signs of OA prior to surgery and their changes after TTA treatment were present.The medical records of dogs with unilateral CCL rupture treated with a TTA procedure were retrospectively reviewed. Records and radiographs from October 2015 through November 2017 were obtained from the archives of the Department of Veterinary Medical Sciences, University of Bologna, Italy. The inclusion criteria were the presence of standard mediolateral projection radiographs ,14 takenThe medical records included the informed consent form signed by each dog owner as required for procedures involving anesthesia. Furthermore, the owners were informed regarding the surgical protocol which did not include the arthrotomy procedure, but that it would be performed only in recurrence of lameness or subsequent meniscal tear.The exclusion criteria were incorrect/incomplete radiographic positioning, the presence of other concomitant orthopedic diseases, having undergone open arthrotomy and meniscal release, occurrence of major surgical complications, such as subsequent meniscal tear, and lameness in the contralateral hind limbs during the 12 months after surgery.All the surgical procedures were performed by the same experienced orthopedic surgeon using the standard TTA technique as described by Montavon in 2004 , with a After surgery, a modified Robert Jones bandage was applied to the limb for 24 hours. Exercise was strongly restricted until suture removal and was then controlled pending the 2-month follow-up.Computed radiographic images  were used to carry out all the radiographic studies, and a specific software program  was used to evaluate the DICOM images.The mediolateral projections were obtained with the joint flexed at 135°, directing the X-ray beam to the center of the medial femoral epicondyle, with superimposition of the medial and lateral condyles; a tolerance of 2 mm of condyle non-overlap was fixed ,27.Evaluation of the signs and progression of OA in the stifle joints was carried out by two veterinarians (a PhD Diagnostic Imaging Postgraduate and an experienced radiologist) who were blinded regarding the different time points. The worst OA score assessed by each radiologist was selected for the statistical analysis.Assessment of the OA was achieved considering the presence of osteophytosis and subchondral sclerosis in10 specific anatomic locations of the stifle joint . The preFor each location, a score from 0 to 3 based on the amount of new bone and bone density  was assigned . The stiThe global OA score of each radiograph was calculated as the sum of the scores obtained for each location  at each time point. The dogs were divided into 4 groups based on the scoring intervals: 0–3 (Group A: no-OA), 4–10 (Group B: mild-OA), 11–20 (Group C: moderate-OA) and 21–30 (Group D: severe-OA).In addition, two groups were created on the basis of cage size: cages less than 9 mm wide  and cages greater than 9 mm wide (Large Cage group).Finally, each anatomic location was evaluated at each time point, and the data were used in order to find the site of the greatest OA changes.Breed, gender, age, weight and limb data were collected. The results from the descriptive statistics were reported as mean, standard deviation (SD) and range.P > 0.05). An analysis of variance (ANOVA) for repeated measures was used to compare the scores of the OA during the five evaluations . The Kruskall-Wallis test was used to investigate the changes in the OA scores for non-parametric data , and the Chi-squared test was used to compare the distribution of the categorical data. The weighted kappa statistic (κ), with 95% confidence interval (CI) [The data were analyzed using a statistical software program . Normal distribution was assessed by means of Levene’s Test  , was useP < 0.05.The dogs were also analyzed individually to identify OA progression of at least one score interval, and to find a correlation between the OA changes and both the duration of lameness and the size (width) of the cage employed. Significance for all the analyses was set at Thirty-eight dogs (38 stifle joints) met the inclusion criteria for the study, and a total of 190 X-ray images were collected. The most common breeds included mixed-breed dogs (n = 9), American Staffordshire Terriers (n = 5), Labrador Retrievers (n = 6) and Cane Corsos (n = 3); other breeds were Australian Shepherds, Beagles, Bernese Mountain Dogs, Border Collies, Boxers, Dogues de Borgeaux, German Shepherd Dogs, Golden Retrievers, Maremma Sheepdogs and Rottweilers (n = 1 or 2 dogs/breed).There were 13 intact males and 3 neutered males, 16 unspayed females and 6 spayed females. The mean age