Parkinson disease (PD) is a chronic degenerative disorder that causes progressive neurological deterioration with profound effects on the affected individual’s quality of life. Therefore, there is an urgent need to improve patient empowerment and clinical decision support in PD care. Home-based disease monitoring is an emerging information technology with the potential to transform the care of patients with chronic illnesses. Its acceptance and role in PD care need to be elucidated both among patients and caregivers.Our main objective was to develop a novel home-based monitoring system (named EMPARK) with patient and clinician interface to improve patient empowerment and clinical care in PD.We used elements of design science research and user-centered design for requirement elicitation and subsequent information and communications technology (ICT) development. Functionalities of the interfaces were the subject of user-centric multistep evaluation complemented by semantic analysis of the recorded end-user reactions. The ICT structure of EMPARK was evaluated using the ICT for patient empowerment model.Software and hardware system architecture for the collection and calculation of relevant parameters of disease management via home monitoring were established. Here, we describe the patient interface and the functional characteristics and evaluation of a novel clinician interface. In accordance with our previous findings with regard to the patient interface, our current results indicate an overall high utility and user acceptance of the clinician interface. Special characteristics of EMPARK in key areas of interest emerged from end-user evaluations, with clear potential for future system development and deployment in daily clinical practice. Evaluation through the principles of ICT for patient empowerment model, along with prior findings from patient interface evaluation, suggests that EMPARK has the potential to empower patients with PD.The EMPARK system is a novel home monitoring system for providing patients with PD and the care team with feedback on longitudinal disease activities. User-centric development and evaluation of the system indicated high user acceptance and usability. The EMPARK infrastructure would empower patients and could be used for future applications in daily care and research. Parkinson disease (PD) is a chronic degenerative disorder that causes progressive neurological deterioration with profound effects on the affected individual’s quality of life -4. It afTherefore, there is a substantial interest in developing home-based care models for PD ,12. The The possibility of home-based continuous monitoring of PD symptoms is now possible using new technologies available today, such as the Internet of Things (IoT), in the form of wearable sensors to capture fluctuating disease activities ,22, poteDespite these technological advances, it is still unclear how these tools could be translated into a better patient self-management and mutual care plan or how they could improve the overall health outcomes . Some imTargeting patients by providing feedback about their disease activities and their related self-management is a promising strategy for PD. Prior publications almost exclusively focused on patient home assessment and measurements as tools for clinical decision-making and targeted clinicians as end users. Home monitoring of disease activities can increase the extent and quality of self-engagement, which in turn can potentially increase patient satisfaction and lead to positive changes in the health-related quality of life and outcomes ,13,31,35We recently published the outlines of an IoT-based system (named EMPARK) aimed at empowering people with PD and their care team ,33. The Improving patient empowerment has been a key concept behind the development of EMPARK. A retrospective evaluation of its ICT design against the ICT for patient empowerment model (ICT4PEM) , togetheAlthough the EMPARK system has not yet been deployed in practice, in this study we demonstrate its system architecture, implementation, and evaluation of user interfaces. As EMPARK is a project under development, our demonstration builds on our prior results regarding the data and interface architecture of the system ,33. As pThe EMPARK system was developed based on the principles of design science research , user-ceAfter a thorough study of the literature and several iterations with experts, we developed the ICT4PEM, a novel framework to support future ICT interventions that primarily aim to improve patient empowerment . To the We applied the ICT4PEM to evaluate the ICT design of the EMPARK system in terms of its relevance and strength for patient empowerment. This was possible by identifying well-defined patient empowerment characteristics within the ICT4PEM that could be easily identified as the primary targets of the EMPARK system interventions. Consequently, we categorized the ICT interventions of EMPARK by strategies, as described in ICT4PEM, and allocated these strategies and ICT interventions to the relevant empowerment characteristics. This analysis of the EMPARK design with the ICT4PEM framework was based on our results from an extensive evaluation of the patient mock-up interface ,33 by paPD is a complex and multimodal neurological disorder that affects the patients’ quality of life. Therefore, the system collects multidimensional data to represent the overall health status of the patients ,40. The Furthermore, decisions regarding the inclusion of variables were made by examining the set of requirements shown in The final selection of individual variables and relevant technologies for home implementation and data acquisition was based on prior literature and recommendations from the Movement Disorders Society Task Force  and by cPotentially empower the patients if they receive feedback on it.Improve understanding of their disease and its relationship with their daily activities and self-management decisions.Improve self-efficacy and control of daily disease management.Improve the overall feeling of support in their self-management and communication with the care providers.People with Parkinson disease, except those with very advanced disease, are capable of self-reporting (regarding self-reported data only).Availability of reliable technology for its objective measurement, and that the technology is nonintrusive in the home environment and nondisrupting regarding the patient’s regular daily activities.Capable of stable wireless data transfer.Preferentially sensor technology with the capacity to provide data for multiple end points (core data).The least possible maintenance dependent.Data are assessed as clinically relevant by expert physicians.Data are assessed as scientifically relevant for future studies regarding their clinical validity.The EMPARK system collects health information from the home environment of patients. The system summarizes the objective data  as well as subjective data  and calculates the corresponding scores per calendar day. All the scores were produced in the range of 0 (low) to 100 (high). Most of these parameters have been previously described elsewhere . NeverthUsing the planned and delivered medication intake times, the medication compliance score was calculated by first calculating the deviation (in minutes) as depicted in the following equation:i iPlanneds the time of a planned medication intake and iTaken is the time of a delivered medication intake. This resulted in scores ranging from 0 to 100. The final medication compliance score per day was calculated using the following equation:where n is the total number of medication intake occasions per day. Patients can take an extra dose to either replace an intended dose that was initially missed or to take another dose. Extra doses administered within 30 minutes before or after a planned time were considered as replacement and omitted in calculations, whereas, for other extra doses, the compliance score was set to the highest score, that is, 100.where This was obtained by using the time information recorded by the bed sensor. A sleep score was calculated based on 3 individual components: sleep duration, habitual sleep efficiency, and sleep disturbance. The components were derived based on the Pittsburgh Sleep Quality Index and the work of Williams and Cook .To calculate sleep duration, the system first calculated the differences  between the time when the bed was occupied and when it was empty and calculated the cumulative hours being in bed:n is the total number of recorded intervals when the individual was in bed. The following rules were applied to calculate sleep duration:where IF Cumulative Hours Being In Bed > 7 THEN Sleep Duration = 0IF Cumulative Hours Being In Bed > 6 AND Cumulative Hours Being In Bed < 7 THEN Sleep Duration = 1IF Cumulative Hours Being In Bed > 5 AND Cumulative Hours Being In Bed < 6 THEN Sleep Duration = 2IF Cumulative Hours Being In Bed < 5 THEN Sleep Duration = 3The second component was the habitual sleep efficiency score, which was calculated by first calculating the ratio between total hours being in bed with interruptions and total hours being in bed without interruptions using the following equation:Min Time is the time when the patient went to bed for the first time during a particular day and Max Time is the time when the patient left the bed the next day. The habitual sleep efficiency score was calculated according to the following rules:where IF Ratio ≥ 85 THEN Habitual Sleep Efficiency = 0IF Ratio > 75 AND Ratio <85 THEN Habitual Sleep Efficiency = 1IF Ratio > 65 AND Ratio <75 THEN Habitual Sleep Efficiency = 2IF Ratio < 65 THEN Habitual Sleep Efficiency = 3The third component that was calculated was sleep disturbances score using the following steps:Total Number Of Interruptions score.Step 1: Count the number of interruptions during sleep, which resulted in Step 2: Apply the following rules:IF Total Number Of Interruptions = 0 THEN Sleep Disturbances = 0IF Total Number Of Interruptions = 1 THEN Sleep Disturbances = 1IF Total Number Of Interruptions = 2 THEN Sleep Disturbances = 2IF Total Number Of Interruptions ≥ 3 THEN Sleep Disturbances = 3Step 3: Calculate the final sleep score using the following equation:The wrist sensor-based system produced scores every 2 minutes for bradykinesia and dyskinesia. To summarize bradykinesia and dyskinesia scores per day, initially the mean values were calculated.An algorithm calculated the alterations from the recommended meal intake time (30 minutes before and 60 minutes after levodopa medication intake) to calculate the score:NWI is the number of reported occasions when meal intake time was within the recommended interval of 30 minutes before and 60 minutes after medication intake, and n is the total number of reported occasions of meal intake during a day.where The score per day was calculated using the following equation:durationExercise is in minutes, modeExercise is the reported physical exercise mode , targetPatient is the individual patient target ranging from 0 to 100, and n is the total number of physical exercise occasions reported per day. As