In order to reduce the risk of data privacy disclosure and improve the effect of information privacy protection, a differential privacy protection algorithm for network sensitive information based on singular value decomposition is proposed. TF-IDF method is used to extract network sensitive information text. By comparing the word frequency of network sensitive information, high word frequency word elements in network information content are collected to obtain the mining results of network sensitive information text. According to the decision tree theory, the equal difference privacy budget allocation mechanism is improved to achieve equal difference privacy budget allocation. By discarding some small singular values and corresponding spectral vectors, the data can be disturbed, and the availability of the original data can be retained, so that it can truly represent the original data set structure. According to the results of equal difference privacy budget allocation and singular value decomposition disturbance, the data of high-dimensional network graph is reduced by random projection, singular value decomposition is performed on the reduced data, and Gaussian noise is added to the singular value. Finally, the matrix to be published is generated through the inverse operation of singular value decomposition to achieve differential privacy protection of network sensitive information. The experimental results show that the privacy protection quality of this algorithm is high and the data availability is effectively improved. For example, through statistical analysis of the records of users' purchase of health care products, it is possible to find out "the age stratification of purchase of health care drugs" or the demand for health care drugs. However, this data contains a large amount of personal private information. Once released directly, it will directly lead to the disclosure of users' personal privacy information, which will not only bring users property information security losses, but also bring legal and economic disputes to the data publisher; On the other hand, even after encryption, privacy protection and other technical processing, attackers can still use data mining, machine learning and other technologies to steal users' personal privacy information. Therefore, the problem of privacy protection needs to be solved urgently4.In the context of the rapid development of Internet technology, data shows an explosive growth trend and is flooding in various fields. According to statistics, the daily average number of microblog releases exceeds 270 million, and the daily average number of searches by Baidu search engine exceeds 1.54 billion. Various social software, online shopping platforms, management systems, etc. are also producing data closely related to people's lives. This data include personal consumption records, travel records, medical records, etc. There is no doubt that these data are very important for data analysts. Especially with the help of diversified data mining5 proposed a differential privacy protection method for sensitive information of the population intelligent perception network. Considering the coupling relationship between the perceived information availability and privacy protection, the perceived information quality and privacy protection are optimized respectively. First, calculate the dispersion rule of the noise range, use Bayes to derive the best estimate of noise dispersion, adjust the noise range of information perception, and search for the best estimated information probability matrix through iterative processing to improve the quality of perceived information. Then, optimize the differential privacy, introduce noise mechanism and sensitivity constraints, and eliminate the correlation between the differential privacy algorithm and the information set. Finally, considering the difference of information types in perceptual information, design corresponding processing mechanisms for numerical and non numerical information respectively. The simulation results show that this method can effectively improve the availability of perceptual information, and has better privacy processing accuracy and execution efficiency. Literature6 proposed a personalized differential privacy protection method based on Skyline computing. First, the attribute vector of users was constructed, and then the method based on Skyline computing was used to evaluate the privacy disclosure level of users, and the user data set was segmented according to this level. Then, the sampling mechanism is applied to achieve personalized differential privacy, and noise is added to the integrated data. Finally, the security and practicality of the processed data are analyzed and published. The experimental results verify that this method has a high quality of privacy protection and has certain application value. Literature7 proposed a privacy protection method for sensitive data based on migration learning, which combines multiple "master" models trained from disjoint sensitive data sets in a "black box" way, and these models directly depend on sensitive training data. The "apprentice" is obtained from the "master" collection transfer learning, and cannot directly access the "master" or basic parameters. The data domain of the "apprentice" is different from but related to the