The COVID-19 pandemic has called for swift action from local governments, which have instated non-pharmaceutical interventions (NPIs) to curb the spread of the disease. The swift implementation of social distancing policies has raised questions about the costs and benefits of strategies that either aim to keep cases as low as possible (suppression) or aim to reach herd immunity quickly (mitigation) to tackle the COVID-19 pandemic. While curbing COVID-19 required blunt instruments, it is unclear whether a less-transmissible and less-deadly emerging pathogen would justify the same response. This paper illuminates this question using a parsimonious transmission model by formulating the social distancing lives vs. livelihoods dilemma as a boundary value problem using calculus of variations. In this setup, society balances the costs and benefits of social distancing contingent on the costs of reducing transmission relative to the burden imposed by the disease. We consider both single-objective and multi-objective formulations of the problem. To the best of our knowledge, our approach is distinct in the sense that strategies emerge from the problem structure rather than being imposed a priori. We find that the relative time-horizon of the pandemic  and the relative cost of social distancing influence the choice of the optimal policy. Unsurprisingly, we find that the appropriate policy response depends on these two factors. We discuss the conditions under which each policy archetype (suppression vs. mitigation) appears to be the most appropriate. The COVID-19 pandemic has called for swift action from public health officials, who have instated Nonpharmaceutical Interventions (NPIs) to curb the spread of SARS-CoV-2 (the virus that causes COVID-19). Because blunt NPIs  have far-reaching consequences, the question of how society should use the available instruments to curb SARS-CoV-2 transmission has been met with a deluge of research and controversy.3. Suppression strategies seek to reduce transmission as much as possible while treatments and/or vaccines are not available through measures such as lockdowns, social distancing mandates, and mask-wearing. Countries known for their strong suppression strategies include New Zealand, Australia, South Asian countries, and others. A mitigation  approach attempts to limit the impacts of the disease on the most vulnerable members of the population while allowing the disease to spread, hoping to balance the costs and benefits of social distancing measures4. The argument underlying this strategy is that social distancing would be too expensive to contain transmission relative to the cost of infection for the average person. For COVID-19, suppression strategies have deserved and received overwhelming support in the scientific community due to the high death rates caused by the disease, the imminent threat to the stability of health systems and continued uncertainty about the duration of immunity acquired through infection5. As the COVID-19 pandemic demonstrated, countries that relaxed suppression strategies too soon  went through worst-case scenarios where health care was severely impacted, and excess death soared7.Broadly, two classes of strategies emerged from this debate: suppression and mitigation13. While infectious disease models traditionally do not allow for endogenous behavioral response to the pandemic14, infectious disease modelers often account for the most biologically-relevant features of pandemics, including heterogeneity in contact rates and disease severity, and stochasticity in contacts. Infectious disease modelers often focus on model inference using computational-intensive inference approaches. Dynamic macroeconomic models that include infectious diseases also offer a useful framework for evaluating social distancing strategies. Starting from an intertemporal utility maximization problem, dynamic models can be used to demonstrate how a society composed of rational individuals would respond to a pandemic16.This paper sits at the intersection of two research fields that have an outsize role in justifying non-pharmaceutical interventions, namely, infectious disease modeling and macroeconomic modeling. Infectious disease models start with a mechanistic description of how a pathogen percolates in society and can be calibrated to data to reproduce the dynamics of a pandemic. During the COVID-19 pandemic, these models have been used to assess tradeoffs associated with pre-specified non-pharmaceutical intervention policies17. Prior work in economic epidemiology can be divided into pre-COVID-19 and post-COVID-19 eras. Much of the work pre-COVID-19 focused on vaccination behavior and decisions19, with some analyses of NPI behavior without a central planner.20 Since COVID-19, many analyses have examined optimal social distancing behavior and policies in the specific context of COVID-19. Most of these setup problems are solved with dynamic programming methods. Dynamic programming is an exhaustive method for optimization but is also computationally intensive.24 It requires the definition of discrete time steps, and the solution may depend on this choice. In contrast, we propose a parsimonious model where a central planner seeks to find a time-varying social distancing policy minimizes the costs of social distancing and infection, which can be solved with variational calculus. Variational calculus is a continuous time model formulation that can be more computationally efficient than dynamic programming methods. This enables us to solve the model for a large sample of parameter space. We solve this model over 4212 combinations of model parameters to investigate how the choice of the strategy to govern nonpharmaceutical interventions depends on a set of biological and economic inputs. In our framework, the optimal social distancing strategy depends on the central planner’s assessment of the time-horizon of the pandemic  and the costs of NPI measures relative to the social cost of infections. We also present a multi-objective formulation that considers trade-offs between the total amount of social distancing and the total proportion of the population infected. The calculus of variations BVP formulation enables us to illuminate the relationship between the single objective and multi-objective formulations and better understand the multiple local minima that arise for some sets of parameters in the single objective formulation.This paper seeks to contribute to the emerging economic epidemiology modeling fieldThis paper couples an infectious disease model with a model describing how a central planner would change their social distancing strategies over time. Our analytical structure pairs a deterministic SIR model with a variational calculus approach to optimize a cost function. The dynamic social distancing strategy is defined by the solution to a boundary value optimization problem (BVP). The central planner assumes a final time horizon of the pandemic  and relative costs of social distancing .While this framework is not meant to capture the complexity of heterogeneous human behaviors or the stochasticity of epidemics, it provides insight into a central planner’s optimal strategy. We show later that strategies that could be interpreted as suppression and mitigation strategies emerge from this simple model. There is a fast switch from mitigation to suppression strategies as the cost of social distancing and the time-horizon of the pandemic decreases.In this section, we present results from both single-objective and multi-objective optimizations. We first present results from our single-objective optimization analysis using the baseline parameter values. We then present the main outcomes of the single-objective optimization for a wide range of parameter values. We performed 4212 optimization experiments to assess how the optimal social distancing policy changes due to economic and epidemiological conditions, as represented by a reduced set of model parameters. Finally, we present results from a multi-objective optimization and show the relationship between these results and the single-objective results.Figure c, the cost of social distancing compared to the cost of infection. Social distancing is the greatest  values of the proportion of the population infected, underscoring the dichotomy of the mitigation vs. suppression strategies found in the single-objective formulation.Figure The results presented revealed the characteristics of optimal social distancing policies under various conditions by formulating the social distancing policy decision as a boundary value problem. In this parsimonious model, a central planner balanced the costs of social distancing against the burden imposed by the disease. To the best of our knowledge, our paper is unique in using a parsimonious calculus of variations approach to examine conditions where a rational central planner would choose a suppression or mitigation strategy. Because this approach does not impose a constraint in the functional form of the solution or impose a discrete time step on which the decisions can be made, social distancing strategies emerge from the problem structure and parameters rather than being imposed a priori. Qualitatively, the results we found in the suppression regime and the mitigation regime are consistent with the findings of prior studies.Perceived time-horizons and relative costs shape society’s response to the pandemic. The most salient finding from the model was that the perceived time-horizon and costs of social distancing provoke a switch from mitigation to a suppression strategy with higher costs of social distancing and a longer epidemic time horizon. This sharp switch from mitigation to suppression might make it challenging for a central planner to maintain the trust of the population in a pandemic with characteristics that fall close to the edge of the frontier revealed in Figure Optimal strategies are decisive in an idealized setting. In this mathematical exercise, society’s response to the pandemic was smooth and decisive, meaning that policymakers did not start with blunt lockdowns only to reverse course a few weeks later and instate restrictions again. Therefore, our model does not reproduce policies seen in the real world, including policies that adaptively imposed and lifted social distancing orders. Adaptive policies25 and policies with fast periodic switching27 were tested in our previous work. One possibility is that more nuanced models would reveal situations in which adaptive and periodic policies are optimal and our simplified analytic machinery is not equipped to identify such policies. This aspect should be investigated with further analysis, specifically with more nuanced models that include heterogeneity and stochasticity.Completely uncontrolled pandemics are not optimal. Under the assumptions made in this modeling exercise, completely uncontrolled pandemics were not found to be Pareto optimal - that is, society always did something to abate the consequences of the pandemic. While this result is a consequence of our model’s deterministic and continuous nature, it reproduces findings from existing macroeconomic models (see16).Optimal suppression strategies do not holdindefinitely. Early in the COVID-19 pandemic, to disseminate basic concepts of epidemiology to the population, a common view was that society ought to keep COVID-19 cases from growing, and economists have gone a step further to propose that keeping 28 is necessary. While this seems a reasonable statement, our findings do not corroborate the idea that indefinitely at all costs. As noted in figures near zero-infections at the beginning of the