there may be more than one exercise occasion, the algorithm first calculates an average score per day followed by its normalization using the patient target. For instance, if a patient reported 2 exercise occasions during a particular day with a target of 80 with the following data: for the first occasion the patient reported exercise mode of 1 and duration of 10 minutes, for the second occasion the patient reported exercise mode of 2 and duration of 25 minutes then the physical exercise score for the day would be 75 × {[10 + (2×25)]/80×100}.where worst imaginable health and 100 is the best imaginable health.This was derived from each day the patients use a custom application to answer 9 health-related questions  taken frRequirements related to patient and clinician interfaces were gathered through discussions with the end users based on the principles of user-centered design .The development of these requirements for the patient interface has been discussed elsewhere ,33. ThisRegarding the clinician interface, a broad set of requirements was identified during 5 group discussions or brainstorming design  sessionsThe mock-up patient interface was subject to extensive user-centric evaluation as previously published . We provthink aloud methodology [Similarly, simulated clinical scenarios of PD with corresponding data sets were developed by collaborating expert physicians to evaluate the clinician interface. The evaluation was performed with the help of 2 professionals (a neurologist and nurse) from the Uppsala University Hospital. After a brief introduction to the functionalities of the interface, the users had to complete different tasks using the prototype clinical interface representing the simulated clinical scenario, following a semistructured interview. The participant were instructed to comment loudly on their thoughts during the completion of the tasks according to the hodology . The tasWe also conducted semistructured interviews  with theEthics approval from the ethics review authority will be applied for at the clinical trial stage according to Swedish law. However, this paper communicates the early evaluation of the clinical interface that was using dummy data with no personal information. This interpretation of the lack of requirement for ethics approval for this step has been checked with the internal policy of our universities.In accordance with the overall study design, the first stage of EMPARK development was the determination of its major goals. The list and definitions of these goals are as follows:System development: to develop an IoT system comprising sensors and mobile technology to deliver home monitoring of objective motor function, medication use, and patient-reported symptoms and outcomes.Patient empowerment: to empower patients and improve their self-management through a better understanding of their disease with the help of feedback from the system.Clinician support: to provide physicians with relevant and useful information derived from the system regarding symptoms, treatment response, and individual patient coping strategies for better clinical assessment and treatment strategy.Improvement and enablement of research: to establish the EMPARK system as a tool for researchers to better understand the complexity of the disease and to develop and monitor new drugs.Methods section to accomplish the major goals. These included selection of patient-related data for longitudinal acquisition, development of visual interfaces to facilitate follow-up of the health status of people with PD by clinicians, as well as to provide feedback to patients on their data.The core tasks of the EMPARK system development were defined as described in the The mock-up patient interface was functional at the time of the development of the clinician interface. The requirements elicited for the patient interface were also found to be satisfactory by the participating medical professionals. These requirements have been published previously . BrieflyThe clinician interface aims to provide access to aggregated and analyzed data of clinical interest. Furthermore, the patient interface can be shared with the physician or care team for shared decision-making and elaboration of a mutual care plan. The main objectives behind the development of a clinician interface were the elaboration of a web-based application for the analysis and representation of EMPARK data. These objectives were defined based on the following list of specific requirements elicited by iterative consultations with the care team:Provide the care team with data on longitudinal fluctuations of disease symptoms, daily patient activities, and self-medication.Help clinicians discover disturbances, limitations of disease self-management, or aberrations from the care plan.Facilitate communication and co–decision-making with patients about treatment based on objective and longitudinal data on disease activities and self-management.Help the care team foster patient empowerment based on objective data.Physicians and nurses also requested access to and visualization of raw data in addition to integrated summaries. A further requirement was an overview graph representing the daily summary with scores from different variables, such as medication, mealtime, exercise, self-assessment, sleep score, and the 2 motor function scores, such as those for bradykinesia and dyskinesia. Other requests were a flexible and interchangeable time axis for the score results with temporal zoom function, allowing discoveries of temporal associations between different disease activities and treatment and the possibility of selecting variables for representation.The EMPARK system , which iThe functional EMPARK system has 2 intercalated application cycles: one for patient empowerment and self-management and one for codecision and facilitation of mutual care plan development . The selThe data processing layer, which consists of algorithms for processing data from different sensors and a custom software for summarizing the scores, is written in the C# programming language. The web application (clinician interface) was developed in Python 3.6 using Dash Plotly for visualization. The tablet app (patient interface) was written in C# using Microsoft Xamarin for Android, and SQLite was used to access the data. The principles of the Model-View-View Model Prism architectural design pattern were followed for the development of the patient interface app to ensure high-level cohesion.This section is based on our 2 previous publications on the EMPARK patient interface. The first publication describes user-centered design and evaluation processes and provides a detailed description of interface functionalities . The secIn the revised version of the patient interface, the following changes have been made:The navigation from the home screen was improved by new functional and design elements that allowed the user to select and open a 2-week view, a 1-week view, and a 1-day view, as well as open views for the 6 scores according to their actual preference .The 1-day and 1-week views and the motor function (bradykinesia and dyskinesia) scores are presented separately, in contrast to the prior presentation of their averaged values .Similarly, the temporal associations among the 6 different scores  became easier to realize, as we completed this view with additional bar and line graphs .Finally, to facilitate the discovery of correlation among the relevant parameters, the correlation view was modified. It is now possible to change the y-axis to the 2 motor function scores .The development of the clinician interface application was based on specific user requirements as previously described.To enable rapid patient status assessment, information in the clinician interface is displayed and ordered using a top-down approach with a general overview of the patient’s scores and assessments. The main page displays the patient’s Daily Summary graph . The DaiThe raw data and more detailed information for each component are shown in speared graphs, allowing the user to subsequently switch between components by using the checkbox list: (1) medicine intake compliance, (2) self-reported meal intake times, (3) exercise, (4) self-reported details, (5) sleep details, and (6) movement indicators.Some of the main components are the composites of several variables. Self-reported details are composed of several subjective variables  that follow a simple scoring system (0-2), where 0 represents the worst result and 2 represents the best possible result. For the most comprehensive overview of all these parameters along the time scale, we chose a color-coded tile for representation. Sleep details represent sleep duration, efficiency, and disturbances in separate graphs. Movement indicators show bradykinesia and dyskinesia as variables. Following the requirements of the end users, these graphs represent the time plot of the raw wrist sensor data, which neurologists are already familiar with.We used standard time-series data visualization techniques . Some faClicking on any designated point over the graph prompts a pop-up window that displays the exact values for that point of time. Moreover, it is possible to zoom in and out by selecting a section of interest. This action will affect all graphs simultaneously.The patient interface, as previously published, was subject to extensive evaluation ,33. OverHere, we demonstrate the results of clinician interface evaluation.The first task series  includedThe second task series  aimed toNotably, there was a marked difference in the response times between the physician and nurse evaluators. The former completed each task faster by using the functionalities of the interface in a more intuitive way. Similarly, we observed an easier comprehension of the complexity of the represented clinical data by physicians compared with the nurses. The physician completed these tasks with only minimal loud comments that did not reveal any experienced difficulties.In contrast, the nurses required a substantially longer time to solve the same tasks. The delay in task completion by the nurse evaluator was also accompanied and well explained by the loud comments about the difficulties. In agreement with our own observations, these comments suggested that the nurses experienced more difficulties in comprehending the complex clinical data.The observations from the analysis of the task completion performance were further elucidated through subsequent semistructured interviews . As the The overall combined assessment of the interview transcripts and observations made by task completion led to the identification of key areas of user interest. These areas were also identified as the main pathways for future development of the system.We summarized our findings by demonstrating relevant sentences from the evaluators for each defined area . The resBoth users appreciated the novelty and intuitiveness of the EMPARK system regarding its potential for making important disease-relevant data readily available to the clinical practice. Similarly, both users highlighted that in their routine clinical practice, they lack