sensitive training data domain. In terms of differential privacy, attackers can query "apprentices" or check their internal work, but they cannot obtain the privacy information of training data. Literature8 proposes a virtual text retrieval privacy protection method. Use carefully designed pseudo queries to mask user queries, thereby protecting user privacy. Designing a system framework based on the client side to protect user privacy does not require changing existing text retrieval algorithms or compromising the accuracy of text retrieval. Define user privacy models to establish the requirements that ideal pseudo queries should meet to achieve sensitive information protection. Literature9 proposes an effective cloud based security management solution, with the basic idea of deploying a trusted local server between an untrusted cloud and each trusted client of a medical information management system, responsible for running the electronic medical record cloud hierarchical storage model and the electronic medical record cloud segmentation query model. The electronic medical record cloud hierarchical storage model is responsible for storing lighter electronic medical record data items on local servers, while encrypting and storing highly private electronic medical records on the cloud to ensure the confidentiality of patient privacy information in the electronic medical records on the cloud. Literature10 proposes a basic framework for comprehensively protecting the privacy of various users in personalized information retrieval. Its basic idea is to construct a set of carefully designed fake requests, and submit them to the server together with each user request to confuse user requests, and then mask the user privacy behind the requests, achieving security protection for various types of user privacy information.Under the above background, literatureAlthough the above methods play a role in privacy protection to a certain extent, there are still problems of poor privacy protection quality and data availability in practical applications. Therefore, this paper proposes a differential privacy protection algorithm for network sensitive information based on singular value decomposition. The organization process of this article's research content is as follows: Firstly, TF-IDF method is used to extract network sensitive information text, collect word elements with high word frequency, and obtain the mining results of network sensitive information text. Secondly, based on the decision tree theory, the equal difference privacy budget allocation mechanism is improved to achieve equal difference privacy budget allocation, which can not only preserve the availability of the original data, but also truly reproduce the structure of the original dataset. Random projection is used to perform dimensionality reduction and singular value decomposition on high-dimensional network graph data, and inverse operations are used to generate a matrix to be published, achieving differential privacy protection for sensitive network information. The test results prove that the contribution of the algorithm designed in this paper lies in improving the quality of privacy protection and effectively improving the availability of network data.The TF-IDF method is used to extract network sensitive information text. By comparing the word frequency of network sensitive information, the high word frequency word elements in network information content are collected, and then the network sensitive information text is obtained. The main idea of TF-IDF method is that if a word or phrase is generated frequently in one article and rarely appears in other articles, it indicates that the word or phrase has good classification ability and can be used for classification. TF-IDF includes TF (Term Frequency) and IDF (Inverse Document Frequency). TF indicates the frequency of sensitive words in document mentclass2pt{minimIn formula , \documeentclass1pt{minima formula :2\documeIn formula  and formAfter obtaining the network information text through the TF-IDF method based on the above analysis, the representative sensitive information features should be selected. Use formula  to calcuIn the formula , \documeThe network sensitive information feature  formula :5\documeIn the above network sensitive information features, Set In the formula , \docume11:The Euclidean distance between sensitive information features is obtained by formula  11:7\docObtain the maximum distance between sensitive information and normal information through formula :8\documeThen the cluster center of network sensitive information mining is obtained through formula  to realiThrough the above analysis, the mining results of network sensitive information are obtained, and the singular value decomposition method is used for the mining results to achieve the differential privacy protection of network sensitive information.13 is a common data mining matrix decomposition method and information retrieval method. Singular value decomposition belongs to a matrix decomposition in linear algebra and is widely used in the field of machine learning to reduce the dimensions of data sets. Singular value decomposition (SVD) can not only eliminate data noise, but also achieve effective privacy protection. Therefore, this paper uses the singular value decomposition method