Steel rebar corrosion is one of the predominant factors influencing the durability of marine and offshore reinforced concrete structures, resulting in economic loss and the potential threat to human safety. Distributed fiber optic sensors (DFOSs) have gradually become an effective method for structural health monitoring over the past two decades. In this work, a strain transfer model is developed between a steel rebar and a DFOS, considering pitting-corrosion-induced strain variation in the steel rebar. The Gaussian function is first adopted to describe the strain distribution near the corrosion pit of the steel rebar and then is substituted into the governing equation of the strain transfer model, and the strain distribution in the DFOS is analytically obtained. Tensile tests are also conducted on steel rebars with artificially simulated corrosion pits, which are used to validate the developed model. The results show that the Gaussian function can be used to describe the strain variation near a corrosion pit with a depth less than 50% of the steel rebar diameter, and the strain distribution in the DFOS analytically determined based on the developed strain transfer model agrees well with the tensile test results. The corrosion pit depth and loading force in the steel rebars estimated based on the proposed model agree well with the actual values, and therefore, the developed strain transfer model is effective in detecting pitting corrosion and loading force in steel rebars. Due to easy accessibility and low cost of raw materials, reinforced concrete (RC) is one of the paramount artificial building materials in the world. It has low cost, good integrity and can be used to manufacture structural elements with any shape. However, during its entire service life, RC structural deterioration is inevitable, especially for those exposed to aggressive environments. For instance, reinforcement steel corrosion is one of the major causes of RC structural degradation in marine environments or in cold districts with frequent application of deicing salts ,2. ReinfConventional sensors to monitor steel rebar corrosion in RC structures are either electrochemical-based methods  or physical-based techniques  ,9. CompaMany researchers have investigated distributed optical fiber sensors (DFOSs) for corrosion monitoring of steel rebars over the past two decades. According to different monitoring objects, the utilization of a DFOS to monitor steel rebar corrosion is generally classified into direct and indirect methods. A DFOS is wrapped directly around the steel rebar to measure corrosion-induced volume expansion according to the direct method , while iLocalized corrosion or pitting corrosion is the most prevalent type of corrosion that occurs in steel rebar for RC structures in a chloride-rich environment. Compared with generalized corrosion, pitting corrosion is more dangerous. It causes stress concentration and strain variation for both RC surfaces and steel bars. There are many strain sensors to monitor strain, such as traditional strain gauges and dual-interrogation-mode radio frequency identification (RFID) strain sensors ,23. HoweMany strain transfer models have been proposed to describe the transfer of substrate strain to optical fiber sensors in the past three decades. Based on the assumptions that all materials are linear elastic and all interfaces are perfectly bonded, Ansari et al.  proposedHowever, few studies discuss the strain transfer effect between DFOSs and steel rebars with pitting corrosion. Therefore, to monitor pitting corrosion in steel rebars based on the strain variation obtained from a DFOS, it is necessary to develop a strain transfer model between a DFOS and a steel rebar with pitting corrosion, which in turn can be used to back-calculate the size of pitting corrosion, as well as the strain level in the steel rebar.This work aims to develop a strain transfer model between a steel rebar with pitting corrosion and a DFOS and, further, to evaluate the size of pitting corrosion and loading force in the steel rebar. First, a small groove is cut along the longitudinal ridge of a steel rebar, and then a DFOS is embedded in the groove with epoxy resin. In the meantime, one V-shaped cut with five different depths is made in the middle of the steel rebar to simulate different sizes of pitting corrosion. Second, tensile tests are conducted, during which the DFOS strain distribution is recorded under different loading forces. Third, finite element models of the steel rebar are established, and the steel rebar strain distribution at the location of the DFOS is obtained, along the length, which is compared with DFOS strain curves. Fourth, a Gaussian function is proposed to fit the strain distribution of steel rebars obtained numerically and then is substituted into the governing equation of strain transfer. The analytical strain distribution function of the DFOS is determined by solving the governing equation. Fifth, the parameters in the Gaussian function are determined by fitting the analytical strain distribution function of the DFOS with those obtained during tensile tests, and then the size of the simulated pitting corrosion and loading force in the steel rebar are estimated and compared with the actual values.Hot-rolled ribbed steel bars (HRB 400) with a diameter of 12 mm and a length of 500 mm were used in this study. The yield strength and elastic modulus of the steel rebars were measured to be 400 MPa and 180 GPa, respectively. In order to quantitatively describe the strain transfer law between the matrix and the optical fiber at the pit position of the local corroded steel bar more accurately, one V-shaped cut was made in the middle of the steel rebars to simulate pitting corrosion, as shown in Commercially available single-mode optical fiber was used as a distributed fiber optical sensor (DFOS), which consisted of cladding and a core with a diameter of 125 µm and 9 µm, respectively. The DFOS had an outer layer of polyimide coating that protected it from damage. To install the DFOS along the lengths of steel bars, a small groove was precut along the longitudinal ridge of each steel rebar. The dimensions of the precut groove were around 1.0 mm × 2.0 mm, as shown in Tensile tests were performed on steel rebars using an MTS machine  with displacement control, as schematically shown in To obtain the strain distribution of steel rebars at the location of the embedded DFOSs, finite element (FE) models were also constructed using Abaqus software. The constitutive law of steel rebars used in the FE analysis is shown in For comparison, the FE-simulated strains at the location of the DFOS are also shown by the dashed lines in As the depth of the V-shaped cut increased to 20% and 30% of the diameter of the steel rebars, as shown in a, b, and c are parameters that can be obtained via curve fitting; It can be observed from the previous section that there are significant differences between the OFDR-measured strain data and the FE-simulated strain distribution, especially near the V-shaped cut section. The FE-simulated strains are considered to be the actual strain of the steel rebar at the location of the DFOS, while the measured strain is the deformation of the DFOS, which is transferred from the steel rebar through the epoxy resin and the fiber coating layer. Before deriving the equation for strain transfer, the strain distribution in the steel rebars at regions near the V-shaped cut is modeled with a Gaussian function, which is mathematically expressed as follows:a and b are given as follows: Based on the parameters of fitted curves in R2 of the two fitting surfaces were both greater than 0.980, indicating that the fitting accuracy could be improved by considering both parameters a and b, and satisfactory pit depth and loading force could be estimated with high accuracy without considering parameter c. Therefore, in the following sections, parameter c is directly assigned as 0.00813, which is the average value of parameter c in The a, b, and c. Then, for physical tensile tests, a new fitted equation derived based on the strain transfer theory should be used to fit the measured fiber strain distribution to get the Gaussian parameters. The process of obtaining the fitted equation is as follows:Equations (2) and (3) provide functions for predicting pit depth and load by Gaussian parameters k is a constant that is dependent on the dimensions and material properties of the DFOS, which is written as follows [As the DFOS was embedded in the host material, all the intermediate materials were assumed to be linearly elastic, and the governing equation of strain transfer from the host material to the DFOS can be expressed as follows ,41:(4)εf follows ,41:(5)k2When substituting Equation (1) into Equation (2), the governing equation is as follows:The solution of differential Equation (4) consists of a complementary solution and a particular solution. The complementary solution can be obtained by solving the following:Assuming a solution of Since Thus,Therefore, the general solution is as follows:The particular solution of Equation (6) can be obtained via variation of parameters. List the basis solutions in The Wronskian of LetThe particular solution can be given with the following:Thus, the particular solution is as follows:Therefore, the solution of Equation (4) is expressed as follows:Parameters Equation (23) will be used to fit the measured fiber strain distribution. The steel rebar with a cut depth of 4.8 mm and a loading force of 8.15 kN was used as an example to validate the proposed strain transfer model considering pitting corrosion in steel rebar. According to the fitted Gaussian function, a, b, and c, which were dependent on the pit depth and loading force in the steel rebar. Therefore, relationships needed to be established between the Gaussian parameters and the pit depth, as well as