information that the EMPARK system provides. The users found the clinician interface simple enough to accomplish simple tasks that simulated the daily applications. The physician user had no criticism and rapidly completed the tasks without assistance. The nurse found some potential flaws in the current design of the interface that could cause potential problems with later widespread application. He found that the data presentation was clear enough. Both users commented on the lack of time-scale harmonization among the displayed parameters, which made the discovery of associations more difficult. One of the users encouraged the development of automated correlation analysis to support the discoveries of potential causative associations. The clinician suggested that the format of motor function data visualization should be in agreement with what they are accustomed to when analyzing the motor data collected by similar systems. The physician would also welcome the incorporation of additional patient-derived data to the EMPARK, such as commenting possibilities for patients to explain their special pattern of symptoms or report on life events , which could have an impact on either the symptoms or self-management. However, it was also added by both users that such extensions may backfire at the level of patient adherence to EMPARK, as simplicity is often the key for long-term patient cooperation.Using the ICT4PEM , we idenControl: The ability by which an individual can decide about their level of engagement in the health care process and participate in decisions regarding alternative treatment options, including when these are performed by professionals.health status, the diseases, and the function of the actual and possibly available health care processes. Notably, understanding, in our definition, represents the patient’s capacity to apply knowledge in the specific and individual context of the disease and health care provision. Information and its availability to the patient serve as a basis for understanding. Consequently, neither knowledge nor information is sufficient as a characteristic of empowerment, although both should be considered as prerequisites for understanding.Understanding: the potential use of the information a patient has regarding their own Self-efficacy: the sum of cognitive and physical capabilities possessed by the patient that can be used for self-care.We were also able to identify several ICT strategies as described by ICT4PEM, which bear obvious relevance to the ICT interventions of EMPARK. In accordance with ICT4PEM, the ICT interventions must target one or several PEM characteristics. Subsequently, we allocated the selected ICT interventions of EMPARK to these intervention categories as described below:FeedbackFeedback about symptoms, medication, sleep, and activities on a daily and weekly basisMonitoringIoT-based home monitoring of disease symptoms, sleep, and self-medicationSelf-reporting of physical activities and mealtimesSelf-reporting of subjective health-related variablesCommunicationProviding a visual platform, with disease data used by both clinicians and patients, facilitating mutual communication for co–decision-making.AnalysisScoring of symptomsScoring of physical activitiesAnalysis of self-medicationScoring of sleepCorrelation analysesThe sessions with patient organization and questionnaires used to evaluate the design confirmed that these ICT strategies would be welcome for the improvement of the 3 empowerment characteristics we want to improve. However, the degree of effect on empowerment requires evaluation studies that specifically target these characteristics after real-life deployment of EMPARK in clinical studies.This study presents the latest results from the ongoing system development and evaluation of a novel IoT-based home monitoring system (EMPARK) for people with PD. The EMPARK system represents a unique conceptual approach for both its design and long-term goals. To our knowledge, EMPARK is a unique ICT intervention among people with PD, as it aims to provide patients with feedback about their disease symptoms and disease management. Accordingly, patient empowerment through various means is one of the main goals of the overall research project. The EMPARK system also aims to support the care team through the dynamic visual representation of previously unavailable clinical information and, as a long-term goal, contributes to the academic research.daily scores of sleep quality and duration, motor function, medication compliance, meal timing compliance, and physical activities. Daily scoring of these parameters enables an easy-to-comprehend visualization for patients, along with the potential to provide physicians or nurses with detailed data for deeper analysis. We must emphasize that we have not yet achieved the final goal of implementing a functional and full-scale EMPARK ICT infrastructure in daily practice. However, our current and previous findings provide evidence that the main components of the system, such as databases, computing, and visual interfaces, are almost fully developed and evaluated. Our results from the evaluation of the interfaces highlight directions for potential future developments. For instance, the users suggested automated correlation analysis for discoveries of potential causative associations among the different parameters and to use them either as part of the patient feedback or as clinician support.Primarily, EMPARK is an ICT system that relies largely on IoT tools deployed in the patient’s home environment as a source for input data, complemented by patient-related outcome parameters of disease activities and self-management. The objectively measured parameters include continuous daily measures of time spent in bed, motor functions, and medication (levodopa). The self-reported parameters were the time of meals, physical activities, and health-related quality of life questionnaires. As we published information previously, EMPARK synthetizes these parameters with various level of complexity to achieve Multiple lines of evidence suggest that the EMPARK system will be empowering for people with PD. The ICT design of the EMPARK system followed a user-centered design and patient-centric development. This included iterative steps of development and evaluation with respect to both the patient and clinician interfaces. We recently published a novel framework (ICT4PEM) for ICT interventions, with patient empowerment as the main target . Importasnapshot outpatient visits. This renders the care team members to be reliant on patients’ memories of their past symptoms in an attempt to obtain a longitudinal picture of the ongoing disease activities and their self-management. Our findings clearly show that care team members, both the physician and nurse, often regard such information as unreliable because of recall bias and find it insufficient for decision-making. Frequent and high-amplitude fluctuations in PD symptoms further emphasize the need for reliable longitudinal follow-up [The system also sets the support for the care team as a main project goal. In this study, we describe the user-centric development of a clinician interface and the results of its user-centric evaluation using multiple methodologies. The professional management of patients with PD relies largely on periodic ollow-up ,12. We bollow-up . ImportaResearch support is also one of the long-term goals of the EMPARK system. We now present clear support for such potential as part of the evaluation of the clinician interface. The evaluators of the clinician interface support our view that the EMPARK infrastructure, with a special focus on the newly defined scores of daily PD-related activities, could serve the purposes of observational or randomized controlled trials in the future. Our findings strongly support the incorporation of the scored parameters developed by the system into clinical trials, which can be justified by their relevance to the clinical decisions, lack of availability via other sources, and the patients’ own judgment about their usefulness. Such trials could help to establish the role of a parameter scoring system in the daily care of patients with PD, either after or partially in parallel with the previously described stages of implementation. In addition, it would also allow the scientific evaluation of a novel care model for patients with PD, with a focus shifted from snapshot controls to longitudinal assessment and mutual care plan implementation.There are several limitations with respect to the generalizability of our results, which are not only with regard to the potential user acceptance of a clinician interface in a large-scale trial.We are aware that the implementation of the EMPARK system is crucial for assessing long-term user acceptance. Evaluators of the clinician interface and professionals with extensive experience in PD care consider the progressive neurological deficits of patients with PD as a potential risk for a diminishing system implication in the home environment over a longer period. Although we agree, we believe this risk is low considering our results that indicate a high level of acceptance and assessed usefulness among patient evaluators. Similarly, a conclusive assessment of patient empowerment and enhanced self-management, which are our main goals, awaits real-life implementation of the EMPARK system.To address these issues and evaluate strategic goals, we are currently undertaking steps toward the experimental implementation of the EMPARK system in a real-life milieu. Early, limited implementation  can follow the design research principles with the potential of an ongoing, on-demand, smaller adjustment of the system architecture. However, the main assessment of long-term goals, such as the effect of the EMPARK system on patient empowerment, overall health status, or auxiliary effects on health care use, would require overall system stability during a larger clinical trial. We suggest that such a clinical trial should also address the role of the scored parameters as tools for daily clinical practice in PD care. Implementation at a larger scale would result in the accumulation of a large amount of clinical data. We believe that the great potential of such a database for auxiliary research can facilitate the implementation of the EMPARK system by health care providers.The EMPARK system is a novel IoT-based home monitoring system for providing patients with PD and team members with feedback about disease activities. EMPARK is unique in its primary aim of providing patients with feedback on disease symptoms and self-management, consequently enhancing patient empowerment. We describe the user-centric development and evaluation of the system’s clinical interface and show results indicating its high usability in clinical management and shared decision-making with patients. We also provide extensive evidence of how the EMPARK system infrastructure would empower patients and suggest future application in PD-related research. Our results represent the last phase in development before the implementation of EMPARK in a real-life environment.