was 5.9 yrs ± 2.5 (range: 2–13 yrs) and the mean body weight was 34 kg ± 9.5 (range: 15–54 kg). The mean duration of lameness prior to surgery was 86.5 days ± 98.6 (range: 1–365 days), 20 dogs presented lameness of 15.3 days ± 11.8 (range: 1–30 days) duration (short term: < 30 days) and 18 dogs showed lameness of 165.5 days ± 91.7 (range: 60–365 days) duration (medium-long term: > 30 days).The TTA procedure was performed on 16 right stifle joints and on 22 left stifle joints.The widths (mm) of the cages used were: 6 mm (n = 8), 7.5 mm, (n = 5), 9 mm (n = 9), 10.5 mm (n = 12) and 12 mm (n = 4).The mean of the OA global scores of the 38 stifle joints was 6 ± 0.5 (range: 0–17) at T0 and 8.9 ± 5.4 (range: 0–19) at T6. The inter-observer agreement for the OA score was good, with κ = 0.84 (95% CI 0.70–0.99).P < 0.001) between the groups. Significant differences were not found between the groups in the distribution of gender, age and body weight. There was a correlation between the duration of lameness and the severity of OA (P = 0.04).The number of stifle joints in the groups according to the scoring intervals of OA were listed in P < 0.001). Nevertheless, an overall evaluation revealed that 25 (65.8%) of the 38 stifle joints preserved their stage of OA between the preoperative and postoperative time periods, and only 13 (34.2%) of the 38 stifles increased their stage of OA by 1 score interval (5 stifles from no-OA to mild-OA and 8 stifles from mild-OA to moderate-OA). No severe-OA was recorded ; however, in Group B, there were significant OA changes from T0 to T3 and T6 (P < 0.001)  .P > 0.05). Moreover, the OA scores were not significantly different between the small and the large cage groups at either time point (P = 0.64 at T0 and P = 0.88 at T6). No correlation was found between the size of the cages and the weight of the dogs: very weak  and weak  in small and large cage groups, respectively.Twenty-two out of the 38 stifle joints were in the Small Cage group and 16 of the 38 stifles were in the Large Cage group. Analysis of contingency table did not find any correlation between the size of the cage used to advance the tibial tuberosity and the change in OA in either group (P < 0.05) in all locations, except for the cranial aspect of the tibial plateau, the popliteal surface femur and the sesamoid bones in which the OA changes were not significant  in the patella apex, in the proximal and distal trochlear ridge, and in the caudal aspect of the tibial plateau. The OA in these locations was greater than in the other locations (mean scores > 0.7). After the TTA procedure, the distal trochlear ridge, the femoral condyle and the caudal aspect of the tibial plateau revealed significant OA progression at T3. Furthermore the OA progression was statistically significant at T6  did not show statistically significant OA progression after TTA for treatment of CCL rupture. The literature has reported that joint stability could play an important role in the reduction of OA development, sustaining the goal of repairing the CCL rupture in order to restore function and prevent subsequent damage to the articular cartilage and the periarticular structures . InverseIn the present study, progression was small, but significant, in the stifle joints with mild OA prior to surgery (Group B). There was an increase in the severity of radiographic signs of OA in less than half (8 stifles out of 19) similar to other reports ,18,30. TThe OA development is attributed to several variables. Age, body weight, duration of lameness, meniscal injury, and surgical procedure such as meniscal release, meniscectomy and arthrotomy, have been described as potential risk factors for the development of OA in an affected stifle joint ,32,34–37Both meniscectomy and meniscal release had an effect on the progression of the osteoarthritis ,37 so muAn arthrotomy procedure could also influence OA changes. Open arthrotomy can result in high morbidity in clinical outcomes and predispose to increasing OA progression as compared to both arthroscopy and limited caudal arthrotomy ,35. It hIn the present study some limitations should be noted. This retrospective study was designed in an attempt to contain the incidence of the aforementioned. The first limitation was that only dogs with intact menisci were enrolled in the study. Dogs which had undergone open arthrotomy, meniscectomy and meniscal release did not meet the inclusion criteria. The aim of this rigid process of the choice of dogs was to select a homogenous group to study and to assess the effects of TTA on OA development. It is well known that this would not reflect the