the loading force in the steel rebar, which in turn could be used to estimate the pit depth and loading force in the steel rebar based on the readings of the DFOS. Based on the fitted parameters in a and b are given as Equations (2) and (3).The purpose of the proposed strain transfer model is to estimate the pit depth and the loading force in the steel rebar based on the strain curve of a DFOS embedded in the steel rebar. It should be noted that the analytical strain distribution obtained from the proposed strain transfer model in Equation (23) was a function of Gaussian function parameters To verify the accuracy of Equations (2) and (3), the analytical strain distribution function obtained from the developed strain transfer model in Equation (23) was used to fit all DFOS strain readings for steel rebars with cut depths ranging from 10% to 40% of the D, and The fitted Gaussian function parameters were substituted into Equations (22) and (23) to obtain the estimated pit depth and loading force in the steel rebars. Hydrochloric acid was used to accelerate the corrosion of steel bars to create a pit. The scanned figure of the final pitting corrosion is shown in A strain transfer model was developed between a corroded steel rebar and a DFOS considering pitting-corrosion-induced strain variation in the steel rebar, and the strain distribution in the DFOS was analytically determined by solving the governing equation of the strain transfer model.A Gaussian function was proposed to fit the strain distribution near the corrosion pit in the steel rebar, and the fitting parameters were dependent on the loading force and the pit depth.The strain distribution of the DFOS analytically obtained based on the proposed strain transfer model agreed well with the actual strain distribution of the DFOSs embedded in the steel rebars during tensile tests.The pit depth and loading force in the steel rebars were estimated based on the proposed strain transfer model, and the estimated values agreed well with the actual pit depth and loading force.The source of errors between the estimated and the actual pit depth or loading force were mainly from (i) the simplified strain distribution near the corrosion pit of steel rebars with the Gaussian function; (ii) the assumed linear elasticity of the intermediate materials between the steel rebars and the DFOS, as well as a perfect bond between them; and (iii) the difference between the FE-simulated strain and the actual strain in the steel rebars during tensile tests.In this work, a strain transfer model between a DFOS and a steel bar with a corrosion pit was developed. A Gaussian function was substituted into the governing equation of the strain transfer to describe the pit-induced strain variation. The proposed strain transfer model was validated via tensile tests of steel rebars with different depths of V-shaped cuts. The main conclusions of this research are summarized as follows:Although the strain transfer model was effective in detecting the corrosion depth and loading force of steel bars, there are some limitations: (1) the proposed strain transfer model was only applicable to a single corrosion pit; (2) the steel bars were in the elastic tension stage; (3) the pit depth should be less than or equal to 40% of the steel bar diameter; and (4) the corrosion pits were artificially V-shaped, which is different from the actual shape of corrosion pits in engineering practice. In the future, a more generalized strain transfer model should be developed that is able to detect multiple corrosion pits when a steel bar is in both elastic and plastic stages and the corrosion depth is greater than 40% of the steel bar diameter. Experimental work should be conducted on reinforced concrete structural members  subjected to different times of corrosion.


Journal of Personalized Medicine, some controversial and scarcely investigated topics related to AF have been introduced, with the aim of providing holistic care and treatment in AF. These topics include improving the detection, adverse outcome prevention, and risk factor optimization in AF patients.Atrial fibrillation (AF) is the most common cardiac arrhythmia in the general population. The high prevalence of this condition—which is expected to be even higher in upcoming years —has motiEscribano et al. aimed to conduct an analysis of the f-wave harmonic spectral structure to improve catheter ablation (CA) outcome prediction through several entropy-based measures computed on different frequency bands in 151 patients with persistent AF under radio frequency CA. Remarkably, the authors demonstrated in this pioneering analysis of the f-wave harmonic spectral structure that the presence of larger harmonics and a proportionally smaller dominant frequency peak was strongly associated with a decreased probability of AF recurrence after CA .To better understand the CA process, Vraka and colleagues have decomposed crucial CA steps, including coronary sinus catheterization and the impact of left and right pulmonary vein isolation (PVI). In brief, they showed that left PVI is the critical part of the CA of PVs for paroxysmal AF patients, significantly altering the P-wave duration, whereas the effect of the CA of PVs on the coronary sinus is less straightforward and is demonstrated to a lesser extent. The authors suggest that other atrial structures may be more indicative of the ablation outcome and should be assessed as alternative references .Osorio et al. compared the performance of cycle length estimations of three different local activation wave detection methods: the hyperbolic tangent (HT) function, an adaptive amplitude threshold (AAT), and a cycle length iteration (ACLI). For the HT method, the accuracy, sensitivity, and precision were higher compared to the AAT and ACLI methods, with even a lower cycle length error. The authors concluded that the high robustness and precision demonstrated by the HT method promote its implementation on CA mapping devices for a more successful location of ablation targets and improving the results of CA procedures .Currently, left atrial (LA) appendage surgical exclusion or percutaneous occlusion have limitations. For this reason, an interesting study by Pasta et al. sought to quantify the hemodynamic and structural loads of a novel potential procedure to partially invert the “dead” LA appendage space to eliminate the auricle apex, called LA appendage inversion (LAAI). This procedure was simulated by pulling the elements at the LA appendage tip and prescribing a displacement motion along a predefined path. Later, the authors used the deformed configuration to develop a computational flow analysis of LAAI, demonstrating that the inverted LAA wall in the inverted appendage undergoes a change in the stress distribution from tensile to compressive, and this can lead to resorption of the LAA tissue as per a reduced stress/resorption relationship .p = 0.004). Indeed, adherence to the ABC pathway was independently associated with a TTR of ≥65% [From a clinical point of view, three original studies performed in-depth analyses of the management of AF. Merino-Merino and collaborators, in a confirmatory study including patients with AF and healthy controls, showed that NT-proBNP, high sensitivity troponin T, and ST2, were significantly related to the presence of AF. Among these biomarkers of cardiac dysfunction, inflammation, and damage, NT-proBNP exhibited the best discrimination ability (with an area under the curve of 0.995) . Pastori of ≥65% .Additionally, two reviews aimed to shed light on very specific patient populations and therapeutic interventions. In the first review, Badescu and colleagues summarized the current evidence concerning the management of AF in people with hemophilia, which is a complex combination in terms of the prevention of bleeding and thromboembolic complications. These patients are often perceived as having a high bleeding risk due to coagulation factor VIII/IX deficiency, but in the presence of AF they also have a high risk of stroke and systemic embolism. Despite the lack of research in this population, it should be highlighted that the treatment offered to the general population, including CA and LA appendage occlusion, can be implemented in hemophiliacs if an appropriate replacement therapy can be provided . BuckleyFinally, AF is generally underdiagnosed, mainly because it can be present without signs and symptoms. For this reason, the real prevalence of AF is assumed to be higher than the known prevalence. In this Special Issue, Jones et al. described the protocol of an interesting study with the objective of investigating the effectiveness of a hand-held device embedded into the handles of supermarket trolleys in screening for AF in the general population. This will be a mixed method two-phase study. The quantitative first phase will be a cross-sectional observational study involving participants from a convenience sample at four large supermarkets with pharmacies. The prospective participants will be asked to conduct their shopping using a trolley embedded with a MyDiagnostick single-lead electrocardiogram sensor. If the device identifies a participant with AF, the in-store pharmacist will be dispatched to take a manual pulse measurement and a static control sensor reading and offer a cardiologist consultation referral. In the qualitative second phase, semi-structured interviews carried out with those pharmacists and store managers during the running of the trial period will be performed to explore the perceptions of staff regarding the benefits of the device .In summary, the studies included in this Special Issue cover different areas in the field of AF and provide an updated overview of the complexities of AF management. These novel insights are of great interest to healthcare professionals treating patients with AF and may assist in decision-making processes.