Treating open fractures in long bones can be challenging and if not performed properly can lead to poor outcomes such as mal/non-union, deformity, and amputation. One of the most common methods of treating these fracture types is temporary external fixation followed by definitive fixation. The shortage of high-quality affordable external fixators is a long-recognised need, particularly in Low- and Middle-Income Countries (LMICs). This research aimed to develop a low-cost device that can be manufactured locally to international standards. This can provide surge capacity for conflict zones or in response to unpredictable incidents and situations. The fixator presented here and developed by us, the Imperial external fixator, was tested on femur and tibia specimens under 100 cycles of 100 N compression-tension and the results were compared with those of the Stryker Hoffmann 3 frame. The Imperial device was stiffer than the Stryker Hoffmann 3 with a lower median interfragmentary motion (of 0.94 vs. 1.48 mm). The low-cost, easy to use, relatively lightweight, and easy to manufacture  device can address a critical shortage and need in LMICs particularly in conflict-affected regions with unpredictable demand and supply. The device is currently being piloted in three countries for road traffic accidents, gunshot wounds and other conflict trauma—including blast cohorts. Every year, there are millions of open long bone fracture cases in Low- and Middle-Income Countries (LMICs) due to high-energy trauma, e.g., traffic accidents and conflict injuries –4. ApproGiven the severity of the soft tissue damage as well as the lack of advanced resources and healthcare training, external fixators play a critical role in treating these fractures in LMICs , 9. HoweTo address the critical needs raised above, the aim of this study was to develop a low-cost, locally manufacturable unilateral external fixator  for LMICs. Not only should this device address the general shortage in those countries, but also enable the surge capacity which is particularly imperative in conflict regions or unforeseeable events, such as the sudden escalation (May 2021) in the Gaza war with nearly 2,000 casualties and no possibilities of importing humanitarian supports , the Bei•relatively lightweight;•easy to use/reuse;•using readily-available material;•manufacturable using conventional workshop equipment; and•provide stiffness similar to commercial fixators.As bone pins were found to be available and easily accessible, these were not included in the specification. The final specifications were communicated to colleagues in other partner locations, including Gaza, and these were confirmed as appropriate, thus permitting these to be considered general to LMICs.This research was conceived due to a shortage of affordable external fixators in Sri Lanka reported by one of the partners, an orthopaedic surgeon. Following detailed fieldwork and documenting clinical and functional requirements, the following specifications were derived:During the project, several versions of the device were developed and modified according to the feedback received from the local partners and surgeons. The final design only is discussed in this paper and other designs were investigated by our partners in Sri Lanka .imperial.ac.uk/external-fixator/drawings.In the standard configuration, each device used to fix one fractured long bone was comprised of four clamping systems and a rod, the component parts which are shown in The device was designed to enable local manufacture in LMICs using conventional manufacturing techniques, i.e., turning and milling. However, during the testing process, it was identified that highly skilled operators were required, resulting in either high labour cost, or low-quality parts. Therefore, a manufacturing toolkit comprising three custom jigs and key required tool parts was also developed . The detIn addition to minimising the required experience/training to produce the devices, using this toolkit leads to increased manufacturing accuracy, decreased manufacturing time, and a more standardised process, as well as being less dependent on the quality of the equipment. Mechanical tolerances are critical to the functioning of the device. In this study, all clamps were quality checked that they complied with the manufacturing tolerances given in the drawing.Cadaver testing was conducted on eight specimens, four femurs and four tibias from four donors . The speReflective markers  were attached to the proximal and distal half of the bone using bi-cortical pins, and a Polaris optical tracking system  was used to track the movement of the bone segments throughout the experiment.Fiducial marker screws were placed on the medial, anterolateral and posterolateral sides of the lesser trochanter, as well as the medial and lateral femoral epicondyles and the proximal and distal side of the fracture . These mUsing the MATLAB script, the PD movement between the proximal and distal ends of the fracture was calculated by projecting the distance between the proximal and distal origin points onto the PD axis. The amplitude of the movement was then found by averaging the peak-to-peak PD movement across the loading cycles.The tibial experiments followed the same protocol as the femur but used different landmarks to construct the axis systems. Markers were placed on the most medial and lateral points of the tibial plateau, and the medial and lateral malleolus of tibia and fibula , and on the proximal and distal ends of the fracture. The direction of the PD axis was defined as the line between the midpoint of the medial and lateral points of the tibial plateau and the midpoint of the malleolar axis. ML axis direction was defined as the line between the medial and lateral points of the tibial plateau. The AP axis was the cross-product between the PD and ML axes. The movement between the proximal and distal ends was again projected onto the PD axis to find the amplitude of the PD movement.Testing for stiffness was performed according to ASTM F1541-17, Standard Specification and Test Methods for External Skeletal Fixation Devices. Specimens were tested under 100 cycles of 100 N compression-tension using an Instron machine and the interfragmentary motion was measured. Stryker Hoffmann®3  was used as the benchmark during the testing process. Four Imperial and Hoffmann®3 fixators were used. The Imperial and Stryker devices weigh 450 and 370 g, respectively. Proximal and distal heads of each specimen were fixed using a short Intramedullary (IM) nail and four pins: two Anterior-Posteriorly and two Medio-Laterally. The specimen was then mounted on the Instron using universal joints .After inserting the bone pins into an intact specimen, the bone was mounted on the Instron and after installing the first fixator, a short segment of bone was cut out using an oscillating saw .Before removing the first device and installing the second one, the gap between proximal and distal parts of the bone was secured using two bone plates (positioned anteriorly and posteriorly) as shown in A Bayesian mixed-effects linear model was run to test for differences in interfragmentary motion between the two devices following the protocol set forth in McElreath . The “rea is the intercept, bonea is the effect of bone (femur vs. tibia), inda is the effect of individual (1–4), and testa is the effect of test . Variable b is a slope, and cycleb quantifies changes in interfragmentary motion over the course of the test , and deviceb quantifies the effect of device . Only the last 59 cycles were used, as the first 31 cycles occasionally applied maximum tensile loads <96 N, and minimum compressive loads >−94 N.Where p > 0.05). Six additional statistical models were run leaving out parameters that appeared insignificant. Watanabe-Akaike Information Criteria (WAIC) was used to compare model performance and choose the best statistical model.Markov Chain Monte Carlo (MCMC) sampling  with weakly informative priors were used, yielding posterior distributions with 8,000 iterations per chain . When examining the posterior distributions, some parameters appeared insignificant  and the Imperial fixator has a median interfragmentary motion of 0.94 mm (95% CI: −1.15 to 3.57 mm). These statistical differences are derived from the WAIC criteria showing that the best model included all parameters except cycle  and the The difference between the performance of the devices can be attributed to the difference in geometry and materials used in Imperial and Hoffmann 3 fixators. The Hoffman 3 is an excellent device, and our data suggests the Imperial fixator can provide similar levels of fracture fixation stiffness, using materials and manufacturing methods that are widely available in Low- and Middle-Income Countries.The Bayesian mixed-effects model used here has enabled the effect of fixator type alone to be assessed accounting for testing sequence and specimens coming from one individual. Therefore, although this model predicts a median interfragmentary motion that is very similar to the median measurement taken from the raw data, the raw data 95% confidence intervals would have been inaccurate, as they would not have taken into account these confounding factors.There have been many studies on low-cost external fixators, but most of them have reported the clinical outcomes , 26–28 oAlthough there is a difference in device stiffness and there is the potential for this to change the local mechanical environment at the fracture site callus , this diOther factors are also important, including cost. The simple design and use of cheap and readily-available materials  and conventional manufacturing processes result in the novel fixator (one rod and four clamps) costing a fraction of the cost of commercial devices. The device is 80 g heavier than Hoffmann 3. No advanced equipment or high level of manufacturing skills are needed when using the manufacturing toolkit. Due to the simplicity of the design and its similarity with Hoffmann 3, the device can simply be implemented with resident-level knowledge. Similar to Hoffmann 3, the novel device can also be used in uni- or bi-planar configurations.This design and testing report has some limitations. Clinical results are not presented and these are required to confirm that the stiffness effects are not detrimental to healing. Also, the 95% CIs for the median interfragmentary motion values are large, reflecting the large level of noise in the data relative to the predictive parameters used in the statistical models. This could be because of the relatively low resolution of the interfragmentary motion data (There is clear evidence of a shortage of high-quality affordable external fixators in low- and middle-income countries, particularly in conflict and other unforeseen events. The affordable unilateral Imperial external fixator for long bone open fractures presented here has comparable performance to a commonly used commercial device and can be manufactured locally to international standards with minimal skills using basic materials and equipment when combined with the provided manufacturing toolkit. Three clinical studies are currently underway in Gaza, Sri Lanka and Ukraine.