epidemic and then later allowed a modest and controlled rise in infections. This finding also is in line with other studies which found that robust COVID-19 reopening strategies had time-varying reopening thresholds with more stringent thresholds at the start of the pandemic and less stringent thresholds towards the end of the pandemic29.mentclass2pt{minimmentclass2pt{minimUncertainty, complexity, and heterogeneity will result in thorny policy tradeoffs. Based on our findings, one might imagine that a simplified optimization framework such as the one used in this paper will provide a rational approach to support decision-making during the next pandemic. If the costs of social distancing relative to the costs of infection are known and if the time-horizon to a vaccine and the disease parameters are set, and if the model structure is correct, then this framework could provide rational decision support to provide optimal policies. However, we warn the reader that none of these assumptions will hold during the onset of the next pandemic. While the optimization structure used in this paper allows for mathematical tractability, both the costs and the time-horizon of a pandemic are uncertain, heterogeneous quantities. Pandemics will be relatively more costly to societies that cannot mitigate the economic costs of social distancing with income support policies financed by debt.30. The result is that different countries will be positioned at different regions in the parameter space we presented. This heterogeneity predictably could cause countries to be forced into different strategies. Moreover, within-country dynamics can also play an important role, with different jurisdictions adopting different strategies. The corollary of these factors is that the world will not adopt a single best social distancing strategy, and chaotic behavior should be expected. In light of these findings, however, one can still resort to decision-making approaches that seek to find policies that are robust to these uncertain factors but achieve acceptable performance25.Similarly, wealthy nations will have access to treatments and vaccines before other nations. And, the costs and benefits of social distancing strategies are not equal for every country25. On a global scale, efforts to expedite the development and global distribution of vaccines can ease the tradeoffs faced by low-income countries.While our framework reveals those tradeoffs mathematically, more work is needed to emphasize how policy options could ease those tensions. At a local scale , policymakers can still resort to decision-making approaches that seek to find policies that are robust to the Uncertainty in the global response to the pandemic but achieve acceptable local performance, as demonstrated elsewhere16. Similarly, a previous study that evaluated a wide range of scenarios found that non-dominated reopening strategies tended to start with stringent reopening thresholds and ended by relaxing interventions towards the end of the pandemic25.Although we are not aware of other modeling studies that used the same approach as this paper, our results share similarities with the results found through other modeling paradigms. For example, an existing SIR-macro dynamic modeling study found that optimal containment policies exhibit a sharp initial effort to contain the pandemic in the first few weeks, with a subsequent relaxationThe COVID-19 pandemic has affected billions of people worldwide and has been unprecedented in scale and duration. During the early stages of the pandemic and in the absence of a vaccine, policymakers had to take extraordinary measures, implementing a range of non-pharmaceutical interventions (NPIs) to mitigate deaths caused by the spread of the highly transmissible virus (SARS-CoV-2). These measures included mask-wearing and social distancing policies ranging from partial closings to complete lockdowns.Despite the deluge of research on COVID-19 policy, the effectiveness of policies as applied to COVID-19 will only partially inform the decision to suppress or mitigate the next pandemic. A new pandemic may bring surprises and different epidemiological characteristics, and the evidence created for COVID-19 might not translate directly to new pathogens with other properties. The intuitive and potentially misleading inclination is to learn what worked for COVID-19 and immediately apply those lessons to a new pandemic. An alternative and complementary learning mode is to understand the fundamental properties of the decision problem we faced in the COVID-19 pandemic and ask how epidemiological and economic parameters should determine our choices in a new pandemic.As seen in the COVID-19 pandemic, social distancing remains a critical intervention to mitigate the spread and deaths caused by a novel, highly transmissible infectious disease. However, prolonged social distancing can lead to significant declines in social well-being and widespread economic hardships and uncertainties. Under these circumstances, policymakers need to make the discomforting decision of social distancing intervention policies that make a tradeoff between lives and livelihoods.In this paper, we investigated how the choice of the strategy to govern NPIs changes depending on a central planners’ assessment of the time-horizon of the pandemic  and the costs of social distancing measures relative to the social cost of infections. In our model, which assumes that society is populated by hyper-rational agents and governed by a rational policymaker, we have found that both mitigation and suppression strategies are possible. Mitigation strategies occur when the central planner believes that social distancing is too costly or if the pandemic would take too long to curb. These results point to the importance of public messaging. They also provide an internally consistent mathematical explanation of why NPIs have enjoyed low popularity and adherence in some world areas.31 epidemic model describing disease transmission with cost functions describing both costs of infections and costs of social distancing specified over the time horizon of interest.Here we provide a brief outline of our approach. The supplementary methods provide mathematical details that will interest infectious disease modelers and mathematicians. To solve our boundary value optimization problem, we use a variational analysis approach, a mathematical technique used to derive functions that minimize or maximize a quantity, such as a cost over an interval. We combine a standard Susceptible-Infected-Recovered (SIR)s), infected (i), and recovered (r) populations. A key model parameter is the basic reproduction number in the absence of any behavioral change, and due to the removal of susceptibles from the population.The state variables of the SIR model are the population densities of the susceptible  describes a relative intensity of social distancing for a given fractional reduction in the reproduction number , we can interpret the final time horizon c as roughly the inverse length of time of social distancing that is as costly as infection (within an order of magnitude). For the value c would be critical in determining the transition between suppression and mitigation. Therefore, we chose to use a wide range of values for c to capture the transition boundary between the two strategies, which, based on its interpretation, are plausible.The estimated value of the basic reproductive rate (mentclass2pt{minim38. This translates to an The parameter s. The first is Interpretation of our final results is aided by understanding two conceptually important values of https://github.com/pedroliman/covid19-bpv/tree/Scientific-Reports-2022/2023.Code and data generated for the current study are available at Supplementary Information.


Postoperative surgical site infections (SSIs) remain common after laparotomy for resections of the gastrointestinal or hepatobiliary tract. Especially organ/space infections (CDC class III SSI) can be life-threatening, require relaparotomy, intensive care or interventional drainage of intraabdominal abscesses. The PAISI study aims to investigate whether the use of prophylactic peritoneal irrigation with NaOCl/HOCl solution can reduce the SSI rates following laparotomy for resections of the gastrointestinal or hepatobiliary tract, compared to standard irrigation with physiological electrolyte solution (Ringer’s solution). Secondarily, to evaluate whether the use of prophylactic peritoneal irrigation with NaOCl/HOCl solution can reduce postoperative morbidity and mortality as well as the rate of re-operations and length of hospital stay.z-test  at the 2.5% significance level with a total of two looks at the data will have overall 80% power.PAISI is a prospective, randomized, observer- and patient-blinded, monocentric, two-arm surgical study in an adaptive parallel groups design, comparing peritoneal and wound irrigation with NaOCl/HOCl (50/50ppm) solution to irrigation with Ringer’s solution. The primary endpoint of the study is the SSI rate within 30 days postoperatively. Since there is no data on incidence rates from randomized clinical trials, the rates for sample size calculation were estimated according to the clinical experience at our institution. Therefore, the study design includes one unblinded look at the data by a second statistician, which will be performed after half of the patients reached the primary endpoint. This interim information will be used to check the assumptions and if needed, the sample size will be adjusted. The O’Brien-Fleming spending function is used to determine the efficacy test boundary and the non-binding futility boundary. The one-sided The results of this study will provide high-level evidence for future research and clinical recommendations regarding the use of NaOCl/HOCl solution in abdominal surgery and provide the participating patients the opportunity of a potentially improved treatment.German Clinical Trials Register (DRKS) DRKS00028037. Registered on 27 May 2022. The order of the items has been modified to group similar items  is still one of the most common hospital infections. In Germany, approximately 200,000 SSIs are reported annually , 2. In aProphylactic intraoperative peritoneal irrigation (IPI) of the abdominal cavity before closure of the fascia with physiological electrolyte or antiseptic solutions hypothetically represents an easy and economical option to reduce SSI rates and is already frequently used in clinical practice. A survey among 153 general surgeons showed that 97% perform IPI, while the frequency of use and choice of lavage fluid varied widely . Howevern=1633) from 2019 which compared IPI vs. suction alone during paediatric appendectomy for perforated appendicitis, showed no significant difference in the incidence of postoperative intraabdominal abscess formation, SSI, and length of hospitalization between the 2 groups. However, the evidence level of the included trials was low . Thi. Thi6]. Figure The sample size was calculated  based on the primary endpoint of the study. Assuming SSI rates of 4% and 16% for the experimental and the standard group respectively (OR=4.571), the one-sided z-test  at the 2.5% significance level with a total of two looks at the data will have overall 80% power to show superiority of the experimental over the standard arm if the study includes at least 232 patients (116 patients per intervention group). The calculation is continuity corrected due to the expected low proportion in the experimental group. The results assume that the group sequential design has one interim sequential test for monitoring and sample size re-estimation , which means that an