to study the differential privacy protection of network sensitive information.How to protect network sensitive information under the premise of effectively mining network sensitive information is an important topic in the field of data processing. Singular value decomposition (SVD)14 to improve the quality of privacy protection.The differential privacy mechanism mainly protects data privacy by adding noise to the dataset. Therefore, the reasonable allocation of the privacy budget is an important point in the algorithm design process. At present, most of the existing methods adopt the traditional privacy budget allocation scheme, that is, half of the remaining privacy budget is allocated to each decision node and leaf node layer by layer. At this time, the privacy budget and added noise of each layer of the differential privacy protection algorithm are the same. With the continuous increase of the number of decision tree layers, the privacy budget allocated to each layer of decision nodes decreases exponentially, so the noise of adding query results becomes larger. At the same time, because the number of sample datasets included in the leaf node is small, the classification accuracy of this node will decline, although the privacy of the data is guaranteed during the operation, the performance of the algorithm is greatly affected and is not applicable to practice. Therefore, this paper improves the existing equal difference privacy budget allocation mechanism according to the decision tree theorySpecifically, the equal difference privacy budget allocation mechanism is as follows: set the overall privacy budget of the algorithm as  formula :10\documAccording to the unique sequential combination characteristic of differential privacy, the privacy protection budget consumed by the algorithm as a whole is equal to the sum of privacy protection budgets consumed by each layer of the decision tree. However, since the data sets used by nodes in each layer for splitting and counting are disjoint, according to the parallel combination characteristics of differential privacy, the privacy budget allocated to each level does not need to be evenly distributed to each node, and each node is directly given the same and equal to its own privacy budget. In the part of the algorithm that adds noise to protect data privacy, because the Laplacian mechanism can better fit the random distribution of noise, the most commonly used Laplacian mechanism is selected to add noise to the count value of data in the leaf node. At the same time, considering that there may be continuous features in the dataset, the algorithm also uses an exponential mechanism to calculate the Gini index of continuous features, so as to select the best continuous features and split points.In the isochromatic privacy budget allocation, perform the following operations for each decision tree:(1) Extract the same amount of data set from the training data set;If the data on the node meets the stop condition, set the node as a leaf node, stop creating sub nodes, use the Laplacian mechanism to add noise to the node's count value, and then select the classification with the most samples as the label of the leaf node;If the data on the node does not meet the stop condition, calculate the number of data sets contained in the node, and use the Laplace mechanism to add noise;Randomly select some features from the feature set. If the sub feature set contains continuous features, execute 4); otherwise, end the algorithm;The privacy protection budget is equally allocated to each feature, and an exponential mechanism is used to select the best splitting feature and mode from all continuous features;Calculate the Gini index of each remaining discrete feature on the data set, and compare it with the Gini index of the local optimal feature to select the global optimal splitting feature and split the nodes.(2) Repeat the following steps until the stop conditions are met as follows;(3) If the stop condition is met, equal difference privacy budget allocation can be realized.Singular value decomposition (SVD) is not a new technology in the application of differential privacy protection for network sensitive information, but its application in the perturbation of information privacy protection is emerging recently. A remarkable feature of singular value decomposition (SVD) is to reduce the dimension of compressed data while maintaining the main data patterns. The main purpose of matrix decomposition is to obtain some low dimensional, approximately related data structures of objects and attributes from the original dataset.Let  formula :11\documThe remarkable feature of singular value decomposition is that it protects the main data patterns while reducing the dimension of compressed data. In the differential privacy protection of network sensitive information, the disturbed dataset Singular value decomposition (SVD) in AI domain is used as a data perturbation strategy to protect data privacy. An undirected weighted network with mentclasspt{minimaFor the adjacency matrix SVD disturbance mainly perturbs the data by discarding some of its smaller singular values and corresponding spectral vectors. If diagonal matrix  formula :14\documThen the adjacency matrix after SVD disturbance is shown in formula :15\documIn order to strengthen the protection of