The Lagrangian vortex method has the advantage of producing highly detailed simulations of fluids such as turbulent smoke. However, this method has two problems: the construction of the velocity field from the vorticity field is inefficient, and handling the boundary condition is difficult. We present a pure Lagrangian vortex method, including a nested grid to accelerate the construction of the velocity field, and a novel boundary treatment method for the vorticity field. Based on a tree structure, the nested grid algorithm considerably improves the efficiency of the velocity computation while producing visual results that are comparable with the original flow. Based on the vortex-generating method, the least square method is used to compute the vorticity strength of the new vortex elements. Further, we consider the mutual influence between the generated vortex particles. We demonstrate our method’s benefits by using a vortex ring and various examples of interaction between the smoke and obstacles. Incompressible flows can be widely observed in our daily life, such as smoke from burning wood and the vortices generated by water flowing through obstacles. As a main research direction in fluid simulation, smoke simulation has drawn substantial attention in industry and academia. The effective use of limited computing resources to obtain a more realistic effect of smoke movement is still challenging.Various categories of numerical methods were developed to explore different types of complex and changing smoke phenomena. In terms of computing variables, these methods are classified for solving velocity, vorticity, wave function, and so on. In terms of discretization forms, these methods are classified as Lagrangian methods, Eulerian methods, and Lagrangian–Eulerian hybrid methods. Because of their unique advantages, these methods can be used to numerically simulate various flows.The Lagrangian vortex method has a unique advantage in the simulation of unsteady flows where the vortex structures play a leading role, such as the dynamical evolution of a forced shear layer , an impuHowever, unlike the velocity-based Lagrangian method , 8, the To solve the first of the aforementioned problem, we use a nested grid to group the vortex particles based on their positions and treat the vortex particles in the same group as one super vortex particle in an approximate manner. When calculating the velocity at a given position, we traverse the super vortex particles instead of all the original vortex particles. Thus, we can reduce the number of traversals to decrease the computational cost. We use the vortex–generating method to handle the boundary condition for the second problem. Unlike the momentum form of the Navier–Stokes equation, the vorticity at the boundary cannot be directly set. The plane method , 11 in cA parallel nested grid method that groups the vortex particles to decrease the number of vortex particles traversed during the velocity computation, thus reducing the computational cost;A novel boundary treatment method based on optimization. The least-square method is used to compute the vorticity strength of the generated vortex particles, satisfying the non-through and non-slip boundary conditions;A pure Lagrangian vortex dynamics framework that simulates complex vortical smoke phenomena with moving obstacles.Modeling the dynamic evolution of smoke is a laborious task. Owing to the development of algorithms and hardware, researchers have adopted physics-based methods to simulate smoke. Stable Fluids  is a claAmong the Lagrangian methods, the most widely studied methods are the smooth particle hydrodynamics (SPH) and Lagrangian vortex methods. The advantage of the SPH method is its high computational efficiency. This is because the SPH method does not have to solve the global Euler equation. However, its accuracy relies on the massive distribution of particles, and this is not suitable for smoke simulation in large spaces. To solve this problem, Ren et al.  further The Lagrangian vortex method is the most efficient method for simulating complex flows with sparse date and minimal numerical dissipation. This method discretizes the vorticity field on the Lagrangian vortex element and implements a velocity field by using the BS law without the numerical dissipation that is associated with projection. The flow data can be stored on vortex particles , 21, 22,O(N2). To overcome this problem, some classic solutions were proposed, such as the Fast Multipole Method (FMM) -1, We derive ub, of the solid for the dynamic boundary treatment. We also need to update the boundary sampling points in each time step, which can be computed by using d is the spatial dimension, and Different from the static boundary, we need to compute the velocity, U* = ug + u∞ + uf − ub.Substituting Our time integration scheme can be summarized as follows. We first update the position of the vortex and tracer particles. In our method, tracer particles are used for visualization. Then, we handle the boundary condition and solve the stretching and diffusion terms. Finally, we construct the velocity field from the vorticity field by using the modified BS law and the background flow. In each time step, we update the states of the flow by using the following steps, as depicted in Advection. Calculate the induced velocity by using Boundary treatment. Perform collision detection between the particles and the solid, and compute the position and vorticity strength of the generated vortex particles.Stretching. Use the vortex segment method to update the vorticity strength of the vortex particles.Diffusion. Use the PSE method to solve the diffusion term.Velocity computation. Obtain the bounding box based on the distribution of particles. Then, calculate the velocity of the vortex and tracer particles using our nested grid algorithm.Background flow. Add the velocity of background flow to the particles.V and the stretching coefficient δ on the simulation. First, we simulate the rising smoke with three different values of V log(2). The vorticity is concentrated in the core of the vortex ring, and the vorticity direction is tangent to the vortex axis and perpendicular to the normal of the vortex ring. The nested grid is a five-layer grid with the configuration of O(Kv).The simulation results of the octree grid , our nesKg is the number of boundary sampling points, uf and uf+ are the velocity of fluid at the boundary sampling points before and after boundary treatment, respectively. u∞ is the velocity of the background flow, and ub is the velocity of the solid at the boundary sampling points. In the Kármán Vortex Street example, the solid is static and the velocity of the background flow is constant. Therefore, e can be simplified as In addition to the visual results, we provide the computation accuracy of the three cases presented in The first column in The second column in We parallelize most of our method’s steps using OpenMP and implement a GPU version of the nested grid method using CUDA, which is the most computationally expensive part of our method. Our examples are performed on a laptop with a 6-core 2.20 GHz CPU and a NVIDIA GeForce GTX 1060 graphics card. We presented a pure Lagrangian vortex method to produce rich details for smoke animation. Our method is efficient and suitable for parallelism on a GPU, thereby indicating its potential to be applied in real-time applications. This framework has two essential components. A nested grid is used to group the vortex particles and effectively reduce the computational cost of the BS law. This is validated by using the vortex ring example. Further, we proposed a novel vortex-generating method that supports dynamic boundary conditions for handling complex obstacles. We simulated a series of complex gas phenomena, such as the Kármán Vortex Street, colliding vortex rings, and interaction of smoke and obstacles.Future work: The nested grid loses some accuracy when computing the velocity. We can improve this by dividing a direct summation area in the finest grid layer, while the other layers remain unchanged. Moreover, the number of generated vortex particles determines the linear equation’s size, making our method challenging in dealing with the interaction between smoke and large-scale obstacles. Reducing the linear equation’s size or splitting the equation into multiple sub-equations could be beneficial. Finally, the two-way fluid rigid body interaction is a prominent research direction for future work.S1 Video(MP4)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.


Metaheuristic algorithms have a wide range of applications in handling optimization problems. In this study, a new metaheuristic algorithm, called the chef-based optimization algorithm (CBOA), is developed. The fundamental inspiration employed in CBOA design is the process of learning cooking skills in training courses. The stages of the cooking training process in various phases are mathematically modeled with the aim of increasing the ability of global search in exploration and the ability of local search in exploitation. A collection of 52 standard objective functions is utilized to assess the CBOA’s performance in addressing optimization issues. The optimization results show that the CBOA is capable of providing acceptable solutions by creating a balance between exploration and exploitation and is highly efficient in the treatment of optimization problems. In addition, the CBOA’s effectiveness in dealing with real-world applications is tested on four engineering problems. Twelve well-known metaheuristic algorithms have been selected for comparison with the CBOA. The simulation results show that CBOA performs much better than competing algorithms and is more effective in solving optimization problems. If we want to solve a real optimization problem, we must first build the corresponding mathematical model. Setting up a model, of course, means creating a complete description of the problem with variables and mathematical relationships so that all the details of the optimization problem are simulated2.The technique of finding the best feasible solution among all existing ones is known as optimization. Optimization is used in designing and maintaining many engineering, economic, and even social systems to minimize the necessary costs or maximize profits. Due to the wide application of optimization in different sciences, this topic has grown a lot, so it is studied in management, mathematics, industry, and many branches of science3.Deterministic optimization methods can be divided into gradient-based and non-gradient methods, which effectively solve linear, convex, and derivable optimization problems and have a continuous search space. On the other hand, many real-world optimization problems have features such as nonlinear, non-convex objective functions, discrete search spaces, non-differentiable, high dimensions, and high complexity4. The simplicity of concepts, easy implementation, efficiency in nonlinear and non-convex environments, and independence of the type of problem are the features that have led to the widespread use and popularity of metaheuristic algorithms5.The inability of deterministic methods to address such optimization challenges has led to the emergence of effective stochastic approaches in such cases. Metaheuristic algorithms, as the most prominent stochastic method, are capable of tackling optimization problems based on a random search, random operators, and trial-and-error processes6, inspired by biology, the particle swarm optimization (PSO)7, the ant colony optimization (ACO)8, the Artificial bee colony (ABC)9, and the Northern Goshawk optimization8, inspired by animal life.The primary source in the design of metaheuristic algorithms is inspiration from various natural phenomena, swarm intelligence, animal life, biological sciences, physical laws, rules of the game, and so on. Among the most famous metaheuristic algorithms are the genetic algorithm (GA)The critical issue with metaheuristic algorithms is that these methods do not guarantee that they will be able to find the optimal global solution. However, the solutions obtained from metaheuristic algorithms are close to the global optimal. The desire to achieve better solutions has led to the development of numerous metaheuristic algorithms.10 states that the success of an algorithm in handling a set of optimization problems cannot be a reason for the successful