real population of CCL rupture in dogs. The second limitation was that the diagnosis of intact menisci was reached on the basis of clinical and/or ultrasonography evaluations rather than on arthroscopy or open arthrotomy. Although clinical and ultrasonography examinations have good sensitivity and specificity  some meniscal injuries could be mis-diagnosed. However, in the present study, the absence of lameness or major surgical complications, such as a subsequent meniscal tear, during the 12-month follow-up, could suggest the accuracy of the meniscal evaluation. The third limitation of this study was that dogs with suspicion of a partial tear of the CCL were excluded. Aware of a possible mis-diagnosis, the cranial drawer shown in both flexion and extension as a sign of complete rupture of CCL was the first point for the recruitment of the dogs. Dogs with a cranial drawer presented only in flexion were excluded, being indicative of torn craniomedial band and an intact caudolateral part . FinallyAs expected, a direct correlation between the severity of OA score and the duration of lameness was found in the present study. In the literature, there are some discrepancies in this correlation. Hoffmann reported that the length of lameness time contributed to the OA score on the preoperative radiographs , contrarIn the present study, no correlation was found between OA development and the size of the cage used to advance the tibial tuberosity. This finding could be suggestive of the accuracy of the preoperative planning and support the biomechanical concept of neutralization of the cranial tibial thrust force ,9,43. DeIn order to obtain more information, the identification of the anatomic locations in the stifle joint in which the greatest progression of OA appeared after surgical repair of the CCL rupture with a TTA procedure was carried out. The authors of the present study agreed with the literature regarding the sequence of the appearance of osteophytes in the specific locations of the stifle joints with CCL rupture. In particular, at the beginning of this study (T0), the OA signs were already evident in the patellar apex, and the proximal and distal trochlear ridges in which the periarticular osteophytes appeared early in the stifles with CCL rupture ,14,15,47The patellar apex, the proximal and distal trochlear ridges and the caudal aspect of the tibial plateau showed a significant increase in OA six months (T6) after surgery, but an individual evaluation revealed that the changes were produced in only a small number of cases. These results could be explained on the basis of the following observations.First, the increasing tension on the patellar tendon consequent to the CCL rupture could have been the cause of the early OA signs in the patellar apex. There are no biomechanical studies which demonstrate the influence of the TTA on tendinous stress, but it has been hypothesized that the altered anatomy created by the TTA procedure could lengthen the lever arm and decrease the stress on the patellar tendon ,48,49. TSecond, similar results were found in the proximal and distal trochlear ridges in which 29 (76.3%) and 27 (71.1%) of the 38 stifles, respectively, preserved the score from T0 to T6. As a result of the TTA procedure, the patella is distanced from the trochlear groove; thus the retropatellar force on the cartilage of the trochlear groove decreased –51. The Third, the different trend in the caudal aspect of the tibial plateau in which the OA increased in 23 (60.5%) of the 38 stifles was interesting. Although the modification of the stifle geometry obtained with the TTA procedure has the aim of neutralizing the cranial tibial subluxation , it doesIn conclusion, the results of this study suggested that the TTA procedure could reduce the development of OA for least 6 months after surgery when performed on dogs without either meniscal lesions and radiographic signs of OA or with OA in an early stage at the time of surgery. In agreement with the literature, the TTA procedure carried out in dogs with mild OA did not halt OA progression but it advanced slowly over time without reaching high scores. The ability of the TTA procedure to reduce the progression of OA is obvious in cases of moderate OA at the time of the surgical treatment, in which no changes in the stage of OA were recorded after surgery.In light of these findings, it is reasonable to assume that the initial stage of osteoarthritis can influence the effectiveness of the TTA procedure; however, additional studies should be carried out to evaluate the effects of TTA over the long-term.