interim analysis is planned after half of the patients have reached 30 days post-surgery. The O’Brien-Fleming spending function is used to determine the efficacy test boundary and the non-binding futility boundary. The group sequential test boundaries  for the interim and the final analysis are as follows:Upper efficacy bounds: 2.963 and 1.969Futility bounds: 0.555 (non-binding) and 1.1969.Net trial network. Therefore, a total of 290 patients (145 per intervention group) should be included in the study.A drop-out rate of about 20% is expected in this study, based on experience from similar trials previously conducted within the CHIR-The recruitment period is expected to be approximately 32 months . In the study site, an average of around 80 laparotomies LOC II–IV are performed per month. Experience from previous clinical studies shows that the recruitment of 10 patients per month is feasible here. To cover any unforeseen recruitment difficulties, for example due to the COVID-19 pandemic, 3 extra months of recruitment time were added. In the case of elective procedures, pre-screening (this is just a pre-selection of eligible patients within the study team) of patients can be performed up to 14 days prior to the scheduled surgical procedure. In case of emergency procedures, screening and inclusion can take place on the day of admission to the hospital, which is usually the same day as surgery.http://www.randomizer.at). Online-Randomization will be performed at the end of the surgical procedure before the abdominal fascia is closed and will be stratified by LOC of the surgical procedure . Participants will be enrolled by the specifically trained medical doctors of the local study team. Participants will be assigned to the intervention groups by the designated study nurse or medical doctor who is effectuating the online randomization.The allocation sequence is generated by the Randomizer tool  on 3 postoperative study visits.Unblinding of outcome assessors is permissible if significant hazards for patients’ safety or welfare occur. In such an unlikely case, the member of the study team responsible for the randomization procedure can unblind the outcome assessor for the randomization result of the concerned patient, only.Screening and inclusion of patients will be performed not earlier than 3 days and not later than one day before the planned surgical procedure, to ensure the patient has enough time to consider the decision to participate in the study. All screened patients are documented in a screening log. If patients do not wish to participate in the study, the reasons will be documented accordingly. If patients fit inclusion/exclusion criteria and agree to participate, they will need to give written informed consent, after adequate time for consideration. Therefore, at the screening visit, a detailed description of the study and further instructions are discussed with the patient, including methods of abdominal and wound irrigation, risk-benefit ratio, and follow-up schedule.After the investigator has reviewed the inclusion and exclusion criteria again and having received written consent by a patient, demographical data and medical history  and the diagnosis will be documented. In addition, the Charlson Comorbidity Index (CCI) will be calculated, which is a prognostic score that is used in many recent trials to simplify the comparability and evaluation of multimorbid study populations . In addiDocumented parameters of the surgical procedure include the urgency (emergency/elective), type of surgical procedure  the duration of surgery (incision until complete skin closure), the LOC according to CDC classification  remain in hospital medical record and information on the eCRF must be traceable and consistent with the original data. Original written informed consent signed by the patient is kept by the investigator and a signed copy will be given to the patient. No information in source documents about the identity of the patients will be disclosed. All data collected in this study must be entered in an eCRF using a REDCap database  , 31 whicThe applicable local regulations of data privacy protection will be followed. The patients will be informed that any patient-related data and materials will be appropriately made pseudonymous and that these data may be used for analysis and publication purposes. Furthermore, the patients will be informed that their data may be inspected by monitors for the purpose of validation of a proper study conduct. Patients who do not provide consent for processing of their data, according to the data protection agreement included in the ICF, will not be included in the clinical study.Not applicable since no biological specimen will be taken.The intention-to-treat (ITT) set consists of all patients who received irrigation of the abdominal cavity before closure of the abdominal fascia with one of the study solutions. Analysis will be performed as randomized regardless of the actual intervention and regardless of any further medical or surgical treatments. The Per-Protocol (PP) set consists of patients treated according to protocol, excluding any major protocol violations. The PP set will be analysed as treated. The Safety (SA) set will consist of all patients in the ITT set, analysed as treated.All primary and secondary analyses will be performed on the ITT set. Sensitivity analysis of the primary endpoint will be performed on the PP set. The SA set will be used for the safety analyses. The incidence of SSI within 30 days after surgery will be compared between the two study groups using the one-sided group sequential test of two proportions at the 2.5% significance level with a total of two looks at the data. The primary endpoint analysis will be performed on the ITT set. Since the ITT set includes all patients who were treated in the study regardless of any further medical or surgical treatments, it is expected, that the SSI rates 30 days post-surgery will be available for most patients. Nevertheless, it is possible that some patients do not reach the primary endpoint due to death, withdrawal of informed consent, loss to follow-up, or other unforeseen reasons. Patients who die before day 30 will be considered as having SSI at time of death regardless of the intervention group, unless SSI was documented earlier. All other missing primary endpoint data will be dealt with using multiple imputations based on binary logistic regression models including LOC, ASA, BMI, age, diabetes, type of surgery, duration of surgery, use of wound-edge protectors, and intraoperative changing of gloves.Thirty days after the first half of the patients has reached the primary endpoint, an interim analysis will be performed by a second statistician, who does not take part in the final study analysis. A decision will be made by the study leadership, using the blinded results to stop the study with proven efficacy, stop the study for futility, continue the study as planned, or continue the study after adjusting the sample size.Operation-related risk factors: (a) type of surgery; (b) duration of surgery; (c) NNIS Risk Score, (d) use of wound-edge protectors; (e) intraoperative changing of gloves before skin closure; (f) presence of an enterostomy; (g) administration and timing of antibiotic prophylaxis;Patient-related risk factors: (g) BMI; (h) ASA score; (i) Age; (j) diabetes; (k) smoking; (l) alcohol abuse; (m) Charlson Comorbidity Index, (n) history of SSI; (o) history of radiotherapy; (p) history of chemotherapy, (q) days of hospitalization prior to surgery.Since randomization will be stratified by LOC, supportive analysis of the primary endpoint will be performed using a binary logistic regression model with dependent variable SSI and covariates intervention group and LOC. In addition, the following parameters might influence the outcome, which is why they will be included as model covariates in an additional model:Supportive analysis of the primary endpoint will be performed on the ITT set using multiple imputations for any missing SSI values and on the PP set. Secondary endpoints will be analysed by intervention arm on the ITT set, using appropriate descriptive statistics. Any explorative statistical testing will be performed using a significance level of 5%. The assessment of safety will be based on the frequency of AE/SAE as defined in the protocol within the safety population consisting of all patients randomized into the study.Multiple imputations will be used for missing primary endpoint data. All other data will be analysed on a complete-case basis.www.drks.de). This includes a summary in lay language for the interested patient community. The full protocol and statistical code can be requested from the authors. Individual participant level data that underline the results reported in this article can be shared after anonymization, with investigators whose proposed use for the data has been approved by an independent review committee identified for this purpose. Proposals can be submitted up to 36 months after publication of the study results.The protocol publication will be accessible on the DRKS website  which is responsible for recruitment of patients and data management. The statistical analysis will be performed by an independent statistician. Trained medical doctors of the local study group will take informed consent. The study leadership will meet once a month to discuss progress and problems regarding the trial. Following the planned interim analysis after 50% of patients are recruited a meeting with the trial statistician and the scientific advisors as well as the funders will be held to discuss the results and consequences. The ethics committee will be informed about the outcome of this meeting. Public involvement is not planned in this study.In this study setting, a data monitoring committee is not planned, as the intervention poses no additional risks for the patients and is a routine medical procedure.Each adverse event (AE) is to be classified by the investigator according to the Common Terminology Criteria CTCAE V 5.0 . SeriousAs this study is comparing two routine surgical procedures, auditing of the trial by external institutions is not required and therefore not planned.Any amendments to the protocol, other than administrative ones (of which the ethics committee will merely be informed), must be reviewed and approved by the ethics committee. The changes will be updated in the clinical register DRKS on a regular basis. If necessary, patient information is updated to inform new participants of the changes.After completion of the clinical study, a manuscript of the study results will be prepared for publication in a reputable scientific journal according to the CONSORT statement. For this manuscript, final analyses will be generated from the study database, and it will be subject to review by the principal investigator. The use of professional writers is not intended.vs. Ringer intraoperative peritoneal and wound irrigation). Internal validity and data quality assurance are established by adherence to the SPIRIT guideline regarding recruitment, methods against bias, outcome reporting and documentation. All patients undergoing gastrointestinal or hepatobiliary surgery (LOC II–IV) by laparotomy within 32 months will be screened for this study. Broad inclusion criteria were applied to ensure rapid and sufficient recruitment of the target sample size. The primary endpoint is the incidence of SSI 30 days postoperatively, according to the CDC definition and classification  –10, 25 a% –10, 25The first patient was recruited in September 2022, therefore recruitment is planned to be completed approximately by May 2025.