performance of this algorithm in dealing with other optimization problems. There is no presumption of the success or failure of a method in optimizing a problem. The NFL theorem explains that no particular algorithm can be introduced as the best optimizer in all optimization applications. The NFL theorem is a source of motivation for researchers come up with better solutions to optimization problems by designing newer metaheuristic algorithms.Given the development of numerous metaheuristic algorithms, the main research question is, is there still a need to design newer algorithms? In answer to this question, the No Free Lunch (NFL) theoremThis paper introduces a new metaheuristic algorithm based on the description of a training process.Every educational process in different types of schools has certain usual properties, forms and stages. In this paper, we were concretely motivated by all specifics of the process of learning the cooking skills of a new chief.The paper provides a mathematical model of two-phase description of the preparation of a new chef, according to the principles of a real cooking school.Both phases are typical of all art schools (including cooking courses) because every student wants to learn from the best chef, but on the other hand, the greatest chefs will not want to prepare weak students. So, in the first phase, the chefs compete with each other so that a table of their quality ranking can be created. Similarly, in the second phase, students compete with each other so that their qualitative ranking can be created according to their cooking abilities.In the mathematical modeling of the first phase, we implemented two master chef strategies. These strategies model the fact that even chefs learn new cooking recipes by observing the teaching of other chefs (Strategy 1), and then they try to improve these observed recipes even more through their autonomous experimentation (Strategy 2).In the mathematical modeling of the first phase, we implemented three student strategies. The first strategy of each student is to choose a chef and learn all of his/her skills. The second strategy of each student is to choose another chef and learn from him/her one skill (one concrete recipe). In the third strategy, students try to improve all their skills by self-experimentation.CBOA ability to handle optimization problems is tested on fifty-two standard benchmark functions and compared with twelve well-known meta-heuristic algorithms. In doing so, CBOA achieves much better results than these competing programs.The innovation and novelty of the proposed chef-based optimization algorithm (CBOA) are:The rest of the structure of the paper is as follows; the literature review is presented in the “Metaheuristic algorithms, according to the primary source of design inspiration, are classified into five groups: (i) swarm-based, (ii) evolutionary-based, (iii) physics-based, (iv) game-based, and (v) human-based methods.11, the African vultures optimization algorithm (AVOA)12, and the snake optimizer (SO)13. The strategy of living things in nature when hunting and trapping prey has been the main idea in designing algorithms such as the grey wolf optimizer (GWO)14, the Golden Jackal optimization (GJO)15, the whale optimization algorithm (WOA)16, the reptile search algorithm (RSA)17, the marine predator algorithm (MPA)18.Theorizing on swarming activities and behaviors in the lives of birds, animals, aquatic animals, insects, and other living things in nature has been the main source of inspiration in the development of swarm-based algorithms. PSO, ACO, and ABC are among the most widely used and popular swarm-based algorithms. The natural behavior of the crowds of birds or fish in search of food have been the main idea of the PSO. Discovering the shortest path between the nest and the food source based on the collective intelligence of ants has been main idea of ACO. Hierarchical efforts and activities of bee colonies in search of food has been the main idea of the ABC. The idea of the ability of living organisms to find food sources in nature has led to the design of several swarm-based metaheuristic algorithms, such as: the tunicate swarm algorithm (TSA)19 are among the most famous evolutionary algorithms whose main design idea is the reproduction process and its concepts.The concepts of natural selection, Darwin’s theory of evolution, and stochastic operators such as selection, crossover, and mutation have been used in the design of evolutionary algorithms. GA and differential evolution (DE)20. Physical forces and Newton’s laws of motion have been the main idea behind the design of methods such as the gravitational search algorithm (GSA) based on gravity force21 and the spring search algorithm (SSA) based on spring force22. Mathematical modeling of the natural water cycle in nature has led to the design of the water cycle algorithm (WCA)23. Cosmological studies and space holes have been the inspiration in designing the multi-verse optimizer (MVO)24. Archimedes principle concepts have been the main idea in the design of the archimedes optimization algorithm (AOA)24.The laws, concepts, and phenomena of physics have been a source of inspiration in designing of numerous methods that fall into the category of physics-based algorithms. Simulated annealing (SA) is the most significant physics-based algorithm produced based on the physical phenomenon of metal annealing24 and the volleyball premier league (VPL)25 are two game-based approaches designed based on the modeling of football and volleyball league, respectively. The strategy of the players to put the pieces together has been the design idea of the puzzle optimization algorithm (POA)26.The rules of the game, the behavior of the players, the coaches, and the referees have been a source of inspiration for designing game-based algorithms. Football game based optimization (FGBO)27. The treatment process that the doctor performs to treat patients has been the main idea in the design of the doctor and patient optimization (DPO)28. The cooperation of the members of a team to achieve success and the common goal of that team has been the main idea in the design of the teamwork optimization algorithm (TOA)29. The City Councils Evolution (CCE) is a human-based approach that is produced based on modeling the evolution of city councils30. The strategic movement of army troops during the war has been the idea employed in the design of the war strategy optimization (WSO)31.Human activities and behaviors in individual and social life have become the idea of designing approaches that fall into the category of human-based algorithms. Teaching–learning-based optimization (TLBO) is one of the most famous human-based algorithms that has been developed based on the simulation of interactions between a teacher and students in the classroomBased on the best knowledge gained from the literature review, no metaheuristic algorithm inspired by the culinary education process has been designed. However, teaching cooking to people who attend training courses is an intelligent process that can be a motivation to design a new metaheuristic algorithm. Consequently, in this study, a new optimization approach has been developed by mathematical modeling the cooking education process, which is discussed in the next section.This article does not contain any studies with human participants or animals performed by any of the authors.Informed consent was not required as no human or animals were involved.This part is devoted to the introduction and mathematical modeling of the proposed algorithm called the Chef-based optimization algorithm (CBOA).Cooking students and young cooks participate in training courses to improve their cooking skills and become chefs. This concept is analogous to metaheuristic algorithms, where several candidate solutions are initialized and then improved through an iterative process to determine the best candidate solution as the solution to the problem at the end of the algorithm implementation. Thus, the process of transforming a cooking student into a chef in a culinary school is a source of inspiration for the design of the proposed CBOA.It is assumed that a certain number of chef instructors are present in a culinary school. Each chef instructor is responsible for teaching a class. Each cooking student can choose which of these classes to attend. The chef instructor teaches students cooking skills and techniques. However, chef instructors also try to improve their skills based on the instructions of the best chef instructor in the school and individual exercises. Cooking students try to learn and imitate the skills of the chef instructor. In addition, cooking students try to improve the skills they have learned through practice. At the end of the course, cooking students become skilled chefs under the training they have received.Mathematical modeling of the above concepts is used in designing the CBOA, which is discussed in the following subsections.The proposed CBOA approach is a population-based algorithm whose members consist of two groups of people, namely cooking students and chef instructors. Each CBOA member is a candidate solution that contains information about the problem variables. From a mathematical point of view, each member of the CBOA is a vector, and the set of CBOA members can be modeled using a matrix according to Eq. .1\documeThe position of the CBOA members at the beginning of the algorithm implementation is randomly initialized for entclass1pt{minimaBy inserting the suggested values of each CBOA member into the variables, a corresponding objective function value is evaluated. As a result, the objective function is evaluated in g to Eq. .3\documeThe values of the objective functions provide essential information about the quality of the candidate solutions. The value of the objective function is the decision criterion for selecting the best candidate solution. Among CBOA members, the member with the best value for the objective function is recognized as the best member of the population and the best candidate solution. During the running of the algorithm, in each iteration, the members of the CBOA are updated, and the corresponding values of the objective function are calculated. It is, therefore, necessary to update the best member in each iteration based on comparing the values of the objective function.After the algorithm is initialized, the CBOA steps are gradually applied to the candidate solutions to improve them. CBOA members consist of a group of instructing chefs and a group of cooking students. The update process for each of these groups is different. Based on comparing the values of the objective function, some CBOA members with better values of the objective function are selected as the chef instructor. Therefore, if the rows of the CBOA population matrix are sorted in ascending order according to the value of the objective function , then the group of the first  in Eqs.  and 5)..\documenIn a culinary school, it is assumed that several chef instructors are responsible for teaching cooking skills to students. Chef instructors follow two strategies to improve their cooking skills. In the first strategy, they emulate the best chef instructor and try to learn the chef instructor techniques. This strategy demonstrates the global search and CBOA exploration capabilities.The advantage of updating the chef instructors based on this strategy is that the top chefs (top population members) improve their skills based on the best chef (best population member) before they start teaching students. Hence, there is no direct dependence on updating the students’ position only on the base of the best member of the population in CBOA design. Furthermore, this approach prevents the algorithm from getting stuck in local optima and causes different areas of the search space to be scanned more accurately and effectively. Based on this strategy, a new position for each chef instructor is first calculated for sing Eq. .7\documeIn the second strategy, each chef instructor tries to improve his cooking skills based on individual activities and exercises. This strategy represents the local search and the CBOA’s exploitation ability. If each problem variable is considered a cooking skill, a chef instructor will try to improve all of those skills to achieve a better objective function value.The advantage of updating based on individual activities and exercises is that each member, regardless of the position of other population members, seeks to discover better solutions near the position where it is located. There is a possibility that better solutions can be obtained based on local search and exploitation, with minor changes in the position of population members in the search space. According to this concept, around each chef instructor in the search space, a random position is generated for ing Eqs.  to 10)..