However, there is growing evidence of the need to advance the existing methods, through more robust and comprehensive fieldwork grounded in design study. It has been shown that the lack of guidance in lesson planning using variation theory is also thought to require particular attention, as the accuracy of the student learning relies significantly on the planning of the lesson. However, little research has outlined the strategy to be followed for incorporating variation theory. This article proposes a method of preparing lesson plans to systematically implement the variation theory in STEM classrooms. The method seeks to design and implement current techniques as follows:  Specifications tableTeaching methods strongly impact student learning Variation theory has been practiced in several educational research disciplines such as clinical education The application of variation theory in STEM education, as compared to other academic disciplines, necessitates careful deliberation due to the unique characteristics of STEM content. Within the STEM disciplines, specifically in domains such as physics, chemistry, biology, mathematics, and engineering, where learning revolves around abstract principles and concepts, variation theory plays a vital role by elucidating the interconnections among the critical aspects and cultivating a deep understanding of concepts Despite the urgent need to include variation theory in STEM education, there are limited articles that outline the implementation process of variation theory. The theoretical basis and potential benefits of variation theory in STEM education are recognized In order to apply variation theory in teaching STEM content, the first attempt that STEM teachers need to make an effort is to understand the key components of the variation theory. Unless they acquire a clear concept of the key terms concerning variation theory, teachers may struggle to adapt it in their teaching. In fact, the first step of good teaching is to plan the lesson in such a way that helps students achieve the learning objectives Pang and Ki defined the object of learning as - “the development of a certain powerful way of experiencing the phenomenon in question and, ultimately, is based on the learner's capability to handle novel situations in which that phenomenon occurs” As shown in The indirect object of learning becomes clearer when we analyze how it appears to particular people . Marton and Pang mentioned three possible ways the indirect object of learning may be experienced: 1) intended object of learning 2) enacted object of learning and 3) lived object of learning It is important to understand the difference between the object of learning and the learning objective when implementing variation theory in classrooms. Object of learning deals with the content to be covered, whereas learning objective focuses on the extent to which the student will be able to comprehend the concepts related to the content discussed in the classroom. Learning objectives are concise statements that explain what teachers anticipate their students will be able to do or exhibit as a direct result of the instruction they receive. They are often more specific, measurable, and action-oriented, which provides clear criteria for evaluating a student's knowledge of the topic being taught. Teachers may sometimes consider Bloom's Taxonomy as a reference to develop the learning objectives, which may sometimes refer to instructional objectives too Before implementing variation theory in the classroom, instructors must be familiar with the four primary patterns of variation proposed by variation theory: Contrast, Separation, Generalization, and Fusion The Contrast pattern entails giving examples that differ in one critical aspect while remaining in all other factors constant. Teachers can direct students' attention to the varying attributes by skilfully manipulating these variations, enabling them to identify and grasp essential distinctions within a specific concept or reality. Understanding this pattern enables educators to create learning scenarios that highlight key differences and increase students' understanding of fundamental concepts.Example: The educator demonstrates the concept of “volume” to middle school students using two cuboids with similar lengths and widths. Nevertheless, one cuboid is taller than the other. Students can determine that the volume grows proportionally with height by altering the height while holding the other dimensions constant.Through the Separation pattern, educators provide examples that vary in numerous critical aspects concurrently. This strategy enables learners to discern the various effects of each variable on the overall notion, fostering their capacity to recognize underlying linkages and dependencies. By using the Separation pattern, teachers can encourage a more thorough comprehension of complicated subjects and enable students to draw meaningful connections between distinct components.Example: Using two different plant species exposed to various degrees of sunlight, carbon dioxide, and water availability, the instructor of high school biology students explains the concept of “photosynthesis” to the class. Students can examine and evaluate the various influences of light, CO2, and water on the rate of photosynthesis by simultaneously adjusting these elements.The purpose of the Generalization design pattern is to reveal underlying ideas or concepts that present themselves in various contexts. Educators teach students to identify universal laws and patterns relevant to a variety of circumstances by offering similar examples with shared basic traits. Familiarity with the Generalization pattern enables teachers to enhance students' capacity to generalize underlying concepts from a variety of situations, resulting in more robust and transferrable learning results.Example: An illustration of this is when a math teacher demonstrates “geometric transformations” by using various shapes (such as triangles and rectangles) and the pictures they take after being translated, rotated, and reflected. Students can generalize that all translations preserve lengths, all rotations preserve angles, and all reflections produce mirror images by finding the common characteristics of each transformation.The Fusion pattern involves the strategic combination of numerous interconnected concepts or elements into a single instance. By contextualizing interconnection, educators improve students' knowledge of how various pieces work together to form a coherent understanding. Using the Fusion pattern permits educators to design learning experiences that combine multiple concepts, encouraging students to comprehend the holistic structure of complex topics and fostering higher-order thinking skills.Example: In a first-year engineering class, students measure current (I) and voltage (V) across a resistor using a battery, ammeter, and voltmeter in a classroom. The teacher starts with a standard battery voltage and resistor resistance, and students measure the current. The teacher then adds a variation by raising resistance while maintaining battery voltage. Students see a decline in current and realize resistance inversely affects current. Another variation shifts the battery's voltage while maintaining a constant resistance, helping students understand voltage and current. Through fusion pattern, students learn how changes in one parameter impact the others, completing their understanding of voltage, current, and resistance in electric circuits.In order to enhance student learning experiences, educators must have a comprehensive understanding of Variation Theory and its core patterns of variation. Teachers can improve the quality and efficacy of classroom learning by implementing the Contrast, Separation, Generalization, and Fusion patterns into their instructional design. This journal article emphasizes the significance of educators being familiar with these patterns and provides practical insights and pedagogical consequences for implementing them. With this information, educators may construct dynamic and engaging learning environments that encourage deeper conceptual understanding among students, empowering them to excel in a variety of academic and practical endeavors.According to variation theory, a critical aspect is a feature or dimension of the object of learning that is changed on purpose in learning situations. These are the key elements that students need to recognize and comprehend in order to get a deep and meaningful understanding of the subject The role of the teacher is vital in determining the critical aspects of a topic of discussion. The selection of critical aspects depends on the unique learning objectives, the topic's complexity, and the learners' proficiency level. Educators can construct interesting and effective learning situations based on the critical aspects that respond to students' different learning requirements and promote successful knowledge acquisition by skillfully designing variations and invariance around the object of learning. When identifying the critical aspects of a STEM topic, teachers need to consider the important features that students need to experience to get a holistic understanding of the topic. An example from the science topic is presented that may be useful for the STEM teachers to identify the critical aspects for their science topic.Example: In explaining the concept of “photosynthesis,” one of the critical aspects might be the “role of sunshine as the Source of Energy”. By exhibiting variants of different plants exposed to varying degrees of sunshine while keeping other factors constant, students can discover the significance of sunlight as a vital aspect in the photosynthetic process. Other critical aspects may be Carbon Dioxide (CO2) and Water (H2O) as reactants, and the Production of Glucose (C6H12O6) and Oxygen (O2). One of the most important features to understand the photosynthesis process is to understand the impact of light on the process. Depending on the intensity of sunlight, the rate of the photosynthesis process varies, which further produces glucose and oxygen from carbon dioxide and water. Students need to discern this critical aspect in order to understand the photosynthesis process.Another important feature of the photosynthesis process is to understand the need for carbon dioxide (CO2) and water (H2O). Students should understand that plants collect carbon dioxide from the air through pores called stomata and water from the soil through their roots. In