Carbon–polymer composite-based pressure sensors have many attractive features, including low cost, easy integration, and facile fabrication. Previous studies on carbon–polymer composite sensors focused on very high sensitivities for low pressure ranges (10 s of kPa), which saturate quickly at higher pressures and thus are ill-suited to measure the high pressure ranges found in various applications, including those in underwater  and industrial environments. Current sensors designed for high pressure environments are often difficult to fabricate, expensive, and, similarly to their low-pressure counterparts, have a narrow sensing range. To address these issues, this work reports the design, synthesis, characterization, and analysis of high-pressure TPU-MWCNT based composite sensors, which detect pressures from 0.5 MPa (4.9 atm) to over 10 MPa (98.7 atm). In this study, the typical approach to improve sensitivity by increasing conductive additive concentration was found to decrease sensor performance at elevated pressures. It is shown that a better approach to elevated pressure sensitivity is to increase sensor response range by decreasing the MWCNT weight percentage, which improves sensing range and resolution. Such sensors can be useful for measuring high pressures in many industrial , automotive , and underwater  applications. Pressure fields and variations are ubiquitous and provide a reliable way to measure both the state of an environment and its dynamics, with examples including weather prediction  and seisCurrent polymer-based sensors typically detect low pressures (<100 kPa) with high sensitivity, but tend to saturate quickly and have a maximum pressure detection limit on the order of 10 s of kPa ,6,7,8. BCurrently, high pressure sensors typically use rigid, non-compliant materials ,10,11 thFor high pressure composite sensors, elastomers are desirable matrix materials due to their elasticity , low cost, and ease of fabrication. Elastomers are also incompressible and can withstand high pressures without material failure. However, the most commonly used elastomers have a low Young’s modulus, limiting their effective pressure sensing range.To measure pressures in the range of 1–100 atm (approximately 0.1–10 MPa), an elastomer with a high Young’s modulus is needed to avoid complete compression within the pressure range, while sensors implementing Polydimethylsiloxane (PDMS) as the matrix have had success with implenting sensors over a wide range of pressures ,15,16,17Compared to the low modulus silicone-based elastomers used in low-pressure composite-based sensors, thermoplastic polyurethanes (TPUs) can increase the pressure range of elastomer-based composite sensors due to their high and tunable modulus. The modulus is controlled by the ratio of hard- and soft-segment molecules used in the TPU formulation.Polymer-based sensors have been explored extensively ,22,23,24Although these approaches successfully developed cost-effective and sensitive devices, the primary focus was to improve the low-pressure (10 s of kPa) sensitivity. This is typically achieved by increasing CNT loading (measured in wt%) and/or introducing microscale features to increase the interfacial surface area ,31,32. TThis work investigates high pressure, low cost, polymer-CNT composite pressure sensors. With reusability and longevity in mind, limiting the maximum sensor strain experienced at the target conditions is of interest in order to prevent matrix failure, promoting sensor robustness overall. A modulus of at least 20 MPa was used as a lower threshold in this work to limit the maximum strain percentage to 50% at 10 MPa applied pressure.First, a composite material to form the sensor is synthesized by dispersing MWCNTs, of sufficient concentration, in a solvent to establish homogeneous conductivity throughout the composite. Sufficient MWCNT dispersion during synthesis allows the percolation threshold and sensor response to better align with the the properties of the nanotubes, rather than their agglomerates (resulting in lower conductivity). This is important because the percolation threshold is both concentration and geometry dependent and the agglomeration of MWCNTs results in a different apparent size and geometry than that of the constituent MWCNTs . TPU is then added to the solvent and MWNCT solution, which is thoroughly mixed to enforce homogeneous MWCNT dispersion throughout the solution. The sensors are then formed from the resulting composite material using injection molding and are characterized with a dynamic testing system. The relevant testing data  are collected for offline processing and analysis. A design of experiments (DoE) is conducted, and statistical analysis is used to characterize the influence of several composite synthesis parameters  on the observed sensor response.Unlike the more traditional one factor at a time (OFAT) experimental approach, a DoE identifies how both factors in isolation (main effects) and interactions between factors affect the measured response. Classical designs, such as factorial or fractional factorial designs, require the boundaries of the experiment to fit specific parameters leading to limited flexibility, a strict number of experiments, and restrictions on the factor types and number of levels. Optimal designs afford greater flexibility by creating an experimental design according to the boundaries of the problem at hand and allow for mixed factor types with any number of levels. As this study involved both categorical and continuous factors with a mixed number of levels, an I-optimal DoE was used, which aims to increase the precision of the response prediction for a given treatment .p-value for multi-factor analysis is calculated to determine if an effect is significant. The test statistic of ANOVA is the F-statistic (mean square treatments (MST)/mean square error (MSE)), which compares the variability between treatments to the variability within a given treatment . Iterative model analysis can reject non-important factors and characterize the effects of the significant factors found. This is particularly powerful because, after non-important factors have been identified, the analysis can be modified so that they are not examined, allowing existing data to be used to increase the power of subsequent designs.A A TPU-MWCNT composite material is synthesized to form the sensors studied in this work. As agglomeration can affect the homogeneity and response of the composite material, solution-based processing  is used to prepare the composite. The synthesized material is injection molded to form the material into the final sensor geometry. The sensor is then cyclically compressed and the relevant response data are collected and processed. The processed data from the optimal design of experiments are then analyzed to determine the effects of tracked synthesis parameters (and their interactions) on the sensor response.t is a fitting parameter based on the dimensionality of the filler, and has been shown both empirically and theoretically to be between one and four for polymer-carbon nanoparticle composites [The percolation threshold is the concentration of a filler material in a matrix that maximizes the probability of long-range connectivity between fillers. The percolation threshold is estimated by Equation  where σ mposites :(1)ΦC=Φ−t, changing the percolation threshold drastically. Changes to the percolation threshold of a phase in a composite directly impact the amount of the phase necessary to establish long-range connectivity (and thus conductivity and sensitivity in this case) throughout the sample. The processing parameters for composite synthesis  affected the span of the normalized response of the implemented sensors. The span of the response range was chosen as the output factor of interest because the sensor response typically approaches the end of its range asymptotically, and so sensors that have a wider response range will be able to better resolve a given pressure range. The span of the response was normalized to be able to compare sensors whose response might not be in the same order of magnitude . Weigh/measure TPU, MWCNTs, solvents and set aside;Add solvent  to MWCNTs ;Mix solvent and MWCNTs ;Place in ultrasonic bath ;Add TPU;Mix ;Place in ultrasonic bath ;Add solution to stirring water (≥250 mL). This drives off and dilutes the solvent, allowing the MWCNT-laden TPU to solidify. After mixing for ≥5 min, larger pieces of material are cut to a size of ≤20 mm on a side. This provides greater surface area for continued removal of the solvent, while still remaining large enough to be handled and not so small that pieces become airborne in later steps. Then, replace water and mix . This ensures that solvent is driven off from the synthesized material as much as possible.Remove material from water and dry in a vacuum oven ;Final material is attained and is ready for injection molding.Once synthesized and dried, the composite material must be formed into a known geometry to reliably characterize and compare sensing performance. Injection molding was used to form the sensors because of its fast fabrication time  and ability to make many samples with identical geometries and internal structures. The process forms uniform samples by heating the composite material and extruding it into a mold. As pressure is applied, the composite material completely fills the mold and any trapped air is compressed and forced from the high pressure mold interior to the lower pressure (STP) exterior through venting ports, forming a bulk (solid) sensor see .This venting also mitigates dieseling (diesel effect—the compression-driven heating/combustion of a gas) associated with trapped gasses, preventing scorching, burning, or decomposition of the composite material.To investigate the effects of the composite material synthesis on the sensor performance, cylindrical sensors with a 10 mm diameter and height  were formed. As relatively small volumes of the composite material are needed to form these sensors, commercially available injection molding systems are not suitable because they require a large amount of material  for processing. To address this issue, a custom injection molding apparatus (IMA), shown in The IMA is shown schematically in To use the IMA, the mold and charge block are disassembled , cleaned, and reassembled with all fasteners torqued to 50 in-lbs with a 1/4 in torque wrench. The mold is attached to the charge block via a threaded coupler. The composite material is added and the piston, loosely held in place by the linear actuator (LA), is positioned in the charge block. The power supply is activated, and the temperature is tracked via a connected computer. When the temperature reaches the target temperature (190 °C), push buttons are used to drive the LA forwards, pushing the piston and injecting the melted composite material into the mold. The power supply is deactivated, with the LA maintaining pressure on the piston and the entire assembly being allowed to cool. When cooling, the sample is easily retrieved from the mold by separating the halves of the mold.As the charge block heats up (≈8 min to the the target 190 °C) and is exposed on all sides, thermal runaway is not a concern and removing power causes the temperature of the block to stop rising quickly (≤5 s). Additionally, the on time quality of the heater elements is varied based on the difference between the measured temperature and the setpoint. This allows the temperature to increase quickly upon a cold start, as well as allow an aggressive response to sudden cooling during operation, such as during the addition of material to the charge block. The cyclic behavior of the fast increase and decrease in temperature in response to the control of power to the heaters causes a controlled oscillation about the target temperature, as can be seen in The linear actuator (Concentric LACT4P) used to eject material from the charge block is powered from the same power supply by way