data, Disturb the singular value of adjacency matrix  formula :18\docum formula :19\documIn formula , \documeAccording to the results of equal difference privacy budget allocation and singular value decomposition perturbation, a differential privacy protection algorithm for network sensitive information based on singular value decomposition is further proposed. In the first step, random projection is used to reduce the dimensions of high-dimensional network graph data. In the second step, singular value decomposition is performed on the reduced dimension data and Gaussian noise is added to the singular value. Finally, the matrix to be published is generated through the inverse operation of singular value decomposition. Compared with adding Gaussian noise directly to the reduced dimension data, adding Gaussian noise to the values in the singular value matrix can effectively reduce the amount of noise added.Assuming that the attacker has strong background knowledge, the Euclidean distance information of sensitive information in the network will not be disclosed. According to network Let Then for any unitary invariant norm  formula :22\documIt can be seen from the above analysis that considering the problem that traditional methods will directly add Gaussian noise when reducing high-dimensional data to low dimensional data, resulting in a large amount of noise, this paper proposes a differential privacy protection algorithm for network sensitive information based on singular value decomposition. Reducing the dimensions of the noise matrix can reduce the amount of noise added, so that the expected value after disturbance is lower. Therefore, singular value decomposition is introduced to decompose the projected matrix. Gaussian noise is added to the singular value and less noise is added to improve the data availability.15 and singular value decomposition to solve the problem of large amount of noise added by traditional methods. First, this method generates the adjacency matrix of social network, uses random projection to convert high-dimensional matrix into low dimensional matrix, then decomposes the low dimensional matrix into left singular matrix, right singular matrix and singular value matrix, and finally adds Gaussian noise to the singular value matrix, the matrix to be published is generated according to the inverse operation of singular value decomposition. The method in this paper adds noise to the singular value matrix, because the singular value matrix only has values on the main diagonal, and the number of values is the rank of the matrix. Compared with the This method combines random projectionThe implementation process of differential privacy protection for network sensitive information is shown in Fig. Preprocess the original network graph and calculate its adjacency matrix Generate unitary matrices Use matrix Singular value decomposition of matrix Gaussian noise is added to singular value;Discard some values in The matrix to be published is generated according to the inverse operation of singular value decomposition to achieve the differential privacy protection of network sensitive information.According to Fig. In order to verify the effectiveness and feasibility of the differential privacy protection algorithm for sensitive network information based on singular value decomposition, experimental research was carried out. The experimental environment of this paper is macOS 10.13.1 operating system, the development environment is IntelliJ IDEA, the programming language is Java, and the experimental data is analyzed using Matlab simulation software. The algorithm was written using the neural network toolbox in the MATLAB companion toolbox.A Inspur blade server is used to simulate the deployment of multi tenant applications, configured with 12 core CPU (primary frequency 3.10 GHz), 32 GB memory, and 2 TB hard disk. The storage layer uses MySQL 5.6.22 as the storage database, and multi tenant applications use Java 1.8 to write programs for simulation. The data set is taken from the data in the basic medical registration information table of the insured in the internal test data set of the social security project, and the data volume is about 3 million pieces. The data selected a total of 20 attributes including family name (fuzzed), medical personnel category, gender, age, trust level, widowhood category, company organization, medical account and other attributes for the experiment. Incompatible privacy constraints are family name, gender, age and company organization.5, literature6 and the network graph published under the algorithm in this paper are used as subgraphs respectively to compare the attack results under the two kinds of background knowledge. The matching degree of attack results is shown in Fig. The verification method is to take the published graph after privacy protection as a sub graph, and check the matching degree between the published results under the sub graph attack and the real dataset. The lower the matching degree, the better the privacy protection effect. First, it is assumed that the attacker has the background knowledge of the target and incomplete subgraph information; Then, the node identification attack is carried out; Finally, the methods in literature5 method reaches 4.1, the maximum match degree of the attack results of the literature6 