the presence of sunshine and chlorophyll, these reactants conduct a sequence of chemical processes to produce glucose and oxygen.Glucose (C6H12O6) and oxygen (O2) are the final products of the photosynthesis process. Students must comprehend that glucose is a sort of stored energy that plants employ for growth and sustenance, whereas oxygen is generated as a byproduct, sustaining the lives of other species, including animals.Merely identifying the critical aspects may not guarantee that students will discern them all unless they are placed in students’ structure of awareness. Carefully altering the critical aspects to the areas of Theme, Thematic Field, and Margin may ensure that students' lived object of learning will be achieved. Therefore, understanding how students’ structure of awareness is utilized is crucial to creating the necessary conditions for learning. An explanation of the use of the structure of awareness is described in the following section.The structure of awareness refers to how students become aware of the critical aspects and variations provided in the learning setting Refer to the previous example of the STEM topic in The procedure outlined above serves as an illustration of how instructors can intentionally manipulate students' awareness to draw attention to particular crucial elements and promote a deeper understanding of challenging ideas like photosynthesis. An explanation of how to implement/utilize students’ structure of awareness is presented in After having an in-depth understanding of the key components of variation theory that have been discussed so far, teachers may endeavor to develop lesson plans for teaching STEM content. This article presents a comprehensive seven-step framework for developing a lesson plan following the VTST method see . InitialStep 1: Identify Object of LearningAt the beginning, teachers need to identify the precise concept or subject matter within the realm of STEM education that serves as the primary focal point of the teaching process. The focal point of the learning experience will be centered on this item of study. The topic may encompass a scientific principle, mathematical notion, engineering technique, or any other subject within the scope of STEM.Step 2: Formulate Learning ObjectiveOnce the object of learning is identified, the teacher may focus on constructing clear and precise learning objectives that indicate what students should be able to comprehend, apply, and demonstrate by the end of the lesson or unit. These objectives must be directly aligned with the selected object of learning and serve as measurable outcomes that guide instruction and evaluation.Step 3: Determine Critical AspectsThis stage is crucial for teachers to identify and present the critical aspects with their characteristics and dimensions in a sequential way that may help students understand well. Understanding the critical aspects are important element that helps students develop a complete understanding of the topic. They will act as key points for designing variations and directing students' attention.Step 4: Design Strategic Variation for Each Critical AspectThe four patterns of variation, namely contrast, separation, generalization, and fusion may be utilized, so students are able to discern the desired critical aspect. The lesson may begin with “Contrast” to stress key differences, “Separation” to expose interconnected effects, “Generalization” to draw out overarching principles, and “Fusion” to stress comprehensive comprehension. Utilizing the patterns of variations in lesson plans ensures the presentation of a critical aspect from different aspects.Step 5: Guided Awareness Shift from One Critical Aspect to AnotherTeachers may guide students' awareness from one critical aspect to another in a systematic manner. The lecture may begin by highlighting a certain important feature of a specific critical aspect. Then gradually move their focus to another critical aspect, providing opportunities for students to identify similarities and differences, promoting a more comprehensive understanding of the topic.Step 6: Reflective Discussion on Critical AspectsOpportunities for reflective conversations and activities are outlined in lesson plans. Teachers assist students in expressing their findings, trends, and conclusions drawn from the variances. Students are encouraged to actively process the concepts in relation to the critical aspect and improve their understanding throughout these discussions. Students may also be encouraged to provide recommendations on how to put newly learned skills to use in real-world circumstances, encouraging the transfer of knowledge. There are feedback loops between steps 6, 5, and 4 . If the Step 7: Assessment and Feedback Alignment with Learning ObjectivesCreate assessment tasks that are aligned with the learning objectives and the concepts of variation theory. Examine students' abilities to differentiate critical aspects, identify the patterns of variations, and apply their knowledge across several variants. Give students feedback that supports constructive thinking and helps them to refine their understanding. After the assessment, if students need a reflective discussion, the teacher may repeat step 6. However, if there are major concerns about the achievement of learning outcomes, teachers may go back to step 3 and modify the critical aspects, or step 2 and modify the learning objectives.By following these steps, instructors in STEM education may systematically utilize variation theory to enhance deeper understanding among students. This systematic method ensures that students connect with critical aspects, recognize variations and invariances, and build a comprehensive grasp of complicated STEM topics.Step 1: Identify Object of Learningobject of learning of this lesson is the Vapor Compression Refrigeration Cycle.The A schematic diagram of a simple Vapor Compression Refrigeration System along with a temperature–entropy diagram is presented in Step 2: Formulate Learning ObjectivesAt the end of the lesson, students will be able to identify the state changes of the refrigerant  through the evaporator, compressor, condenser, and expansion valve in a vapor compression refrigeration System (VCRS).Step 3: Determine Critical Aspects(1).Critical Aspect 1: State of refrigerant in Compressor.(2).Critical Aspect 2: State of refrigerant in Condenser.(3).Critical Aspect 3: State of refrigerant in Expansion/Throttling Valve.(4).Critical Aspect 4: State of refrigerant in Evaporator.Step 4: Design strategic variation for each Critical AspectStep 5: Guided Awareness shift from one Critical Aspect to another creating variance and invarianceSteps 4 and 5 are the main steps where teachers utilize the patterns of variations and grab students’ awareness of the critical aspects one by one or simultaneously. The following section describes how steps 4 and 5 are implemented in STEM classrooms utilizing seven activities.Activity 1: In this activity, the teacher may describe the critical aspect 1 (CA1), which is the compressor, including its basic functioning function, the different types of compressors, what occurs when vapor refrigerant enters the compressor, and the condition of the refrigerant after compression. The instructor also explains its application. The instructor may use lecture and discussion, and instructional materials may include PowerPoint presentation, multimedia projector, Whiteboard, and marker. At this stage, the state of the refrigerant before entering and after leaving the compressor will be contrasted while the discussion on the condenser, expansion valve, and evaporator will remain invariant. Activity 02: In this activity, the teacher may introduce critical aspect 2, which is the condenser, including its basic functions such as how the condenser exchanges temperature with the atmosphere and condenser cooling system, and the different varieties of condensers and their applications. The instructor also explains the state of the refrigerant through the condenser. The following questions also need to be highlighted by the teacher - How refrigerant is converted from vapor to liquid in the condenser? Which principles govern condensation? What does the term condensation mean? At this stage, the state of the refrigerant before entering and after leaving the condenser will be contrasted while the discussion on the compressor, expansion valve, and evaporator will remain invariant. Activity 03: In this activity, the teacher may describe the expansion valve using an animation video and show different images of the expansion valve, for instance, the basic function of the expansion valve, how the expansion valve reduces pressure as the refrigerant flows through it, different types of expansion valves and their application. In addition, the instructor describes the state of the refrigerants in the expansion valve, how to shift high-pressure refrigerant to low-pressure refrigerant using various instances, and the principles that govern the expansion of refrigerant. At this stage, the state of the refrigerant before entering and after leaving the Expansion Valve will be contrasted while the discussion on the compressor, condenser, and evaporator will remain invariant. Activity 04: In this activity, the teacher will describe the evaporator using an animation video and show a different image of the evaporator, for example, the basic function of the evaporator, how the evaporator exchanges temperature with its surroundings, how to collect heat from the evaporator chamber, and how refrigerant evaporates in the evaporation, as well as the various types and applications of the evaporator. The instructor also describes how refrigerants evaporate in the evaporator and the process through which liquid refrigerant is transformed into vapor in the evaporator, which principles govern evaporation? And what does the term evaporation mean? At this stage, the state of the refrigerant before entering and after leaving the evaporator will be contrasted while the discussion on the compressor, condenser, and expansion valve will remain invariant. In activities 1 to 4, among the four critical aspects, only one critical aspect was in the point of discussion retaining the remaining three as invariant. The teacher tries to grab students’ structure of awareness to one critical aspect at a time. To accomplish so, teachers usually employed contrast on the state of the refrigerant before and after passing through a component of the refrigeration system. In activities 5 and 6, the teacher can take