of two half bridges (Infineon BTN7960P) that are controlled with two push buttons  during actuation, ensuring that all samples experience the maximum force that the LA is able to impart. After the initial DTS, the IMA is left to sit (heaters powered) for three minutes. The linear actuator is then DTS a second time, and left to sit powered for another 3 min. The linear actuator is then DTS a third time, the heaters are powered down, and the cooling fan is turned on, allowing the molded sensors to cool and solidify before being removed from the mold. After being removed from the mold, the formed sensor is left to sit for 24 h before testing to allow for complete cooling and relaxation of residual stresses from the injection molding process.Sensors made with composite materials typically experience a permanent change in resistance during the first few (≤15) cycles ,32,37, hDuring this break-in period, for each cycle, a sample is preloaded with 5 N of compressive force. After a 60 s delay, the sample is compressed at a rate of 50 N/s to a final loading of 800 N. These break-in conditions are chosen because they simulate the conditions the sensors experience after multiple cycles of the characterization cycle. Furthermore, the accelerated loading of the break-in cycles exposes the sensors to greater stress and strain rates than are experienced during the characterization cycle, ensuring that any changes to the sensor or response properties occur before characterization. The sample is then unloaded at a rate of 90 N/s to the preload force, and the cycle repeats. During the characterization cycles (first and last cycles of the routine), the sample is compressed at a rate of 5 N/s to a final loading of 800 N.Samples were compressed using a dynamic test system . Applied force and subsequent displacement were reported by the Instron and converted to analog voltages onboard. These voltages were measured with a data acquisition unit  and the sensor resistance was measured with a source meter (Keithley 2400) configured to provide 2 V with a compliance current  of 105 The response of similar composite-based sensors is typically modeled via a piecewise linearization with two or three sections ,30. ThesPrior to biexponential fitting, the collected raw data were separated by cycle, cleaned, smoothed, and filtered. Cleaning entailed removing erroneous measurements (negative resistances), exceptionally high resistances  were calculated. If the error associated with a data point with respect to the fit of the data is more than two standard deviations from the RMSE, it is considered an outlier and is removed. After doing so, a new biexponential is fit to the remaining data. The outlier removal improved the fit by removing data points that skewed the biexponential parameters. The outlying measurement points were likely due to very high or very low readings reported erroneously from the source meter or caused by noise on the sensing lines. After this process is applied to all cycles for all samples, the final cycle for each sample is used to characterize its response. The final cycle was used because any permanent changes to the sample response (break-in) occur in the first few cycles after fabrication. The number of break-in cycles ranges from 5 to 15 in literature, and so greater than 20 cycles were used. It was observed empirically that, after 20 cycles, the sensors exhibited similar behaviors among subsequent cycles .p > 0.05 used). K1 demonstrated showed statistically significant correlation with MWCNT loading , as they determine shape of response see . HoweverForemost, it was demonstrated that, through careful selection of the matrix and its properties, as well as processing parameters, the pressure sensing range of the composite sensor can be controlled and significantly extended. The sensor is able to detect pressures up to at least 10 MPa (limits of the pressure testing setup) versus the 10 s of kPa for polymer composite pressure sensors reported in literature, as shown in It was found that increasing the MWCNT loading did not necessarily increase the sensitivity. This appears counter-intuitive at first, as increasing the MWCNT loading improves the sensitivity for small pressures and is the defacto method for eliciting increased sensitivity from similar composites. Using this approach, similar composites have been reported to sense pressures in the 1–10 Pa range. However, this causes the response of such sensors to saturate at a lower pressure, degrading the response at elevated pressures and decreasing the effective sensing range. MWCNT loadings that were too high (such that the response of the sensor saturated quickly) or too low (such that the sensor was not responsive) led to a decreased response span, degrading sensor performance at elevated pressures, as shown in TPU formulation affected the response range of the sensors, as most of the formulations using the stiffer TPU formulation needed to be removed due to lack of response and non-repeatable measurements see . The effp > 0.05) with the explored treatment parameters. However, the shape of the response did exhibit different behavior across treatments, implying that varying the carbon nanotube loading, matrix type, or solvent has little effect on the shape (relative sensitivities in different areas of the response curve) of the response. K1 is shown to increase towards maximum sensitivity (as a function of MWCNT loading) at a pressure that aligns with the maximum span as a function of MWCNT loading. This reinforces that span and sensitivity (at least at the lower end of the pressure range) are related and that the behavior of the sensor is in accordance with findings and mechanisms found in existing works.While k1 was shown to have a relationship with MWCNT loading see  in accorAfter cleaning the data as outlined in p-value greater than the significance level of 0.05 were eliminated via backwards removal.The metrics of all samples were plotted on a histogram, and samples with metric in or above the 85th quantile were removed due to significant deviation between the fitted biexponential and the measured data. Analysis was then performed iteratively on the remaining data to maintain statistical power for examined factors. Primary effects were examined in isolation, and non-significant effects were dropped from consideration. Secondary effects containing significant primary effects were then considered. Following this approach, few (5 of 16) samples made from treatments that comprised the comparatively stiffer TPU formulation remained. Of those that remained, treatments with similar parameters had significantly different responses (discussed in p = 0.53) to ensure good overlap between the distribution of the error and a zero-centered normal distribution. Plots relating the residuals to the predicted span  sensors are typically employed for environmental measurements. The presented sensor can serve as a low-cost solution for implementing the depth sensing functionality in such a system.The hydrostatic loading experienced will cause a different sensor response curve with respect to the axial compression presented thus far; however, sensing range is still a function of MWCNT loading. When compressed axially without a die, the samples expand perpendicular to the loading direction. The die restricts this expansion by applying pressure to the sample from all directions, simulating the isometric, hydrostatic loading experienced underwater. As shown in Pressure is also applied cyclically to measure the response time of the sensor. The responses of the sensors from cycle to cycle were consistent, with p > 0.05) with the explored treatment parameters but did exhibit different behavior across treatments. This implies that the variation in the shape of the response is caused by material properties of the solutions of different treatments that were not varied or controlled for, such as viscosity, mix time, or mix speed. While the exponential coefficients of the biexponential fits of the sensor responses did not exhibit good correlation, a trend was still apparent. Because of this, the normalized span of the response was examined, as it is affected in part by the sensitivity of the sensor, as well as by the differences in the material and electrical properties resulting from the treatments applied. Normalization was applied to compare samples of varying orders of magnitude, as biexponential fits can vary significantly when scale changes, which is exacerbated when the response of the sensor is near the transition point of the curve defined by the fit. Normalization allowed the response of each sensor to be compared to itself, facilitating performance comparisons across sensors.It was found that the shape of the response (relative sensitivities at different pressures) did not demonstrate significant correlation  matrix choice does have a significant effect on additive dispersion and sensor performance ; (2) an uncontrolled fabrication parameter has a significant effect on the resulting composite properties at the given processing parameters; and (3) the aforementioned fabrication parameter is likely related to, or a function of, the matrix choice. The most likely parameter is viscosity, which was not controlled for and would have a significant impact on how well the composite solution is mixed, and would vary based on matrix type if a fixed amount of solvent was used across treatments. Ineffective or incomplete mixing would then have an effect on sensor conductivity, likely by way of either variation of the percolation threshold as a function of matrix-related additive agglomeration, or inadequate MWCNT dispersion/composite homogeneity. This can be explored by conducting a similar DoE, which instead controls or modulates the solution viscosity and different process parameters related to MWCNT dispersion , in addition to matrix type and MWCNT loading.Pressure sensing is an important capability in measuring and interacting with environments. As such, being able to sense a wide range of pressures (including those ≫ 1 atm) is critical in enabling such capabilities and expanding the space of applications associated with them. By selecting a matrix material of appropriate stiffness and targeting suitable MWCNT loadings, it was possible to implement a soft composite material to be used in a sensor capable of measuring pressures in excess of 10 MPa.t), which change the percolation threshold (MWCNT dispersion is an important factor for increasing composite homogeneity and reducing additive agglomeration. Agglomeration and dispersion affect both the apparent volume fraction of the filler in the composite (p > 0.1) with any of the tracked treatment parameters, implying that varying the carbon nanotube loading, matrix type, or solvent has little effect on the shape (relative sensitivities in different areas of the response curve) of the response.An optimal design of experiments was used to explore the relationships of composite formulation on sensor response shape and sensitivity, which allowed for the examination of the interaction of effects as well as determining which parameters had a significant effect on the examined output. In exploring the effects of processing on the shape of the resistance response, the values of the exponential coefficients were found to have a weak correlation (Surprisingly, increasing MWCNT concentration was shown to decrease sensor performance at elevated pressures, which is different from the current approaches to improving the performance of similar composite-based sensors for low pressure sensing. Increased MWCNT concentration caused the response to saturate at a lower pressure, degrading the response at elevated pressures and thus decreasing the bandwidth of the sensor. Such a sensor is well suited for measuring pressures in industrial, automotive, and underwater applications due to its ease of fabrication and integration, repeatable response, good sensitivity, low cost, reusability, and overall robustness.