Meanwhile, the high efficiency and high precision of the presented approach become more obvious with the increasing simulations. The efforts of this study provide a promising approach to improve the dynamic reliability analysis of complex structures.To reveal the effect of high-temperature creep on the blade-tip radial running clearance of aeroengine high-pressure turbines, a distributed collaborative generalized regression extremum neural network is proposed by absorbing the heuristic thoughts of distributed collaborative response surface method and the generalized extremum neural network, in order to improve the reliability analysis of blade-tip clearance with creep behavior in terms of modeling precision and simulation efficiency. In this method, the generalized extremum neural network was used to handle the transients by simplifying the response process as one extremum and to address the strong nonlinearity by means of its nonlinear mapping ability. The distributed collaborative response surface method was applied to handle multi-object multi-discipline analysis, by decomposing one “big” model with hyperparameters and high nonlinearity into a series of “small” sub-models with few parameters and low nonlinearity. Based on the developed method, the blade-tip clearance reliability analysis of an aeroengine high-pressure turbine was performed subject to the creep behaviors of structural materials, by considering the randomness of influencing parameters such as gas temperature, rotational speed, material parameters, convective heat transfer coefficient, and so forth. It was found that the reliability degree of the clearance is 0.9909 when the allowable value is 2.2 mm, and the creep deformation of the clearance presents a normal distribution with a mean of 1.9829 mm and a standard deviation of 0.07539 mm. Based on a comparison of the methods, it is demonstrated that the proposed method requires a computing time of 1.201 s and has a computational accuracy of 99.929% over 10 Creep is induced by the excessive plastic deformation of high-temperature components in an aeroengine, and seriously influences the performance of blade-tip radial running clearance (BTRRC) and aeroengine. Therefore, effectively designing and controlling the BTRRC is significant in the development of high-performance and high-reliability aeroengines . Under aWith the development of probabilistic design in structural reliability ,6,7,8,9,With the development of artificial intelligence, the presence of generalized regression neural network (GRNN)  opens thTo improve the computational efficiency and precision of BTRRC dynamic reliability analysis with many objects, multiple disciplines, high nonlinearity, transients, and hyperparameters, this paper proposes distributed collaborative generalized regression extreme neural network (DCGRENN) method, by incorporating both the highly nonlinear mapping ability of ERSM and the MOMD coordination potential of DCRSM. In the DCGRENN, the GRENN is used to handle the transient problem by simplifying the response process as one extremum value and address the nonlinearity by the nonlinear mapping capacity. The thought of DCRSM is applied to handle MOMD analysis with hyperparameters and high nonlinearity by decomposing the “big” model into a series of “small” sub-models with few parameters and low nonlinearity. The DCGRENN is employed in order to carry out the reliability analysis of turbine BTRRC subject to the creep behaviors of structural materials by considering the randomness of influencing parameters. In addition, the comparison of methods is conducted to validate the DCGRENN. The remainder of this paper is organized as follows. The theory and method of DCGRENN are discussed in ε of structural materials with time t, as explained in In mechanical strength, the creep of a structure is the permanent deformation of aeroengine turbine structures induced by high temperature load when the stress is less than yield strength . ObviousiC  is the parameter of material creep; T is test temperature.In engineering, the Norton implicit model is usually adopted to express the second constitutive relation of structural materials , i.e., under cyclic loading, the creep data are obtained. Based on the least squares method , the creC1, C2 and C3), the creep model of GH4133Bis built as presented in Equation (1), and this will be used in the calculation of blade-tip clearance in the investigation below, regarding GH4133B as the material of the BTRRC. With respect to the obtained creep parameters  is a nonlinear regression-based feedforward neural network model, including an input layer, a hidden layer, and an output layer . The GRNX and T are the matrices of input samples and output samples, respectively; Q × R indicates the dimensions of matrix LW1,1, which is the weighted matrix in the hidden layer, where Q and R are the numbers of training samples and input parameters, respectively; ||dist|| denotes the Euclidean distance function; b is the threshold of Q neural cells in the hidden layer; n1 expresses the network vector of the hidden layer; △ indicates the transfer (Gauss) function; a1 is the output of the neuro cell; S × Q indicates the dimensions of the matrix LW2,1, which is the connection threshold value between the hidden layer and the output layer, where S is the number of output parameters; nprod is the weight function of the output layer; n2 indicates the network vector of output layer; Θ is the purelin transfer function of the output layer; y = a2 explains the outputs of the neuro cell in the output layer. The input layer transmits the sample X into the hidden layer, in which one nerve cell has one sample and there are Q nerve cells. In the process of transmission, the transfer function is a Gauss function with the matrix of weights b. The third layer is the output layer to which the information is transferred from the hidden layer with respect to the matrix of weights LW2,1. Herein, the weight function is the normalized dot product function denoted by nprod.In jth output jn of the GRNN model, the mathematical model of GRNN for the response of the jth group of training samples is expressed byexp is the natural exponential function; Q nerve cells corresponding to the jth group of input samples, in which i = 1, 2, …, Q) is the ith element in With respect to the line transfer function Since dynamic probabilistic analysis is a random process, it is difficult to resolve the probabilistic analysis of complex structures by directly adopting the GRNN method. In this case, the traditional approaches involve fitting a large number of response surface models in the time domain, and then artificially selecting the response at one time point as the probabilistic computing point . Howeverith input sample in the time domain  and Q is the number of samples. In i indicates the ith training sample; j expresses the ith random variable. Based on the mathematical model of GRNN in Equation (2), the mathematical model of GRENN isAlthough the GRENN method holds promise with respect to solving the transient problem in structural dynamic probabilistic analysis, it still poses one challenge in handling the dynamic probabilistic analysis of structural systems involving multiple objects, multiple disciplines, and hyperparameters. If the GRENN is directly applied to the probabilistic analysis of MOMD structure, it is unworkable for effectively dealing with the analysis problem of many objects and multiple disciplines simultaneously. To address this issue, the DCGRENN method is developed by integrating the thoughts of DCRSM  and GRENm (m∈Z) objects (substructures) and the analysis of each object involves n (n∈Z) disciplines, with respect to the DC strategy, the complicated MOMD analysis is transferred into a series of simple SOSD analyses. When Xpq), the DGRENN model is defined asqth discipline in the pth object as the random input variables pth object model analysis, i.e.,Regarding the output responses pth object, the response surface function (DGRENN) of objects isWhen Similarly, regarding the outputs From the above analysis, the whole GRENN model in Equation (4) is divided into many small GRENN models, such as the DGRENN models in Equations (7) and (9) and the CGRENN model in Equation (11), to address the dynamic probabilistic analysis of complicated MOMD structure. This method is called the DCGRENN method in this paper. Yd(t), Yb(t) and Yc(t) are the radial deformations of turbine disk, blade and casings at time t, respectively, the deformation of BTRRC τ(t)  , in whicIn line with the proposed DCGRENN method, the flowchart of the reliability analysis of BTRRC is structured in Step 1: Structure the FE models of the turbine disk, blades and casings through the decomposition of the BTRRC analysis problem into the radial creep problems of the three objects ;Step 2: Implement the thermal-structural coupling deterministic analysis of the three objects in the time domain  to acquire the change rule of BTRRC and determine the computing point with the minimum BTRRC by considering the input random variables , the related boundary conditions, and multiple disciplines ;Step 3: Extract the handful of samples for the random input variables by Latin hypercube sampling (LHS) technology [chnology , to perfStep 4: Normalize the