\documening Eqs. .8\documeCooking students attend culinary school to learn cooking skills and become a chef. In the design of CBOA, it is assumed that cooking students follow three strategies to learn cooking skills. According to the first strategy, each cooking student randomly chooses a class taught by one of the chefs, and then he is taught cooking skills by this chef instructor. The advantage of updating cooking students based on this strategy is that there are different chef instructors available to lead them, resulting in cooking students learning different skills  based on the guidance of the chosen chef instructor. On the other hand, if all cooking students learn only from the best chef-instructor , then an efficient global search in the problem-solving space would not be possible. This strategy is simulated in the CBOA in such a way that first for each cooking student, a new position is calculated based on the training and guidance of the chef instructor, for mentclasspt{minimaThis new position replaces the previous position for each CBOA member, if it improves the value of the objective function. This concept is modeled for N by Eq. .13\documIn the second strategy, since each problem variable in the CBOA is assumed to be a cooking skill, each cooking student tries to learn one of the skills of the chef instructor completely and fully imitate the chef instructor . This strategy enhances the global search and exploration capabilities of the CBOA. The advantage of this strategy is that instead of updating all candidate solution variables , only one variable  changes. It may not be necessary to update all member position coordinates to achieve better solutions.In the design of CBOA, this “skill’’ represents a certain component of a vector of cooking skills of a randomly selected chef instructor According to this concept, a new position is calculated for each CBOA cooking student member using Eq. .14\documd on Eq.  if it imIn the third strategy, each cooking student tries to improve his cooking skills based on his individual activities and exercises. In fact, this strategy represents the local search and the CBOA’s exploitation ability. The advantage of updating cooking students based on the strategy of individual activities and exercises is that it increases the power of local search and exploitation of the algorithm in achieving better possible solutions near the discovered solutions. In this strategy, similar to the local search strategy of chef instructors, cooking students try to converge to better solutions with small and precise steps. If each problem variable is considered a cooking skill, a cooking student will try to improve all of those skills to achieve a better objective function value.According to this concept, around each cooking student in the search space, a random position is generated by Eqs. , and 9)9) and a d by Eq. .17\documA CBOA iteration is completed by updating all members of the population. The CBOA enters the next iteration with these new statuses, and the groups of chef instructors and cooking students are respecified. The population members are updated based on the implementation of the CBOA steps according to Eqs.  to 17)  17) untiT is the maximum number of CBOA iterations and In this subsection, the computational complexity of the CBOA is analyzed. Preparing and initializing the CBOA for an optimization problem, with the number of decision variables This section presents simulation studies and an evaluation of the ability of CBOA to solve optimization problems and real practice tasks. For this purpose, a set of 23 standard benchmark objective functions has been employed. For this purpose, a set of 23 standard benchmark objective functions has been employed. The reason for choosing this collection is as follows. Seven unimodal functions mentclass2pt{minimThe performance of the proposed CBOA approach in optimization is compared with the results of 12 well-known metaheuristic algorithms. The criterion for selecting these 12 competitor algorithms is as follows. PSO, GA, and DE are three prevalent algorithms that have been employed in many optimization applications. CMA, GSA, TLBO, GWO, MVO, and WOA are the six most cited algorithms that always have interested researchers. Finally, the three algorithms, MPA, TSA, and HBO, are the algorithms that have been released recently and have received a lot of attention and application in this short period. The values adopted for the control parameters of the competitor algorithms are specified in Table The CBOA and each of the competing algorithms are tested on benchmark functions in twenty independent implementations while each execution contains 1000 iterations. Optimization results are reported using six indicators: mean, best, standard deviation (std), median, execution time (ET), and rank.The CBOA and each competing algorithm are tested on benchmark functions in twenty independent implementations, while each execution contains 1000 iterations. Optimization results are reported using six indicators: mean, best, standard deviation (std), median, execution time (ET), and rank.The optimization results of the unimodal functions Results of CBOA and all competitor algorithms on high-dimensional multimodal functions of The results of the CBOA and competitor algorithms for the fixed-dimensional multimodal functions In the other cases where the CBOA has the same conditions in terms of the “mean index’’, it performs more efficiently than the alternative algorithms due to better values for the “std index’’. Analysis of the simulation results shows that the CBOA performs better than competitor algorithms and has a remarkable ability to strike a balance between exploration and exploitation.In other cases where the CBOA has the same conditions in terms of the “mean index’’, it has more efficient performance than the alternative algorithms due to better values for the “std index’’. Analysis of the simulation results shows that the CBOA performs better than competitor algorithms and has a remarkable ability to strike a balance between exploration and exploitation.The performance of CBOA and competitor algorithms in evaluating the benchmark functions entclass1pt{minima32 with the significance level In this subsection, a statistical analysis of the performance of the CBOA compared to competitor algorithms is provided to determine whether the superiority of the CBOA is statistically significant. To provide this analysis, the Wilcoxon test of rank sumsThe proposed CBOA is a stochastic optimizer that can achieve the optimal solution by using its members’ search power in an iteration-based process. Therefore, the values of the parameters In the first study, to analyze the sensitivity of CBOA to the parameter In the second study, to analyze the sensitivity of CBOA to the parameter Metaheuristic algorithms are random approaches with which their main idea employed in the optimization process is random search in the problem-solving space. This random search at both local and global levels is the key to the success of metaheuristic algorithms. In optimization studies, the local search power, which indicates the potential for exploitation, causes the algorithm to look for better solutions around promising candidate solutions and move closer to the optimal global solution. The capability of the “exploitation phase’’ in metaheuristic algorithms is best tested when implemented on functions that have only one main solution. Unimodal functions with this feature are good options for evaluating the exploitation ability. The optimization results of unimodal functions The power of global search, which demonstrates the exploration potential of metaheuristic algorithms, allows the algorithm to scan different areas of the search space to discover the optimal global area. The capability of the “exploration phase’’ in metaheuristic algorithms designed for optimization can best be evaluated using optimization problems with several local optimal solutions. Therefore, high-dimensional multimodal functions are a good choice for evaluating exploration ability. The implementation results of CBOA and competitor algorithms on functions The critical point in the capability of metaheuristic algorithms is that in addition to having the desired ability in exploitation and exploration, there must be a balance between these two capabilities so that the algorithm can find the main optimal region and converge towards the global optimal. Fixed-dimensional multimodal functions are good options for testing the ability of metaheuristic algorithms to strike a balance between exploitation and exploration. Optimizing the The simulation findings show that CBOA has a high quality in exploitation, exploration, and balance between them, which has led to its superior performance compared to similar competing algorithms.33. The To analyze the capability of the proposed CBOA approach in complex optimization problems, the proposed algorithm is implemented on the CEC 2017 test suite. This set includes three unimodal objective functions 34, for SRD in Refs.36, and for WBD and TCSD in Ref.16. The optimization results of these four engineering optimization problems are published in Table In this section, we will show the effectiveness of CBOA in solving real-world problems. To this end, CBOA and competing algorithms are used in the optimization of four engineering applications: (i) pressure vessel design (PVD), (ii) speed reducer design (SRD), (iii) welded beam design (WBD), and (iv) structural tension/compression springs (TCSD). Mathematical models, details, and information about these technical challenges are expressed for PVD in Ref.This paper introduced a new human-based metaheuristic algorithm called the chef-based optimization algorithm (CBOA) and designed it to address optimization issues. The process of learning cooking skills by people who attend training cooking courses inspired the implementation of the proposed CBOA. Different phases of the cooking training process were mathematically modeled to design the CBOA implementation. The CBOA’s performance was evaluated on fifty-two benchmark functions, including seven unimodal functions, six high-dimensional multimodal functions, ten fixed-dimensional multimodal functions, and 29 functions of the CEC 2017 test suite The optimization results showed that CBOA could be used effectively in solving optimization problems due to its ability to maintain a balance between exploration and exploitation. Moreover, the simulation results showed that CBOA is more efficient and competitive than the twelve compared algorithms because it usually provides better solutions.In addition, the employment of the CBOA on four engineering optimization issues demonstrated the high ability of the proposed approach to address real-world applications.The proposed CBOA algorithm is a stochastic approach and therefore has some shortages and limitations. As with all metaheuristic algorithms, there is no guarantee that the solutions obtained from the CBOA for optimization problems are equal to the global optima of those problems. Although the CBOA has provided reasonable solutions to most of the objective functions studied in this paper, according to the NFL theorem, there are no preconditions for its successful implementation in all optimization applications Therefore, of course, there is a shortage and limitation of the proposed CBOA that its application may fail in some optimization problems. Also, it is always possible that researchers will design newer metaheuristic algorithms to provide better solutions to real optimization problems than existing algorithms, such as the proposed CBOA method.The introduction of the CBOA opens research directions and tasks for future work. The most specific research potential for the CBOA is the development of binary and multi-objective versions of this proposed approach. The employment of CBOA in optimization applications in various sciences and real-world challenges are other proposals in this paper.