To accurately evaluate the mechanical performance of three-dimensional (3D) braiding composites, it is essential to consider the braiding process and generate realistic representative volume element (RVE) structures. An efficient simulation methodology based on truss elements was used to simulate the 3D four-directional (3D4D) braiding process utilizing the finite element method (FEM) on the macroscale. The goal was to obtain the spatial trajectories of yarns and establish the relationship between the braiding parameters and the preform structure. Based on the initial yarn topology, the yarns were discretized as bundles of virtual sub-yarns. Then, a temperature drop simulation using hybrid elements was implemented to deform the yarn cross-section and obtain the interior, surface, and corner cells on the mesoscale. The simulation results show good agreement with the experiment. A parametric study was deployed to identify the effect of the model input parameters on the computation cost and accuracy. Furthermore, the approach applies to the other braiding processes, such as the cylindrical braiding composite. Composite materials are an effective means of lightweight design . Three-dThe macro-mechanical properties of 3D braiding composites are primarily determined by the preform’s mesostructure and the constituent materials’ mechanical properties. Accurate mesostructure is a precondition for calculating the mechanical properties of composite products. The representative volume element (RVE) is the smallest volume over which a measurement can be made to yield a value representative of the whole . Wang etThe preceding studies have constructed the RVE based on many assumptions with respect to yarn geometry. For example, the yarn sections are unchangeable or are several simple sections, the yarns do not slip against each other, or the yarn path in the preform is identical to the carriers’ path in the machine bed. However, a 3D braiding fabric has a complicated structure, often with multidirectional deformation, as well as changes in the cross-sectional shape owing to yarn compaction. Therefore, many researchers have made experimental investigations to obtain accurate RVEs. Byun et al.  polishedTM software, based on the digital element method, obtained a good agreement with X-ray CT images of a 3D woven textile composite [TM [TM [It is time-consuming to use these experimental-based approaches to obtain fabric structure, which can only be used to observe product results rather than for early predictive guidance on the process. The simulation-based method is excellent for studying the process and mesostructure of a composite. Wang and Zhou ,15 develomposite ,17. A cosite [TM  and TEXG [TM [TM ,20. Gree [TM [TM  simulate [TM [TM . However [TM [TM . This so [TM [TM ,25 model [TM [TM . Yang et [TM [TM  simulateThis paper proposes a multiscale methodology for obtaining accurate RVEs. The study is organized as follows: The 3D braiding fabric is woven by the alternate movements of yarn carriers in row and column directions. m and n are the row and column yarn numbers in the main part, respectively, and N is the total number of yarns. After m and n.The count of carriers in the rectangle pattern is determined by the row and column number of yarns of the main part These yarns in the Simulation of the 3D4D braiding process on the macroscale: The braiding process was simulated according to Sub-yarn discretization: The yarns in the two pitches of the preform at the stable braiding stage b were diSub-yarn deforming simulation on the mesoscale: The contraction process was accomplished by imposing the temperature drop load with an appropriate thermal expansion coefficient d. The suMesostructure reconstruction: Since the FEA analyses require yarns with a solid geometry rather than fibers, the chains of sub-yarns must be converted to solid geometry. Another Python script was written to extract the section shapes of different yarns and reconstruct the accurate yarn structure e. EventuThe workflow of the proposed modeling methodology is illustrated in The braiding process simulation model takes the machine control and process parameters as inputs and generates the braiding structure as an output. As shown in Since a yarn consists of a substantial number of fibers, the bending modulus of yarns is much lower than the value calculated using Young’s modulus in the fiber direction. The primary purpose of the braiding process simulation is to achieve the topology structure of the preform. Using truss elements (T3D2) that neglect the bending stiffness approximates the actual state of yarns in the braiding process ,28. In S group 1 b is the It is well known that the braiding process parameters must match each other to obtain a consistent fabric structure. For example, the fixed height of the interweaving point and the distance between two yarn carriers determine the braiding angle. The take-up speed and the time for each carrier to move one step decided the interweaving point of the braiding process. Therefore, the model with the take-up velocity as zero was implemented to investigate the relationship between braiding angle and interweaving point height. Despite the fluctuations in the braiding angle and height measurements of the experimental specimens, the simulation results are in good agreement with the experimental results, as shown in The yarn center curves are obtained from the simulation method described in The sub-yarn discretization is implemented in a custom Python script. The translational transformation was conducted to ensure that points The rotational transformation was deployed to ensure that points The rotation matrix ue lines b are subTaking the vector However, in some exceptional cases, the coordinate matrix does not have an inverse matrix, making it impossible to calculate the transformation matrix All nodes in the original sub-yarn layout can be transferred to the target location by the following expression:The extrusion deformation among yarns is the dominant form in sub-yarn shrinkage simulations. The section shape of the yarn is mainly influenced by fiber bending stiffness that affects the realignment resistances, so the bending stiffness of virtual sub-yarns cannot be neglected. A new mesh technique was used to consider the appropriate bending stiffness of yarns by overlaying the truss element (T3D2) with beam elements (B31) with the coincident nodes , as showThe 3D4D braiding composite is periodic in the braiding direction. Taking into account the edge effects and the computing cost, two pitches in a stable braiding state were chosen for sub-yarn deformation compression analysis. The end nodes of every bundle of sub-yarns were coupled to a control point using a uniform coupling constraint. The periodic boundary conditions (PBC) were applied to the two corresponding control points b. The liTo achieve a realistic braiding fabric structure, the temperature dropping load was imposed on all elements to ensure that the yarns squeezed with each other, which was equivalent to exerting tension force during the braiding process. The temperature drop stopped until the average stress of all elements was equal to the tension stress produced by the tension force of the yarn carrier. The following equation determines the average stress:The virtual yarn structure and the experiment results were compared, as shown in The evenly distributed rays are drawn along the circumferential direction, with the center of the section as the starting point, as shown in The centers of all big circles are connected to form a curve. Then, the curve is offset by the radius of the big circle inward to obtain a curve that surrounds all fibers, that is, the cross-sectional profile of the yarn.All the cross-sectional profiles are joined to a multi-section surface, as shown in Most braiding composite FEA analyses are based on the yarn level. Fiber-level geometry needs to be transferred to yarn-level geometry. The center fiber a determiThe essential purpose of our work is to obtain accurate RVEs for subsequent mechanical calculations. The solid structure models of three types of RVEs, including the interior, surface, and corner cells, are periodic, as shown in The parameter study is performed to verify the accuracy and convergence performance of the finite element model. How to set the number of virtual sub-yarns to balance the calculation accuracy and efficiency, and the effects of sub-yarn stiffness, tension force, and yarn twist on the structure need further study.Owing to the enormous computational effort required, it is impossible to model each fiber as a single chain of beams. A parametric study of the sub-yarn number must be performed to balance the discrete precision of yarn cross-section deformation and the computation cost. Four models, discretized as the 19, 61, 92, and 133 chains of sub-yarns per yarn with the same yarn bending stiffness, were simulated to study the convergence of the model to reproduce an accurate braid structure. A higher number of sub-yarns leads to greater freedom of deformation of the yarn, so the average stress rises more slowly. The curve of 92 sub-yarns almost coincides with the curve of 133 sub-yarns, demonstrating that the model converges using 92 sub-yarns. Meanwhile, the ratio of total width change (l) to the width (w) at a specific tension force The braiding angle decreases as the height of the braiding point increases and vice versa for pitch length.(2)To achieve a realistic interior cell, surface cell, and corner cell, a temperature drop simulation with hybrid elements was conducted to make the yarn cross-section deformable. The simulation result shows good agreement with the experiment.(3)The parametric study shows that the use of 92 sub-yarns represents the cross-sectional deformation well. A smaller bending stiffness leads to a larger total width variation, resulting in a higher yarn volume fraction at the same tension force. The yarn deformation degree is positively related to the tension force of carriers. Finally, the twisted yarn has a higher resistance to cross-sectional deformation than the straight yarn.(4)The simulation methodology presented here is a versatile tool that can study the relationship between the different braiding processes and the mesostructure of the preform.The present research developed a multiscale simulation methodology based on the virtual sub-yarns to establish accurate RVEs. The simulation results were compared with the micro-CT and SEM structures in the literature. A parametric study was conducted to validate the model. The multiscale method yields accurate results with a relatively small computational cost. Furthermore, the method could give some predictive guidance on the process design in the early stage. The following conclusions can be drawn:This paper proposes a numerical method to obtain the accurate RVEs. Future works will integrate the source codes see  into Aba