method reaches 3.7, while the maximum match degree of the attack results of the algorithm in this paper is only 2.3. It can be seen from the comparison that the data matching degree of the algorithm proposed in this paper under node attack is obviously smaller than the methods in literature5 and literature6, indicating that the data availability of the algorithm proposed in this paper is relatively good, that is, the privacy protection quality of the algorithm proposed in this paper is higher.It can be seen from Fig. How to avoid data destruction on the premise of ensuring data privacy is the key to verify the effectiveness of the method. Calculate the data loss rate and evaluate the data availability according to this indicator. The comparison results of data loss rates are shown in Fig. 5 reaches the maximum, which is 12.5%; When there are 50 node attacks, the data loss rate of the method in literature6 reaches the maximum, which is 11.3%. The above experimental results show that the data loss rate of this algorithm is low, indicating that this algorithm can not only improve the quality of data privacy protection, but also reduce data loss as much as possible.It can be seen from Fig. It can be seen from Section "In formula , the maxFigure TF-IDF method is used to extract network sensitive information text, and the result of network sensitive information text mining is obtained, which provides a data basis for privacy protection.Using singular value decomposition to disturb the confidential numerical attributes can not only meet the requirements of protecting sensitive data attributes, but also obtain accurate data analysis results.By discarding some of its smaller singular values and corresponding spectral vectors, the data can be disturbed, which can not only retain the availability of the original data, but also truly represent the original data set structure.The analysis of experimental results shows that this algorithm can show the effectiveness of the maximum mutual information privacy leakage, and the maximum data loss rate of this algorithm is only 5.8%, which fully verifies its application value.At present, information differential privacy protection methods applied to various networks are mainly about small social networks. Although these privacy protection methods can resist background knowledge attacks to achieve the purpose of protecting social networks, with the advent of the big data era, the number of users increases and user attributes increase. These methods need to add a lot of noise, resulting in poor data availability. In order to reduce the risk of data privacy disclosure and improve the effect of information privacy protection, a differential privacy protection algorithm for network sensitive information based on singular value decomposition is proposed. The main innovations of the algorithm are as follows:


Coronary computed tomography angiography (CCTA) is widely used due to its improvements in computed tomography (CT) diagnostic performance. Unlike other CT examinations, CCTA requires shorter rotation times of the X-ray tube, improving the temporal resolution and facilitating the imaging of the beating heart in a stationary state. However, reconstructed CT images, including those of the coronary arteries, contain insufficient X-ray photons and considerable noise. In this study, we introduce an image-processing technique for noise reduction using singular value decomposition (SVD) for CCTA images. The threshold of SVD was determined on the basis of minimization of Jensen–Shannon (JS) divergence. Experiments were performed with various numerical phantoms and varying levels of noise to reduce noise in clinical CCTA images using the determined threshold value. The numerical phantoms produced 10% higher-quality images than the conventional noise reduction method when compared on a quantitative SSIM basis. The threshold value determined by minimizing the JS–divergence was found to be useful for efficient noise reduction in actual clinical images, depending on the level of noise. Coronary computed tomography angiography (CCTA) has been widely used in recent years due to its the improved performance ,2. In paThe second approach is that the use of artificial intelligence has recently been proposed to address this problem, and the potential of deep convolutional neural networks to improve CT image reconstruction has been investigated . Deep leThe third approach is to process the reconstructed image. This method is more advantageous than the above two methods because it can use previously acquired images and does not require special hardware. In addition, the simplicity of implementation and the comprehensibility of the process make it easy to interpret the results, and does not significantly affect the diagnosis of medical images. Therefore, we aimed to provide a mathematically consistent method to reduce noise in medical images, especially to focus on noise reduction in CCTA images. To achieve this goal, singular value decomposition (SVD) is the main method used in this study. SVD is used alongside principal component analysis as a method of dimensionality reduction and has been used in a wide range of fields ,9,10. SVSingular values reduction method using threshold value is called low-rank approximation. The low-rank approximation is a minimization