more than one critical aspect at a time keeping the other two components constant. Here instructor can choose to build a separation between the compressor and expansion valve in activity 5, and also make a separation between the condenser and evaporation in activity 6. In both activities the functioning principle of the pair of components is opposite and therefore separation may be the preferred choice as the pattern of variation.Activity 05: As discussed earlier, the working principle of the compressor and the expansion valve is just the opposite, where the refrigerant gains high pressure and temperature after passing through the compressor. Whereas the refrigerant loses its pressure and temperature after passing through the expansion valve. Utilizing the separation pattern of variation, the teacher would strategically isolate and emphasize the contrasting effects of the compressor and expansion valve on the refrigerant within the refrigeration cycle. Discussion of the compressor and expansion valve together, keeping the other two components invariant, allows students to discern the difference between the working principle of compressor and expansion valve. Activity 06: Activity 6 is just a repetition of activity 5. In activity 6, instead of focusing on the compressor and the expansion valve, the other two components compressor and evaporator are presented together to the students’ structure of awareness. Before going into the condenser, the refrigerant has just left the compressor and is in the form of a high-pressure vapor. As the refrigerant moves through the condenser, a big change happens: the refrigerant loses heat to the environment, which causes it to change. At this point, when the refrigerant goes through the condenser, it changes from a high-pressure gas to a high-pressure liquid. By switching the focus to the evaporator, students can see how the evaporator works differently from the condenser. Before going into the evaporator, the refrigerant is in the form of a high-pressure liquid. This is because the condenser has cooled it down. As the refrigerant moves through the evaporator, it picks up heat from its surroundings. In this case, the refrigerant goes from being a liquid under high pressure to a gas under low pressure. Activity 07: Through Activity 01 to 04 students got familiar with the working principle of each critical aspect separately by contrasting the state of the refrigerant before and after each component. Hence students got a nuanced grasp of the working principle of each component. Afterwards, in activities 05 to 06 students were able to discern the separation between the working principles of two sets of components. Now, at this stage, using a fusion pattern of variation, the teacher tries to gather all concepts together to make a holistic understanding of the VCRS, illustrating the focus of the state change before and after all four components. The compressor drives the refrigerant from a low-pressure to a high-pressure vapor, giving it the energy, it needs for the following steps. A crucial transition from a high-pressure vapor to a high-pressure liquid, which releases heat into the surroundings, takes place as the refrigerant moves toward the condenser. The refrigerant undergoes this transformation to get ready for the expansion valve, where it changes from a high-pressure liquid to a low-pressure vapor. As the refrigerant absorbs heat to complete the cycle, the evaporator converts it from low-pressure vapor into a low-pressure liquid.At the end of Activity 07, it is expected that students understand how in the Vapor Compression Refrigeration System, the compressor, condenser, expansion valve, and evaporator function as interlocking puzzle pieces to create a fascinating journey by changing their state as they pass through each component. Step 6: Reflective discussion on Critical AspectsReferring to Step 7: Assessment and feedback alignmentReferring to Overall, the interaction of variation and invariance in teaching the VCRS promotes a thorough comprehension of the complex mechanics of the cycle. Students are given the skills necessary to recognize underlying concepts and comprehend how various elements work together holistically. This method not only encourages active learning but also helps students develop the critical thinking abilities needed to apply their knowledge in real-world situations, improving their capability to identify and resolve refrigeration system problems.Despite different methods exist, however, when considering the evaluation of achieved learning outcomes, particularly in settings that involve the utilization of variation theory, it is recommended to employ a specific assessment approach known as phenomenography. This method was initially developed by Ference Marton and his research team at the University of Gothenburg in Sweden Two groups of students were the sample of this study. Using a traditional method, an instructor presented the material to a control group, followed by a 30-minute student response window. Also, using variation theory, another instructor presented an identical subject to an experimental group. Both groups were given the same written question for evaluation, with the goal of determining the impact of variation theory on their understanding of the learning objective. This article reviews the key components of the variation theory and provides a guideline about its implementation. Particularly it discusses how the complex STEM topics could be taught in such a systematic way so that the STEM teachers could replicate the proposed VTST method. From the learning perspective, this article creates a profound basis for an argument that if teachers can develop lesson plans utilizing the VTST method, it will create the necessary conditions for learning and help students comprehend the complex problems of STEM education. Researchers in the field of STEM education can take this article as a reference to develop authentic learning experiences for students. Future research may utilize the sample lesson plan presented in this article and further investigate the effectiveness of VTST adapting a phenomenographic approach. Another future research avenue could be the integration of other methods with VTST to investigate their usefulness for more favorable student learning.Mahbub Hasan: Conceptualization, Methodology, Writing – original draft, Writing – review & editing, Project administration. Md Shahadat Hossain Khan: Conceptualization, Methodology, Writing – review & editing. A.K.M. Foysal Ahmed: Conceptualization, Methodology, Writing – review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


These results demonstrated that the proposed cycling ergometer device is capable of applying asymmetric loading to lower limbs, and thus has the potential to improve the outcome of exercise interventions in patients with asymmetric function in lower limbs. Dynamic loads have short and long-term effects in the rehabilitation of lower limb joints. However, an effective exercise program for lower limb rehabilitation has been debated for a long time. Cycling ergometers were instrumented and used as a tool to mechanically load the lower limbs and track the joint mechano-physiological response in rehabilitation programs. Current cycling ergometers apply symmetrical loading to the limbs, which may not reflect the actual load-bearing capacity of each limb, as in Parkinson’s and Multiple Sclerosis diseases. Therefore, the present study aimed to develop a new cycling ergometer capable of applying asymmetric loads to the limbs and validate its function using human tests. The instrumented force sensor and crank position sensing system recorded the kinetics and kinematics of pedaling. This information was used to apply an asymmetric assistive torque only to the target leg using an electric motor. The performance of the proposed cycling ergometer was studied during a cycling task at three different intensities. It was shown that the proposed device reduced the pedaling force of the target leg by 19% to 40%, depending on the exercise intensity. This reduction in pedal force caused a significant reduction in the muscle activity of the target leg ( Exercise is one of the noninvasive interventions for treatment and pain management of patients with lower limb conditions. Although the risks of injury due to falling, joint sprain, and muscle strain are minimal in aquatic interventions ,2,3,4, tSupervised cycling exercise training using stationary bicycles, called cycling ergometers, has been used as a surrogate land-based exercise for cardiovascular disease , knee OATherefore, the first gap in using conventional cycling ergometer devices is the lack of a system to collect, analyze, and monitor patient performance, giving the practitioner a tool for data-driven assessment of treatment effectiveness. To achieve this with conventional cycling ergometers, a secondary system for monitoring health and performance factors should be improvised during the exercise, which would require bulky instrumentation and on-site supervision . For insThe present work seeks to develop a novel rehabilitation tool and prove its potential in exercising legs with different intensities such that the injured leg (target limb) is burdened with less mechanical loads than the healthy leg during the pedaling task. Therefore, this project aimed at prototyping the Adaptive Pedalling Assistant Device (APAD), and showing that it can provide asymmetrically-assisted cycling torque without significantly affecting kinematics. It was hypothesized that APAD would maintain the kinematics of pedaling while reducing the muscle force of the targeted leg. To assess the study hypothesis, the kinematics of movement was analyzed using the motion capture system, while the effect of asymmetric assistive torque on the kinetics of lower limbs was quantified using the pedal force sensors and muscle electromyography (EMG). The central device of this project, APAD, was built off a Rad Mission™ electric bike  equipped with a 450 W brushless direct current rear-hub motor and a 48 V battery. The original Rad Mission ebike had a throttle control to adjust the motor output power . In thisThe force transducer was based on strain gauges connected using a Wheatstone  bridge amplifier circuit  glued toAs shown in The logic flow of the motor control program is described in Bilateral lower-limb joint angles were recorded using a Vicon 9-cameras capture motion system at 100 Hz . 