In view of the difficulty in obtaining the membrane bioreactor (MBR) membrane flux in real time, considering the disadvantage of the back propagation (BP) network in predicting MBR membrane flux, such as the local minimum value and poor generalization ability of the model, this article introduces tent chaotic mapping in the standard sparrow search algorithm (SSA), which improves the uniformity of population distribution and the searching ability of the algorithm (used to optimize the key parameters of the BP network). The tent sparrow search algorithm back propagation network (Tent-SSA-BP) membrane fouling prediction model is established to achieve accurate prediction of membrane flux; compared to the BP, genetic algorithm back propagation network (GA-BP), particle swarm optimization back propagation network (PSO-BP), sparrow search algorithm extreme learning machine(SSA-ELM), sparrow search algorithm back propagation network (SSA-BP), and Tent particle swarm optimization back propagation network (Tent–PSO-BP) models, it has unique advantages. Compared with the BP model before improvement, the improved soft sensing model reduces MAPE by 96.76%, RMSE by 99.78% and MAE by 95.61%. The prediction accuracy of the algorithm proposed in this article reaches 97.4%, which is much higher than the 48.52% of BP. It is also higher than other prediction models, and the prediction accuracy has been greatly improved, which has some engineering reference value. In recent years, with the rapid economic development and industrial progress that has been seen, water resource fouling has deteriorated dramatically, sewage treatment appears to be particularly important, environmental science for sewage treatment requirements and its provisions has also been greatly valued, and the research on sewage treatment is increasing ,2. In thThe degree of membrane fouling is related to the value of the membrane flux. In practical applications, the fouling status of the membrane can be analyzed by predicting the value of the membrane flux. However, the membrane flux cannot be directly measured and is affected by the variables of the sewage treatment process. In order to achieve membrane permeation for the detection of the rate, researchers have conducted a lot of research. Chellam  and Al-ZIn recent years, describing membrane contamination process based on intelligent simulation model has become a research hotspot of MBR simulation system. More and more scholars pay attention to the method of predicting membrane flux using intelligent algorithms. For the prediction of membrane fouling, many scholars have proposed different intelligent prediction methods. Through mechanism analysis, Han et al.  obtainedAt present, swarm intelligence optimization algorithms such as the sparrow search algorithm (SSA) have been widely used in engineering problems. The sparrow search algorithm (SSA) is a new metaheuristic algorithm proposed by Xue and Shen in 2020 . Liu et However, SSA, like other population intelligence optimization algorithms, still suffers from the problems of decreasing population diversity and easily falling into local optimality when its search is close to the global optimum. Considering the ergodic uniformity and fast convergence of tent map, this study proposes an improved sparrow search algorithm (Tent-SSA). In order to effectively select auxiliary variables, establish a suitable membrane flux prediction model, and realize the online accurate prediction of membrane flux, firstly, the mechanism of membrane fouling factors is analyzed in this paper, and secondly, principal component analysis (PCA) is applied. Select auxiliary variables, and then introduce tent mapping to initialize the population to increase population diversity. Finally, the Tent-SSA-BP neural network was combined to establish a Tent-SSA-BP membrane flux soft-sensing model, and the simulation data of Seong-Hoon Yoon’s spreadsheet model was used to verify the reliability and stability of the model and to prediction of membrane flux value .The BP neural network has the ability of self-organization, self-learning and self-adaptation, and its principle is simple and easy to implement . It has E is the total network error. The error reduction is carried out in the direction of the negative gradient, and it is easy to get into the dilemma of local minimum value. In order to make the deviation between the actual output and the target value of each unit smaller than the specified value, the connection weights need to be constantly adjusted. When there are too many training samples or the relationship between input and output is complex, the convergence speed of the network will become slow  interval, the computer performs a tent mapping to left-shift the binary number of the fractional part. This transformation is suitable for computing large-scale data. The bernoulli shift transformation is shown in Formula (7).The chaotic sequence generated by tent chaotic mapping in the  interval is periodic, but there are also unstable periodic points. Because tent chaotic sequence iteration may fall into small and unstable periodic points, a random variable The expression after bernoulli shift transformation is shown in Formula (9): In conjunction with the above description of the tent mapping properties, the basic steps for generating a tent mapping chaotic sequence within a feasible domain are as follows:Step 1: Randomly generates the initial value Step 2: Iterate by Formula (9), increasing by 1 each time, resulting in sequence Step 3: If it reaches the maximum number of iterations, it goes to Step 5. Conversely, if it falls into an unstable periodic point, it goes to Step 2. Step 4: Change the initial iteration value by formula Step 5: In the end, saving sequence The initial location information of the sparrow population is randomly generated by the standard SSA at the beginning of execution, which results in poor diversity within the sparrow population. As a result, the algorithm finds a solution that is not globally optimal and affects the convergence speed and accuracy of the SSA . We use Step 1: Initialize SSA parameters;Step 2: Use the tent chaotic mapping function to generate a uniform chaotic sequence, the initial position of members of the sparrow population;Step 3: Calculate the fitness value of each sparrow to determine the position of the individual with the best and worst fitness value;Step 4: Determine the number of explorers in the sparrow population and calculate their updated locations based on Formula (3);Step 5: Determine the number of followers in the sparrow population and calculate their updated positions based on Formula (4);Step 6: Determine the number of warners in the sparrow population and calculate their updated location based on Formula (5);Step 7: Calculate each sparrow’s fitness value and update it if the new fitness value is better than the previous one;Step 8: If the maximum number of iterations of the algorithm is reached, the location information of the sparrow with the best global fitness value is output. Otherwise, go to Step 4 to continue execution.The properties of membrane components, operation conditions and characteristics of sludge mixtures are the main influencing factors of membrane fouling . The proThe principal component analysis (PCA) algorithm is a widely used data dimensionality reduction algorithm. The PCA algorithm can more scientifically and effectively screen out the auxiliary variables with the greatest correlation with membrane flux .Set the research of a certain thing to involve variable :(10){Y1=In the formula, if Step 1: Select the initial analysis variable;Step 2: Find the principal component from the correlation matrix;Step 3: Find the eigenvalue of the correlation matrix and the corresponding standard eigenvector;Step 4: Calculate the variance contribution rate and the cumulative variance contribution rate of each principal component and select the principal component.In this article, we use the membrane flux as a predictor; combining with the specific conditions of the experiment, we pretreat the principal component analysis of the original data when using MATLAB. When reducing the dimension, it is stipulated that 85% of the data information is guaranteed, so that the data loses less data information when reducing the dimension. The values of each index were counted, and normalized and standardized. The index data were analyzed by SPSS, and the eigenvalues and cumulative contribution rates of each principal component were obtained as shown in The eigenvalues of the first three principal components are all greater than 1, and the cumulative variance contribution rate is 89.308%, which has a large contribution to the explanatory variables. Most of the information affecting membrane fouling is included, so the first three are extracted as principal components. Taking the ratio of the variance contribution rate corresponding to each principal component to the cumulative contribution rate as the weight, the calculation of the sustainability index is shown in Formula (11).In the formula, Finally, we summarize six of the most obvious factors affecting the membrane fouling: TSS, MLSS, total resistance, TMP, SRT and water production pressure.Membrane flux is an important index parameter reflecting the degree of membrane fouling; therefore, we use it as the output of the model, and we use six factors after the principal component dimension reduction as input. Finally, we establish a prediction model for membrane fouling based on improved SSA (Tent-SSA) and the optimized BP network as shown in This article optimizes the learning parameters of the BP network based on SSA. First, we optimize the weights and thresholds of the BP network by using improved SSA; second, we assign these optimization values to the network to get the optimized BP network, tent-SSA-BP network; then, the BP algorithm is used to complete the final network training; finally, we evaluate the performance of the optimized network by simulation data. The algorithm flow is shown in Step 1: Auxiliary variable selection and preprocessing, and use PCA for dimension reduction;Step 2: Initialize relevant parameters, initialize population, introduce tent mapping, and improve initial population distribution uniformity;Step 3: Compute and sort the fitness values according to the objective function;Step 4: Use Formulas (4) and (5) to update follower and guardian positions;Step 5: Determine whether to stop, execute exit or continue cycle;Step 6: Train the BP network and use it for prediction.In order to make the output accuracy more intuitive, we introduce the following evaluation indicators.(1)MAPE)Mean absolute percentage ((2)RMSE)Root mean square error ((3)MAE)Mean absolute error  on eight benchmark functions to obtain the mean and standard deviation of the function. The experimental data  are shown in It can be seen from Ascan be seen from 2. In MBR reaction pool, the microorganisms and pollutants in the pool are complex, so the selection of membrane contamination influencing factor largely determines the accuracy of membrane contamination prediction. In order to improve the prediction accuracy, finally, we determine 592 sets of data for model simulation by PCA dimension reduction and normalization: 500 sets of data are used for model training, and the remaining 92 sets are used for model testing.The experimental data in this article come from a spreadsheet model of Seong-Hoon Yoon. The data related to membrane fouling can be simulated and processed according to the experimental requirements to ensure that the data are closer to the actual data. The subjects of study are all polyvinylidene fluoride (PVDF) hollow microfiltration (MF) components. The water inlet mode is external pressure, and the effective usage area of the membrane is 20 m(1)Comparison of results before and after improving optimization algorithm.The simulation results of the actual operation data are shown in From the simulation curve in (2)Prediction accuracy of different soft measurement modelsIn order to compare the prediction accuracy of the soft sensing model proposed in this article, the measurement models are built under the same experimental conditions by using GA-BP, PSO-BP, SSA-ELM, SSA-BP and Tent-PSO-BP models. The prediction results of different soft sensing models are shown in According to the data in (3)Variable noise membrane flux prediction results and analysis with different prediction methodsIn the actual operation process of MBR, environmental noise exists when the membrane module is treating sewage. At the same time, due to the characteristics of the membrane module, there is also noise, which produces unnecessary randomness in the collection of membrane fouling data. It is very important to add variable noise experiment to the membrane flux prediction, for the simulated data needs to be more in line with the uncertainty of the operation of membrane module under actual working conditions. In this article, aiming at the membrane fouling data as the training sample, we add Gaussian white noise with a signal-to-noise ratio of 4, 8 and 12 dB to the test sample, and compare the obtained membrane fouling prediction results with other prediction methods. The experimental results are shown in It can be seen from the comparative data in (1)We use PCA to reduce the initial auxiliary variables. At the same time, we improve the efficiency of the algorithm and reduce the probability of over-fitting. In order to solve the problem that the diversity of population is reduced and the local optimal solution is easily trapped in the later stage of the optimization algorithm, we introduce the tent chaotic map to improve the uniformity of initial population distribution and the ability of the algorithm to find the global optimal solution. Tent-SSA-BP can find the global optimal solution more easily and quickly.(2)Based on the Tent-SSA-BP method proposed in this article, the prediction model of membrane flux in membrane fouling, whether it is the training speed or prediction accuracy of the model, shows better performance than other methods , which is more suitable for the prediction model of membrane flux. This also provides a possibility for the complete data prediction of subsequent membrane components and membrane fouling requirements.(3)In the future research work, data are an important basis and resource for large data prediction research. Therefore, it is of strategic significance to establish a large database of membrane fouling standards for membrane components, to explore deep migration learning methods for predicting technological innovation, and to reveal the evolution mechanism of membrane fouling.The accurate prediction of membrane fouling has an important impact on the sewage treatment process. To achieve accurate measurement on-line, we propose a Tent-SSA-BP prediction model. First, we optimize the improved SSA, then use the PCA algorithm to reduce the dimension of the auxiliary variables after pretreatment, and we use the improved SSA to optimize the key parameters of the BP network. Finally, we use the optimal parameters to predict the membrane flux. The results are shown as follows:


Existing fusion rules focus on retaining detailed information in the source image, but as the thermal radiation information in infrared images is mainly characterized by pixel intensity, these fusion rules are likely to result in reduced saliency of the target in the fused image. To address this problem, we propose an infrared and visible image fusion model based on significant target enhancement, aiming to inject thermal targets from infrared images into visible images to enhance target saliency while retaining important details in visible images. First, the source image is decomposed with multi-level Gaussian curvature filtering to obtain background information with high spatial resolution. Second, the large-scale layers are fused using ResNet50 and maximizing weights based on the average operator to improve detail retention. Finally, the base layers are fused by incorporating a new salient target detection method. The subjective and objective experimental results on TNO and MSRS datasets demonstrate that our method achieves better results compared to other traditional and deep learning-based methods. Image fusion is an image enhancement technique that aims to integrate complementary and redundant information from multiple sensors, which can generate more reliable, robust, and informative images. Infrared and visible image fusion is an important field in image fusion . InfrareIn general, existing image fusion frameworks mainly include multi-scale transform , sparse In recent years, deep learning methods have developed rapidly in the field of image fusion. Liu et al.  used CNNTo solve the above problems, a new infrared and visible image fusion framework is proposed, which preserves the details as much as possible on the basis of considering the spatial scale, reduces the generation of artifacts, and improves the saliency of the target. Since multi-level Gaussian filtering (MLGCF)  can bett(1)We propose a novel infrared and visible fusion method, which can effectively retain detailed information and maintain the target saliency. This method can be widely used in the military, target detection, and other fields.(2)More abundant details can be obtained from the source image by employing MLGCF and ResNet50 to extract features.(3)A new approach to constructing saliency map (FT++) is proposed, which can productively retain the thermal radiation information. Extensive qualitative and quantitative experiments demonstrate the superiority of our method compared to the latest alternatives. Compared with other competitors, our approach could generate fused images looking like high-quality visible images with highlighted targets.The main contributions of this paper are as follows:The remainder of this paper is organized as follows. He et al.  proposedWhere Achanta, R. et al.  proposedFT algorithm carries out saliency detection from the perspective of spatial frequency, which has simple and efficient advantages. However, because the original FT algorithm employs GF to process the input image, the strong and weak edge information of the image is easy to be blurred by GF, and the key information of the image cannot be fully extracted. To solve these problems, in recent years, Hou et al. improved the FT algorithm by guide filter . As an eThe FT++ method is shown in We compare FT++ with the original FT method to verify the effectiveness of the method, see The infrared and visible image fusion based on multi-scale decomposition and FT saliency can effectively retain the texture details of the source image and enhance significant targets. After decomposing the source image using MLGCF, the base layer saliency map is extracted by FT++, the large-scale features are processed by introducing ResNet50 etc., and finally the final fused image is reconstructed. The flow chart of the method in this paper is shown in The edge-preserving filter can improve the common problems in the multi-scale decomposition process, such as the tendency to produce halo artifacts , and doe(1)Using GF to smooth small structure information:(2)Using GCF for the edge recovery process:(3)Combining GF with GCF using a hybrid multiscale approach for a three-stage decomposition:i-th GF process of the input image i-th GCF process. The parameter To verify the advantages of the MLGCF decomposition, the MLGCF is compared with the RGF decomposition. As can be seen in In the past, most of the base layers were fused using simple averaging or weighted averaging, although these methods are simple to operate, they tend to lead to problems such as poor target saliency and low overall contrast of fusion results. To solve these problems, we adopt the FT++ method to process the infrared base layer and deploy its normalized result as the fusion weight. The specific steps are as follows:(1)FT++ method: The FT++ method in this paper only processes infrared images, so the input image for this process is the infrared image Calculating saliency map:(2)Normalizing the significance map to obtain the base layer fusion weights (3)Fusion of base layers using a weighted average strategy:The texture information of the source image is contained in the small-scale layer. Usually, the larger the pixel value of the small-scale layer, the more texture information is retained , so for Small-scale texture detail fusion results:Small scale edge detail fusion results:The edge information and structural information of the source image are contained in the large-scale layer. Although deep learning fusion methods can effectively extract deep features, most of them only extract features without processing the extracted features, which may lead to the degradation of fusion results . In orde(1)t-th convolutional block, and we take c-th channel of the output feature, and Feature extraction: First, the large-scale layer (2)The extracted features are ZCA processed to obtain the new features  be lost , so we t(3)Construction of initial weight maps using Softmax:(4)Using a maximum weight construction method based on average operator (MWAO) method: In order to obtain as much detail information as possible, the largest pixel value in Equation (13) is taken on each large-scale layer as the fusion weight for that layer. Finally, the obtained weight is used to reconstruct the large-scale layer of fusion image:The MWAO method is compared with the method of constructing weight map  to verifReconstruction of the fused image using the obtained fused base layer This section first introduces the datasets and evaluation metrics, as shown in Subjective and objective evaluations of our method were carried out on two different datasets. The datasets are derived from TNO  and MSRSIn order to reduce the interference of human consciousness in subjective evaluation, we chose six evaluation metrics, namely Entropy (EN) , StandarEN computes the amount of information contained in the fused image based on information theory. The higher the EN, the richer the information contained in the fused image:SD is used to describe the statistical distribution and contrast features of images. The larger the SD, the higher the image contrast:AG is used to reflect the sharpness of the image. The larger the AG, the clearer the texture of the details contained in the image:VIF can objectively express people’s feelings when observing images. The larger the VIF, the better the visual effect of the images. The building process is divided into four steps: First, the two source images and their fusion results are divided into blocks; second, evaluating the visual information of the first step’s block results, both with and without distortion; third, calculating the VIF of each sub-band; fourth, calculate the overall indicators.MI indicates the amount of information obtained from the source image, the larger the MI, the more information is obtained.CE is the average value of the relative entropy between the two source images and the fused image, which is used to characterize the pixel difference at the corresponding position between the two source images and the fused image . The smaThe subjective evaluation of fusion results on the TNO dataset is shown in In We employ the six evaluation metrics mentioned in To demonstrate that the methods can produce beneficial effects, we conduct ablation experiments for the base and large-scale layer methods separately. The experiment consists of six parts: (i) Removing the large-scale layer  fusion method from this paper and using FT++ for the base layer; (ii) removing the large-scale layer fusion method and using FT for the base layer; (iii) removing all three methods; (iv) keeping the large-scale layer fusion method from this paper only; (v) keeping the large-scale layer fusion method and using FT for the base layer; (vi) keeping the large-scale layer fusion method and using FT++ for the base layer (our method), where the removed methods are replaced with those of the corresponding scales from the Ref. . Table 2It can be seen that our method achieves the optimum in EN, SD, AG, and CE metrics, which shows that our method has great advantages in information and contrast. The main reason for the lack of advantages in VIF and MI is that our method discarded unnecessary redundant information in the fusion process, which led to the reduction of some reference-based evaluation metrics. However, combined with the subjective evaluation results, our method has clear details and prominent targets, so it provides a good visual effect. In addition, it can be seen from the values of each evaluation metric that the FT and FT++ methods have higher metric values, and among these methods, the combination of ResNet50 and FT++ methods have the best overall performance. This phenomenon shows that the method achieves a better fusion effect overall. It can therefore be shown that the FT++ method and the MWAO method based on the average operator help to improve the image fusion quality.Based on the above subjective and objective evaluation, it can be seen that our method is significantly better than other methods, which proves that our method can more effectively obtain high-quality fused images.Because the hybrid multi-scale decomposition and ResNet50 fusion rule are relatively time-consuming, the running time of our method is slightly longer than that of other traditional methods. However, in terms of fusion effect, compared with the optimal method in the comparison method on TNO dataset, the EN, SD, AG, VIF, MI, and CE of our method are improved by 3.82%, 29.78%, 5.47%, 14.96%, 3.82%, and 30.41% on average, respectively. On MSRS dataset, the EN, SD, VIF, MI, and CE of our method are improved by 5.79%, 14.06%, 24.46%, 5.79%, and 17.51% on average, respectively. Analyzing the above time and performance together, our method is far superior in performance to other comparative methods. Therefore, the cost of a reasonable increase in running time is feasible and worthwhile in order to obtain better fusion results for precise and widespread application in various fields.In this study, we design a novel infrared and visible image fusion method based on significant target enhancement. The proposed method solves the problem regarding the preservation of thermal radiation features. MLGCF is deployed to decompose the source image and extract useful information accurately. To provide smooth and prominent base layers for fusion results, we propose a new method (FT++) to construct the fusion weights for the base layer. Large-scale features are extracted and processed by ResNet50 and ZCA in such a way as to preserve useful details in the source images effectively. The subjective and objective comparison results on TNO and MSRS datasets demonstrate that our method achieves better results compared to the traditional and deep learning-based alternatives. Although our method has shortcomings in terms of running efficiency, the fusion results are improved significantly over other approaches. In upcoming future research, we will further improve this method by reducing the time consumption and deploy it to the target detection task.