training samples to obtain the optimal smooth factors, the weighted values in the hidden layer and the connection weights between the hidden layer and the output layer using the cross-validation method [n method , and theStep 5: Check the precision of each object model. Return to Step 3 if the computational accuracy does not satisfy engineering requirements, or continue to Step 6;Step 6: Conduct reliability analyses of the three objects’ radial creep deformations with the DGRENN models to obtain the distribution features of the maximum output responses;Step 7: Establish the collaborative generalized regression extremum response surface (CGRENN) model ) of BTRRC by adopting coordinative method to coordinate the three DGRENN models;Step 8: Implement the reliability analysis of BTRRC with the required CGRENN model by performing enough simulations and considering the creep deformations of the turbine disk, blades and casings as random input variables.As shown in ω, gas temperature T, heat conductivity coefficient λ, elasticity modulus E, convective heat transfer coefficient α, and material density ρ, are considered to be random input variables. These are assumed to be mutually independent and to follow normal distributions. The distribution characteristics of the variables are listed in T stand for the temperatures on the areas of A1, A2, A3, B1 and B2, respectively, and the subscripts d1, d2 and d3 of α indicate the convective heat transfer coefficients on B1, B2 and B3 on the disk model, respectively. For the variables of the blade, the subscripts b1, b2, b3 and b4 are the locations B1, B2, B3 and B4 on the blade model, respectively. In the variables of the casing, Ti and To are the temperatures inside and outside the casing rings respectively, and the subscripts c1, c2, c3, c4 and o of α indicate the convective heat transfer coefficients on segments A, B, C and D and the outside of casing ring.In this paper, many parameters, such as rotational speech Yd(t), Yb(t) and Yc(t) with time are shown in δ = 2.0 mm, in line with Equations (12) and (13), the variation of BTRRC Y(t) with time are required in In the deterministic analysis of aeroengine BTRRC, the aerodynamic load was ignored because it is not significant in terms of its contribution to the stress for the turbine disk and casing, in comparison to the temperature load and the centrifugal load . With ret = 180 s, the BTRRC reaches its minimum and increases a bit when the aeroengine starts to cruise. Obviously, the dangerous point with respect to BTRRC occurs at t = 180 s, at which point gas temperature and rotational speech reach their maximum. The creep deformations of three objects at t = 180 s are shown in As illustrated in t = 180 s, the maximum creep deformations of the turbine disk, blade and casing were 1.765 mm, 1.4892 mm and 1.2716 mm. At that point in time, the maximum creep deformation of BTRRC is 1.9826 mm. Therefore, t = 180 s was selected as the computing point for BTRRC reliability analysis in this paper.As revealed in With respect to the distribution features of random variables in LW1,1 was computed using the Euclidean distance function [LW2,1 of the hidden layer and the output layer. To avoid excessive modeling error, the data of the acquired samples were normalized. The normalized data were applied in order to train the DGRENN model by computing the parameters of DGRENN using the cross-validation method [LW1,1 in the hidden layers of three objects , the weight matrix LW2,1 in the output layer, and the threshold matrix b, which are illustrated in Along with the theory and concept of the DCGRENN method and BTRRC reliability analysis, in the GRENN model, the Gauss function is selected as the transfer function in the hidden layer, in which the weights matrix function ,34,35. Tn method . Finally4 times using the MC method in order to complete the dynamic probabilistic analysis of the three objects  and then to acquire the creep deformations of objects. The histograms of creep deformations are shown in Yd, Yb and Yc are displayed in The DGRENN models, instead of the FE models, were simulated 104 simulations using the MC method. Based on this analysis, the history simulation graph, histogram and probabilistic cumulative graph of the maximum creep deformation of BTTRC at t = 180 s are shown in In line with the DCGRNN method, the creep deformations of three objects were considered as the inputs of BTRRC reliability analysis. Equations (12) and (14) are regarded as the CGRENN models of BTRRC probabilistic analysis with 10δ = 2.2 mm. On the basis of engineering experience, these results are basically appropriate