24 retroreflective motion capture markers were used to track left and right lower-limb and crank kinematics. There were three cluster markers on each thigh and shank, as well as a marker on each leg to indicate the hip, knee, and ankle joints as per Vicon  documentation . MarkersFour EMG sensors  were placed on the legs; over the left and right vastus-lateralis-quadricep (VL) muscles in the same orientation as that of Zebis et al. , as wellThe crank orientation was calculated once from the motion capture system using the markers attached to the cranks, pedals, and the proposed crank position sensing system, and results were compared to validate the performance of the crank position sensing system. Amongst kinematics parameters measured using the motion capture system, the knee joint angle and knee lateral deviations are more relevant to the present study. The knee joint angle was calculated by measuring the angle between the line segments representing the femur and tibia; the femur line connected the lateral knee (epicondyle) with the greater trochanter of the femur, and the tibia line connected the lateral ankle  with the lateral knee (epicondyle). The lateral-medial movement of the knee joint was identified by the trace of the marker attached to the head of the fibula in the transverse plane. Five healthy participants  completed the test. Each participant provided written, informed consent and the study was approved by the institutional ethics review board (REB: 21-12-022). The APAD was mounted onto a Saris M2 Smart Trainer™  that provided resistance through magnetic impedance and controlled over Bluetooth™ by modulating the power of the resistance. The participant was asked to place the ball of their foot slightly ahead of the axis of rotation of the pedal to conform to recommended cycling practice . A 5-minAssessment of kinematics of motion: Assessment of kinematics of motion: To verify that the APAD did not significantly change the kinematics of the pedaling task, we computed the variation in pedaling cadence and knee lateral deviation in the transverse plane  was conducted to evaluate the significance of parameters variation between two test conditions, including the area under the pedal force curve (AUC) of full cycles for sessions (A) and (I) to verify that the force reduction was significant. The CP-LMP of sessions (A) and (I) were not statistically different, indicating that the knee lateral-medial displacement was unaffected when the APAD became active. For both sessions (A) and (I), the crank angular velocity had about ±10 RPM real-time variation  compared to the corresponding session (I) for the target leg. However, the significance level of muscle activity reduction should be studied because there is a possibility that the activity of the muscle of interest was not affected. The gastrocnemius (GM) and vastus lateralis (VL) muscles are among the major contributors to force production in the pedaling task. The APAD capability in providing asymmetric pedaling torque assistance allows for optimizing the intervention programs for patients with lower limb conditions. However, some limitations in the current design of the APAD should be addressed to make it a clinical tool. The strain gauge-based force sensor in the present study was not sensitive enough to measure crank axial force. Although the crank axial force does not contribute to the pedaling torque, it should be measured to determine the foot force, an essential parameter for musculoskeletal analysis. The other limitation of the present study relates to recruiting healthy subjects for the experiments, which was a safety consideration when testing the first prototype of APAD. The performance of APAD in reducing the pedaling force and muscle activity and its effect on the pain level will be studied in future human studies on patients with knee OA and ACL injuries. Finally, the open loop motor control system of APAD should be improved to a feedback loop control system, where the biomechanical responses, such as pedaling power, and physiological responses, such as heart beat rate, of the user are used to control the magnitude and duration of the motor power assistance. The next study will address those limitations to take the APAD one step closer to becoming a clinical human assistive device. The instruments designed and built for APAD were able to track crank angle and crank perpendicular force with acceptable accuracy. The results of the human study with healthy participants showed that APAD did retain the pedaling kinematics while the foot force and muscle force (kinetics) of the target leg were reduced. APAD showed that it could successfully assist the participant asymmetrically. However, the human study in the present work was limited to healthy participants. Thus, the next step is to evaluate the effectiveness of APAD as a rehabilitation device using human studies on patients with lower limb asymmetric function, such as post-stroke patients.


Plasmodium falciparum malaria, rely on vast diversity of genes encoding surface proteins targeted by the immune system. The large number of resulting “strains” (different gene combinations in pathogen genomes) challenges application of standard epidemiological models. Motivated by the malaria parasite, we present and analyze a modeling framework that tracks gene diversity explicitly together with immune memory of previous exposure. Dynamics exhibit alternative equilibria of high and low prevalence and an associated tipping point as transmission decreases. Thus, a sharp drop in prevalence can occur with intervention, but only under a drastic reduction in pathogen diversity to prevent rapid rebound of infection levels in the population.As an immune evasion strategy under high transmission, important pathogens of wildlife and humans, including  Plasmodium falciparum, relies on multigene families to encode antigenic variation. As a result, high (asymptomatic) prevalence is observed despite high immunity in local populations under high-transmission settings. The vast diversity of “strains” and genes encoding this variation challenges the application of established models for the population dynamics of such infectious diseases. Agent-based models have been formulated to address theory on strain coexistence and structure, but their complexity can limit application to gain insights into population dynamics. Motivated by P. falciparum malaria, we develop an alternative formulation in the form of a structured susceptible-infected-susceptible population model in continuous time, where individuals are classified not only by age, as is standard, but also by the diversity of parasites they have been exposed to and retain in their specific immune memory. We analyze the population dynamics and bifurcation structure of this system of partial-differential equations, showing the existence of alternative steady states and an associated tipping point with transmission intensity. We attribute the critical transition to the positive feedback between parasite genetic diversity and force of infection. Basins of attraction show that intervention must drastically reduce diversity to prevent a rebound to high infection levels. Results emphasize the importance of explicitly considering pathogen diversity and associated specific immune memory in the population dynamics of hyperdiverse epidemiological systems. This statement is discussed in a more general context for ecological competition systems with hyperdiverse trait spaces.A hyperdiverse class of pathogens of humans and wildlife, including the malaria parasite  Plasmodium falciparum, rely on vast and evolving antigenic variation to evade host adaptive immunity under high transmission intensity   and also in bacteria and fungi of direct transmission  (Hyperdiverse pathogens of humans and wildlife encode variant surface antigens (VSA) with multigene families . As an eotein 1) . This protein 1) . Successvergence . Vast coo vector . High reo vector –12. In ao vector , 14. ExaLarge antigenic diversity enables immune evasion and therefore high asymptomatic prevalence in host populations despite repeated exposure of individuals to the pathogen throughout their life . AlthougAgent-based models (ABMs) that track each individual host and its specific memory of previous infections have been formulated to model transmission dynamics in a way that incorporates the combinatorial genetic diversity of the malaria parasite underlying antigenic variation , 22, 23.Materials and Methods). As a unique feature, our model also tracks the number (but not the identity) of different parasite genes the hosts of a particular age have encountered previously. Besides age-structured, the model is hence also immunity-structured, as hosts build up a memory of previous infections during their life . Hosts may become infected through transmission events, the frequency of which is proportional to a transmission intensity parameter, the contact rate Materials and Methods). The number of unique parasite genes in a repertoire is determined by the diversity in the total parasite gene pool, which itself is dynamic. Parasite diversity increases through mitotic recombination of existing genes in an infection as well as through introduction of new genes by immigrating hosts carrying an infection . Key features of the model are an inclusion of an explicit equation for the rate of change in genetic diversity, and the tracking of the fraction of this changing diversity a host has been exposed to. For simplicity, we consider here that different genes encode different VSAs. We also refer to gene diversity with the understanding that this maps to antigenic diversity, an aspect we later discuss. We also subsumed transmission through the vector in a contact rate parameter . For default parameters, a low-prevalence equilibrium state occurs for all values of the transmission intensity, in which the force of infection, the parasite gene pool diversity, and the fraction of infected host individuals are all low. Parasite diversity in this state is mostly determined by immigration of infected individuals. Above a threshold level of transmission potential, however, a high-prevalence equilibrium state occurs, in which the majority of host individuals are infected and both the force of infection as well as the parasite gene pool diversity are one to two orders of magnitude larger than those in the low-prevalence equilibrium. Numerical simulations of the model reveal that both equilibrium states are stable . An unstable equilibrium .The two alternative equilibrium states co-occur when the transmission potential is above a threshold