Sodium-cooled reactors (SFR) have always been recognized as one of the most promising candidates for the fourth-generation nuclear systems as announced by the Generation-IV International Forum. In the design of SFR, helical wire-wrapped rod is applied to stabilize the structure of the rod bundle and enhance coolant mixing. Although there has been considerable research on SFR in computational fluid dynamics (CFD), the phenomenon of heat transfer has rarely been paid attention to. This article discovered that there exists reversed heat flux from coolant to wrapped wire, which is contrary to our usual understanding. This phenomenon has not been reported in previous CFD calculations. Hence, a solid heat conduction model is proposed to prove this phenomenon and analyze the heat transfer process. The simulation results show that the wrapping wire embedding depth, the shape of the calculation domain and the physical properties of all components have great influence on the magnitude of the reversed heat flux. The present findings will have strong influence on the temperature field and maximum value of the fuel rod as well as profound reference value for future flow calculation, especially in grid generation and treatment of the junction between the winding wire and fuel rod. It has been widely acknowledged that fast reactors have a higher neutron utilization compared to thermal reactors. So far, historical experiences of design, construction, testing, operation, inspection and repair of past or existing demonstration and/or prototype SFRs, such as PFR (UKAEA), BN-350 (Kazakhstan), BN-600 (Russia) and Monju (Japan), have established the technological basis of the SFR . Wire-wrNovendstern developed a semi-empirical model to predict pressure drop in a wire-wrapped fuel pin bundle, which is able to predict the value of the pressure drop within 14% over a wide range of geometries in the turbulent flow regime . GajapatTao Wu et al. conducted numerical research on microchannel heat sinks under high temperature conditions for diverse cross-section shapes, different liquid metal and various inlet velocities . It was Bovati et al. used Reynolds-Averaged Navier-Stokes (RANS) models to predict the axial and transverse pressure drops for a range of Reynolds numbers from 1270 to 100,000 in the numerical investigation of the 61-pin wire-wrapped bundle. They demonstrated that RANS is a suitable approach in predicting velocity and pressure fields in wire-wrapped rod bundles, with a relatively low computational effort [Jeong and Song used an SST turbulence model to conduct a numerical investigation of a JAEA 7-pin fuel assembly experiment with local blockage for SFR. They compared the results with the experimental data and found small-scale vortex structures significantly enhance the convective heat transfer while large-scale vortex structures supply thermal energy near the heated cladding wall surface .From all the above summaries, the conclusion can be drawn that, previous researches focused more on the fluid field because of the complex geometry, and so some details in heat transfer and temperature were ignored. At the same time, the grids or meshes near the wrapping wire are always sacrificed or compromised for the flow field calculations for CFD analysis. The most common method is to embed the winding wire into the fuel rod. Obviously, it will have a strong influence on the local heat transfer. This article discovered a phenomenon that reversed heat fluxes exist in the junction between the wrapping wire and the fuel rod which do not appear to have been reported. Hence, a solid model of heat transfer is proposed to prove this phenomenon and explore the factors which may have influence on it.As Merzari et al.  reportedtar CCM+ . Kays prThe initial turbulent intensity I is set to 5% which is a default value of Star CCM+. Based on turbulent intensity, turbulent kinetic energy is evaluated by 9 W/m3) is used only in the rod bundle ρ=1012, separately. Their physical properties are listed in The applicable temperature range of the above fitting formulas was 373.15 K to 1073.15 K. In the simulation of flow, the reference temperature was selected as 645 K. The materials of cladding and fuel rod bundle were stainless steel Ti316 and UOThe mesh was created by Star CCM+ . The primulation . Due to mulation , more memulation  by Wang Volume change is a very important value which can measure the quality of the mesh unit in Star CCM+. If the value is 1.0, it means that the mesh has a larger or equal volume than its neighbors, and if the value is 0.01 or less, it is considered a poor mesh quality . As showIn this study, the fluid case was calculated by commercial CFD codes of Star CCM+ on a 32-core computer. The convergence criterion was set to There are many factors that will have influence on heat exchange in the simulation of fluid and as the above shows, the phenomenon is not very obvious in fluid calculation. The velocity of flow in the junction is much smaller than in the main flow so the heat conduction plays a major part of heat transfer in the junction. After considering these, a solid heat conduction model is proposed, in which only the fluid region is turned into a solid one, to prove the existence of this phenomenon. In the solid model, the properties of sodium are kept the same as fluid. There are four potential paths that the heat flux may pass through the wire and cladding to the sodium as Furthermore, since the thermal resistance from flow to wrapping wire in fluid is obviously smaller than that in solid, the tendency of reversed heat fluxes in fluid is stronger than it in the solid. Therefore, if reversed heat fluxes still exist in the solid model, they must also exist in the fluid model.In order to reduce the amount of calculation, a one-pin model was selected as simplification. Geometric dimensions of rod, winding and wire are the same as fluid model shown in Surface reconstruction and repair technology and polyhedral mesh generator of star CCM+ are applied to generate high-quality grids. Curve control near the junction is used to generate denser grids so that the shape of the junction is closer to reality and the accuracy of simulation can be higher. Furthermore, it can get more accurate values such as temperature, fluxes, and so on. Mesh resolution can have a great influence on the simulation accuracy. Thus, to evaluate the dependency of simulation accuracy on the mesh resolution, three different mesh types were considered in the validation calculation. Base size is an important value which can decide the scale and number of the grids generated by Star CCM+. With a larger base size, less mesh is expected. In the three cases, mesh base sizes in region of Na and wire cladding are respectively set to 0.1 mm, 0.12 mm and 0.16 mm, while base size of rod is still 0.26 mm. Mesh numbers for each case are shown in To prove the calculation results are independent of mesh resolution, 15 points with radially equidistant interval of 2 mm were selected in the section perpendicular to the pitch direction, at the middle length of fuel rod. In The contact between wrapping wire and cladding has a significant effect on the calculation results because the geometry at the junction will change with it. The embedding depth is often described by the distance from wire to rod (“e”) as defined in From case 1 to case 3, the embedding depth gradually decreases which means the distance “e” increases and the sharp corner at the junction gets more distinct. In this way the situation is approaching engineering practice. As shown in Since the solid model is a simplification of the flow model, the size of calculation domain may have an effect on the results. Therefore, three cases in which the value of side length “a” in Considering that for smaller embedding depth, the phenomenon is more obvious and easily observed, the embedding depth “e” is set to 3.45 mm, and in In SFR the coolant is sodium and material of cladding and wrapping wire is Ti316 alloy. Because thermal conductivities vary in different materials, which directly affects the thermal resistance, physical properties have a significant impact on such phenomenon. To figure out how the physical properties affect the phenomenon, four cases were calculated for comparison and are shown in In Case 1, conductivity of sodium doubles as before which means its thermal resistance becomes half of the previous value. Thus, heat transfer is better in the coolant, and heat fluxes only transferred by coolant are more than going back through the wrapping wire. In this way, the phenomenon of reversed fluxes become weaker. Under the same logic, the phenomenon gets stronger with the decrease of thermal conductivity of sodium as seen in As described in this article, a reversed heat flux phenomenon near the junction between wrapping wire and cladding was discovered by accident in the simulation of a sodium-cooled 7-pin wire-wrapped rod bundle model. The same phenomenon in an imaginary solid thermal conductivity model confirms that it does exist. Some factors have been considered and researched. The main conclusions are listed as follows:With an increase in embedding depth, the phenomenon of reversed heat flux is enhanced and the average value of the reversed heat flux gets larger. The traditional embedding method in CFD may not get this phenomenon because it may obtain an incorrect local temperature field.Thermal conductivities of coolant and wire cladding both have great influence on the reversed heat flux by the thermal resistance on the path of reversed flux. Increasing the thermal conductivity of the wrapping wire or decreasing the thermal conductivity of the coolant can significantly enhance this phenomenon. When the thermal conductivity of sodium is eight times its actual value, the phenomenon will disappear.Finally, in previous simulation research of flow, regarding the walls of wrapping wire as adiabatic and choosing homogeneous surface heat fluxes boundary condition are often adopted to reduce computation quantity. However, according to present results, it is obvious that such simplifications are unreasonable to some extent. Moreover, though high temperature near the junction between the wrapping wire and cladding has already been noticed, it is often explained by low coolant velocity near the wall, but the results in this article may provide another explanation. Furthermore, the work in this article can provide reference values for future flow calculation, especially in grid generation and treatment of the junction between the wrapping wire and the fuel rod.