for BTRRC design and control.As shown in ® Core™ i7-8400 processor and 16 GB RAM (Random Access Memory). The computing precision and the time required by the three methods were assessed under different simulations  with static blade-tip clearance δ = 2.2 mm. The analytical results are listed in 4 simulations, the computing precision To validate the DCGRENN method, the reliability analyses of BTRRC were conducted using the MC method, the distribution collaborative response surface method (DCRSM) , and the2 simulations to 106 simulations, the DCGRNN method only increased about two-fold, while the DCRSM increased more than 100-fold. Additionally, it is amazing that the MC method increased more than 100-fold from 102 simulations to 104 simulations; (2) DCRSM and DCGRENN required far less time that the MC method to carry out the same number of simulations, because surrogate model-based simulation is easier and faster than FE-based simulation. This is why the surrogate model was used to perform the reliability analysis of BTRRC in this study; (3) the MC method cannot conduct the probabilistic analysis of BTRRC when the number of simulations is larger than 104, due to the unaffordable computational burden. In this case, the results of 104 FE simulations were used as a reference for assessing the computational time and efficiency of the other methods in this study, because the credibility of reliability analysis is positively correlated the number of FE simulations in engineering reliability design; (4) the developed DCGRENN method showed greater computational efficiency than DCRSM, and the strength of the DCGRENN method was more obvious with the increase in the number of simulations, since the speed of GRNN in simulation is a result of its advantage of a small number of samples relative to quadratic polynomials.As seen in 4 simulations. It should be noted that the DCGRNN method is better able to ensure computing precision for small simulations. For example, the DCGRENN method is improved by 2.017% at 100 simulations. The reason for this is that the GRENN has good properties with respect to the handling of highly nonlinear and transient problems in structural dynamic probabilistic analysis, and the DC strategy is able to process MOMD analysis problems for complicated structures by reducing the nonlinearity.As revealed in In conclusion, the proposed DCGRENN method is able to improve the precision and efficiency of the reliability analysis of complex structures, in addition to the BTRRC, in aeroengines.The aim of this paper was to develop a distributed collaborative generalized regression extremum neural network (DCGRENN) method by integrating the generalized regression extremum neural network with nonlinear fitting ability and a small numbers of samples with the distributed collaborative response surface method with multi-object multi-discipline coordinative capability. The developed approach is applied in order to improve the efficiency and precision of the simulations for the purpose of high-pressure blade-tip radial running clearance reliability analysis subject to creep behavior. The main conclusions are summarized as follows:t = 180 s. At this moment, the maximum creep deformation of the blade-tip clearance was 1.9826 mm. This study selected t = 180 s as the computing point of the blade-tip clearance reliability analysis. The creep-based dynamic reliability analysis of the blade-tip clearance reveals that the creep deformation of blade-tip clearance obeys the normal distribution with the mean of 1.9829 mm and the standard deviation of 0.07539 mm, and the reliability degree of the blade-tip clearance was 0.9909 when the steady blade-tip clearance δ was 2.2 mm, which provides a significant reference for blade-tip clearance design in engineering.From the deterministic analysis of blade-tip clearance with creep, it is illustrated that the maximum creep deformations of the turbine disk, blade and casing were 1.765 mm, 1.4892 mm and 1.2716 mm at 4 simulations in blade-tip clearance reliability analysis, owing to the capabilities of the generalized regression extremum neural network in terms of addressing highly nonlinear analysis problems.With respect to computational efficiency, the method developed in this study was validated to have high computational efficiency in the dynamic probabilistic analysis of complex structures, thanks to the strengths of the generalized regression extremum neural network and the distributed collaborative strategy. With respect to computing precision, the proposed method was higher by 1.23% than the distributed collaborative response surface method under 10