level and the probability that immigration of infected hosts leads to an increase in the parasite diversity is low . When thThe high-prevalence equilibrium state is very resilient against perturbations and drastic interventions are required to induce a shift of the host population from the high-prevalence equilibrium state to the low-prevalence equilibrium state. We assessed resilience of the high-prevalence equilibrium state by analyzing whether or not the host population would return to the high-prevalence state when a random fraction of infected host individuals was cured of the disease and parasite diversity was independently reduced by a particular fraction. With these computations, we obviously ignore the fact that from a practical viewpoint such independent manipulation of the fraction of infected hosts and the parasite diversity is largely unrealistic, as the latter would generally accompany parasite clearance from hosts via drug treatment and other interventions reducing prevalence. Nevertheless, a shift from a high-prevalence to a low-prevalence equilibrium state can only be achieved by a significant reduction in parasite diversity, whereas there is only a minor effect of the fraction of infected host individuals that is cured . If k0 iilibrium A, wherea a shift B and C.Similarly, a temporary reduction in contact rates only leads to a shift from the high-prevalence to the low-prevalence equilibrium state if the reduction in transmission intensity lasts sufficiently long, roughly a period equal to the average lifespan of the host individuals D–F. The  reduced F, wherea reduced E. When tSI Appendix, Fig. S2). Specifically, in the low-prevalence equilibrium infection levels never exceed 30% at any age, whereas in the high-prevalence equilibrium, virtually all young hosts are infected, while the infection levels never drop below 80% among older hosts. Furthermore, superinfection almost never occurs in the low-prevalence equilibrium, whereas in the high-prevalence equilibrium superinfection is common, in particular, among young hosts. Remarkably, though, the fraction of the total parasite gene pool that hosts have encountered from birth up to a specific age does not differ between the two types of equilibrium states, despite the large difference in parasite diversity in the two states. This fraction rapidly increases with age to an asymptotic level of around 0.9 . The similar age dependence of this fraction in the two states suggests that the build-up of immunity during life is not crucial for the occurrence of the two alternative equilibrium states. Based on this observation, we derived a simplified version of the immune memory–structured SIS model, in which we assume that the fraction of the parasite gene pool previously encountered by host individuals is equal to a constant SI Appendix; from here referred to as the simplified ID model). Analogous to our original model, this simplified ID model also predicts the occurrence of alternative stable equilibrium states over similar ranges of parameter space as the full model  population.In practice, parasite diversity in malaria and other hyperdiverse pathogens can only be reduced indirectly by interventions that decrease transmission. Together with the demonstrated extreme reduction in diversity required to reach the low-prevalence equilibrium, this fact severely limits, if not prohibits, the likelihood of observing in nature the low-prevalence alternative state in areas where contact rates are above the critical point. Thus, a main implication of bistability in this system is not the actual observation of alternative steady states, but the introduction of a critical point, and therefore a threshold, in contact rates, at which prevalence changes drastically. . Two major empirical observations in malaria epidemiology are nevertheless consistent with the existence of the transition we have described. The first one concerns the resilience of high-transmission regions to control efforts, whereby the relaxation of transient strong interventions has been typically followed by the rapid rebound of the system to originally high prevalence levels –33. The The existence of the threshold we propose here opens the door for investigating indicator quantities related to parasite diversity that would signal the approach to a drastic transition in prevalence. For increased realism, this avenue could be pursued with extensions of the model in the form of agent-based formulations (ABMs). We expect our results to provide a basis for comparison with the dynamics of detailed stochastic ABMs concerning responses to intervention efforts. Prior research has shown the advantage of synthesizing results from the two approaches: The abstract PDE formulation provides a more complete inventory of the dynamic patterns that can occur in ABMs and also informs potential cycles initiating from unstable steady states in the ABM . The difPrevious mathematical models of malaria transmission considering generalized but not specific immunity have shown that superinfection and reinfection can both lead to alternative steady states , 21, 27.SI Appendix, Fig. S5 for details). Such a minimum is biologically realistic and was necessary to approach the disease-free equilibrium in a meaningful manner, as our original formulation assumed that SI Appendix, Fig. S5). The existence of two bifurcation points is robust to changing the imposed lowest value of diversity, with this value determining the transmission potential at which disease invades .The lower equilibrium in our models differs from a disease-free one because we have considered an open system, with a contribution to the force of infection from outside the local population from immigration. Although this setup is realistic, it impedes consideration and analysis of a disease-free equilibrium at low levels of transmission intensity, in the traditional sense of invasibility of infection at a threshold value of P. falciparum in high-transmission endemic regions, from the perspective of the multigene family that encodes the major antigen of the blood stage of malaria infection. Additional epidemiological considerations that can be incorporated into this framework for future application to malaria include 1) effects of generalized immunity representing protection from infection conferred from more conserved antigens , 2) seasonality of transmission, and 3) explicit vectors. The implicit treatment of transmission via vectors with a parameter akin to vectorial capacity . This modified model exhibits the classical pattern of a stable, disease-free equilibrium at low transmission potential . Importantly, though, the bistability and the associated saddle–node bifurcation that occurs when contact rate is sufficiently high are unaffected by the change in model structure.Key to our model is an explicit equation for pathogen genetic/antigenic diversity and the tracking of the fraction of this changing diversity a host has been exposed to. We have considered a detailed expression for the generation of novelty but not for its loss. For simplicity, we assumed this loss rate to be constant Eq. P. falciparum populations in high transmission regions  without making an explicit distinction between genes and their products. This is akin to the current study of strain structure from se types , 7. A be studies . We note regions , 41 woulInterestingly, a parameterization of our model on the basis of the malaria literature, without any calibration, produces an intriguing similarity to the empirical relationship between prevalence rate and force of infection . It is w1 to 0.8  dependin1 to 0.8 . Since t1 to 0.8  and cont1 to 0.8 . BecauseMore broadly, we can ask whether positive feedback between genetic diversity and intensity of ecological interactions (here competition of parasites for hosts) can lead to critical transitions in other hyperdiverse systems. The relevant diversity would encode here phenotypic traits that influence ecological interactions; these interactions would in turn influence individual fitness in a frequency-dependent manner. Theory in community ecology has begun to examine analytically models with such interactions through “environmental feedback” , and theSI Appendix for detailed model derivation), such that it is only necessary to track the fraction i) the introduction of a second individual-state variable besides age, to describe the specific immune memory individuals build during their lifetime from infection history; and ii) an explicit equation describing temporal changes in the overall genetic diversity of the parasite population encoding the variant surface antigens of interest.We use an age-structured SIS model in terms of susceptible and infected individuals , assuminWe assume that hosts receive mosquito bites at a constant rate, independent of their age and infection status, with the force of infection In this expression, Discussion). These SI Appendix). Infection is assumed to occur when at least one of these unique genes has not been previously encountered by the host. To track immune memory, we introduce During a biting event, a package of SI Appendix for the derivation).while the rate at which new parasite genes are delivered during successful infection events is given by:SI Appendix for the derivation).Another parameter influenced by immune memory of the host is the recovery rate from the infected into the susceptible class. Its inverse is the duration of infection, whose value is key to parasite fitness. We adopt a well-known superinfection model by ref. Taken together, the infection dynamics of the host population is described by the following partial differential equations:in which We assume that new parasite genes to emerge due to mitotic recombination inside infected hosts at a rate that is proportional to the total number of infections in the host population and the number of different gene pairs each parasite harbors. Following the superinfection model , the avewith genetics , 50[8]Φiin which new gene , definedwhere The selection differential Finally, we assume that genes disappear from the parasite gene pool at a rate SI Appendix.For the choice and estimates of parameter values, see Dynamics of the immune memory–structured SIS model specified by the partial differential equations [Steady states of the immune memory–structured SIS model Eqs. The two unknowns SI Appendix for details). Finally, to compute curves of steady-state solutions as a function of model parameter, we use the R package FindCurve Click here for additional data file.


Accurate assessment of upper-limb movement alterations is a key component of post-stroke follow-up. Motion capture (MoCap) is the gold standard for assessment even in clinical conditions, but it requires a laboratory setting with a relatively complex implementation. Alternatively, inertial measurement units (IMUs) are the subject of growing interest, but their accuracy remains to be challenged. This study aims to assess the minimal detectable change (MDC) between spatiotemporal and quality variables obtained from these IMUs and MoCap, based on a specific protocol of IMU calibration and measurement and on data processing using the dead reckoning method. We also studied the influence of each data processing step on the level of between-system MDC. Fifteen post-stroke hemiparetic subjects performed reach or grasp tasks. The MDC for the movement time, index of curvature, smoothness (studied through the number of submovements), and trunk contribution was equal to 10.83%, 3.62%, 39.62%, and 25.11%, respectively. All calibration and data processing steps played a significant role in increasing the agreement. The between-system MDC values were found to be lower or comparable to the between-session MDC values obtained with MoCap, meaning that our results provide strong evidence that using IMUs with the proposed calibration and processing steps can successfully and accurately assess upper-limb movement alterations after stroke in clinical routine care conditions. Instrumental assessment of movement characteristics is a crucial component of post-stroke upper limb rehabilitation and longitudinal follow-up, and it is being recommended as a complement to clinical assessment ,2,3.Movement analysis consists of the characterisation of various tasks mimicking everyday life, such as drinking from a glass or reaching for a switch. It looks at different spatiotemporal and quality characteristics of the movement such as duration, hand trajectory, smoothness, and trunk contribution to hand displacement ,5.Marker-based motion capture (MoCap) offers advantages in terms of accuracy, spatial resolution, and capturing complex movement details . HoweverWith regards to the above limitations to obtain informed outcomes using IMUs, it is important to consider that the most widespread approach when assessing upper limb kinematics is to compute the orientations of the segments of the limbs ,21,22,23In contrast, the dead reckoning (DR) method directly provides the trajectory of an IMU. It still requires computing the orientation of the sensor in a fixed frame, but then a double integration is carried out to obtain the position. Consequently, this method does not require any sensor-to-segment calibration or a kinematic model. However, this approach is particularly sensitive to drift errors due to the integration steps, hence the need for offline calibration steps and other correction techniques . Cahill-In summary, IMUs are relevant motion analysis tools because of their ease of use, but they require sophisticated algorithms and analysis techniques to extract meaningful information. There are few data on their usability in routine care from which spatiotemporal and quality variables can be collected, including those that are based on the study of hand and trunk trajectory to assess upper limb movement alterations in post-stroke subjects.The aim of this study was to investigate the agreement between the spatiotemporal and quality variables obtained from IMUs and a gold-standard MoCap for assessing movement alterations of the upper limb in post-stroke subjects in the context of routine care. As a secondary objective, we assessed the contribution of some IMU processing steps in increasing the agreement with the gold standard.Data were included from 15 post-stroke hemiparetic subjects (14 hemiparetic on the right and 1 on the left) assessed in routine care during their routine follow-up medical consultation or while they were hospitalised in rehabilitation. The detailed characteristics of the subjects are reported in The wearable IMU system consisted of Delsys Avanti Trigno sensors  placed on the subject, with one on the dorsal side of the paretic wrist, and the other one on the upper part of the sternum, as depicted in Motion capture, used as the gold standard, was carried out using an Optitrack system  with eight cameras. One reflective marker was put on each inertial sensor.The acquisitions were made with a sampling rate of 148 Hz for the IMUs and 250 Hz for the MoCap system.w when the For each subject, before placing the IMU sensors, a static calibration  was perfurntable , and thiDRINK task or a switch for the LIGHT task) was placed such that the wrist had to cover 80% of the subjects’ arm length from the starting position to the object, without engagement of the trunk.After the calibration, the IMUs equipped with a reflective marker were placed on the subject. For the starting position, subjects were sat on a chair with their back against the backrest, their hands flat on the table, and their elbows flexed at 90°. The target . Position data from each reflective marker were filtered using a low-pass fourth-order zero-phase Butterworth filter, with a cut-off frequency of 10 Hz.Using the calibration parameters determined during the calibration procedure , accelerAccelerometer and gyroscope data were then filtered using a low-pass fourth-order zero-phase Butterworth filter, with a cut-off frequency of 10 Hz.d) and need to be rotated in the constant laboratory frame (noted as g) whose z-axis is vertical and up.Accelerometer data are collected in the IMU frame  , based oFinally, the velocity was integrated a second time using the trapezoidal rule to obtain the final position vector.Disabling the calibration ;Using the Madgwick filter  .The approach phase was selected .The start and end of the approach phase were defined by a tangential velocity threshold along the antero-posterior axis > and < at 1 cm·sApproach phase delimitation was performed using the same algorithm for both the MoCap and IMU data, which is based on selecting the sagittal velocity peaks on the wrist IMU sensor/reflective marker:An example of one series is shown in Movement time (MT) (in seconds): duration between the starting point and the end point of the approach.Index of curvature (IoC): ratio of the movement arc length to the shortest distance between the start and end points. Its value theoretically goes from 1 (perfectly straight trajectory) to Number of submovements (nSUB): number of sagittal velocity peaks; it is an integer from 1 to Trunk contribution (TC) (in %): ratio of the sagittal length covered by the trunk to the sagittal length convered by the wrist.For each approach phase, four spatiotemporal and quality movement variables were computed:For each series and each subject, the first repetition was taken as a test run and was not considered. Moreover, as some recent papers suggest reducing the number of repetitions to between 3 and 5 ,31, datar and its p-value. A distribution was deemed heteroscedastic when the p-value was lower than 0.05, meaning that the differences tend to increase when the measured value increases [T being the value obtained from the t-table with 29 (or 14 for the trunk contribution) degrees of freedom) [n is the number of series (with outliers excluded), s is the standard deviation, and For each variable, we first checked the distribution of the absolute differences between the two systems and the value of the MoCap system using the Pearson correlation coefficient ncreases . Dependincreases , we thenfreedom) . With ouAmong the 15 subjects, 13 of them were able to perform the DRINK task and 2 performed the LIGHT task , meaning that the inertial sensor reported fewer velocity peaks than MoCap, as well as had a high MDC (39.62%). The number of submovements is a very versatile variable as it may count very small peaks. For example, some of these peaks at the beginning or at the end of the movement could have been suppressed because the delimitation of the approach phase between the IMUs and MoCap was independent, or during very low-speed phases these peaks could have been considered as a period of stability by the ZUPT algorithm. Looking at the Bland–Altman plot, this negative bias (less than 3) mostly came from the lower values of the number of submovements with the IMU system, likely meaning that the inertial system missed 1 or 2 peaks at most. This limit of the number of submovements seems hard to overcome, and some recent papers suggest calculating other variables such as the SPARC to represent the smoothness of the movement .There was a significant negative bias for the IoC with a small MDC, meaning that the inertial system tends to provide more direct trajectories. One plausible explanation is that small constant offsets still existed for the IMUs despite the calibration steps, adding some “straight” components to the trajectory and leading the IoC to slightly decrease. A major cause for changing offsets is temperature . The calThe trunk contribution had an MDC of around 25%. It was the only variable that depended on the two inertial sensors, and therefore was more sensitive to sources of errors. It was also much more sensitive to noise, as the trunk movements were most often slow and of a small amplitude.It is relevant to interpret the level of measurement error computed between the IMU and MoCap systems with regard to the between-session test–retest measurement error obtained with a reference MoCap system for similar tasks ,37,38, aEach of the signal processing steps carried out with the IMUs showed its relevance in calculating a position that is sufficiently reliable to automatically delimit the approach phases of the tasks. Doing otherwise would involve manually selecting the task with a video or using another system (as we did for this part with MoCap) and would increase the time required in routine care. The choice of the VQF fusion filter instead of the Madgwick filter was the most crucial element associated with the greatest decrease in error margins ag=RSuch errors are unacceptable  for our application and explain why choosing an appropriate fusion filter is particularly important.Calibration also played a major role in reducing the measurement error. However, the importance of the calibration may vary depending on the type of sensor given the recent advances and the development of IMUs. We chose to do the calibration before each subject to keep the same processing for each, but, especially in routine care, it may be worth lowering that requirement and investigating the impact of reducing the frequency of calibrations, even though carrying out the calibration only takes a few minutes.The influence of ZUPT was moderate on the IoC and TC, and there was no significant modifications to the nSUB, which was expected as it was dependant on the acceleration (the number of velocity peaks being the number of times the acceleration crosses the zero line). There was still a small general decrease in the number of peaks, likely due to peaks being ignored during stability periods.This study provides strong evidence for the relevance of using inertial sensors to assess spatiotemporal and movement quality alterations in the upper limb in post-stroke subjects in the context of routine care. By applying appropriate calibration to the sensors and data processing to mitigate the errors of the IMUs, we showed this method has high agreement with the MoCap system. We focused on using an easy and suitable procedure for implementation in routine care, meaning that replacing MoCap with wearable inertial sensors could lead to shorter subject care time and could be transposed in any environment outside laboratory rooms.