problem in which the evaluation function measures the goodness-of-fit between the given data and the approximating matrix. The appropriate evaluation function affects the determination of the threshold value and quality of the approximated image. The Frobenius norm is often used as an evaluation function to measure the level of approximation between noise-free and noisy images in low-rank approximations using SVD. This is a natural generalization of the 2-norm of a vector into a matrix. The 2-norm is known to be robust against noise; however, its convergence performance is poor, and it does not accurately capture the structure of medical images ,12. The We evaluated the performance of the low-rank approximation through numerical experiments simulating medical images. First, various levels of noise were added to a numerical phantom that simulated a medical image, and a detailed study of the noise and singular values was conducted. The numerical phantom produced noise-free images of various noise levels and was used for thresholding to obtain the minimum JS–divergence. We also compared the results obtained by the proposed method with other noise reduction methods and confirmed the superiority of the proposed method. We then performed denoising for CCTA images from clinical CT scanner with the threshold value obtained by the numerical phantom and found that the proposed method was high performance. The advantage of using the minimum of the JS–divergence as the threshold decision is that it can be objectively determined on the basis of image quality.The relationship between noisy and noise-free images can be described using the following equation:Noise A. i denote the number of nonzero singular values of A or, equivalently, the rank of A  bWe aimed to validate the proposed method on a numerical phantom by using CCTA images obtained from a clinical CT scanner. Unlike numerical phantoms, noise-free images are difficult to obtain in clinical imaging. However, using the results obtained from previous numerical phantoms, noise reduction can be applied to clinical images. CCTA images were acquired from a 320-row CT Aquilion ONE Vision Edition  by ECG-synchronized scanning. The scan conditions were as follows: tube voltage, 120 kV; tube current, 600 mA; and rotation time, 0.275 s. The entire heart was scanned once as a volumetric scan. The thickness and spacing of the reconstructed slices were 0.5 mm. Image reconstruction was performed using half-reconstruction. As seen from First, to determine the threshold in the clinical image, the region of interest (ROI) shown in k = 66, which is the lowest value of the evaluation function when k = 66. The density profiles are shown with normalized scaling, such that the maximum value is at 1 and the minimum value is at 0. As with the numerical phantom, the red line shows the profiles before and after noise reduction. As can be seen from the images and profiles, the randomness owing to noise was reduced. The results obtained from the numerical phantom were used to determine the threshold value for noise reduction, and as with the numerical phantom, noise reduction with a high level of accuracy was achieved.Although it is difficult to estimate the amount of noise directly from clinical images, the simplest method is to obtain the standard deviation from the ROI. The standard deviation in this CCTA image was Another advantage of noise reduction using SVD is that it can reduce the dimensionality of the image because it removes singular values from the image by thresholding, whereas noise reduction using ordinary pixel-based filtering cannot reduce the dimensionality of the image. Reducing the dimensionality of features by removing noise, which is an additional component in machine learning, is advantageous for building an efficient learning system. The thresholding method based on JS–divergence proposed in this study enables noise removal while preserving the important components of the image.We proposed a new thresholding method for noise reduction by SVD using JS–divergence as an evaluation function. A noise-free image cannot be obtained in clinical imaging. However, by using a numerical phantom, noise-free images were obtained for use in thresholding based on the minimum value of JS–divergence. JS–divergence functioned as an evaluation function to separate important structures from noise in the image and provided high-quality images. Furthermore, by comparing the threshold value obtained from the numerical phantoms with the noise levels of clinical CCTA images, we justified that this approach for noise reduction is also effective for clinical images. By using JS–divergence, a well-known tool for comparing probability distributions, as an evaluation function, it is possible to compare pixels as probability distributions. By mapping comparisons between distributions to noise-free and noisy images, the minimum value of JS–divergence can provide the threshold that yields the best image, as opposed to SVD, for which the determination of the threshold has traditionally been empirical. In the future, we plan to develop a new method to reduce noise in more complex structures of numerical phantoms and use clinical images other than CCTA. Furthermore, it is necessary to examine how the noise and dimensionality reduction functions of SVD affect the results and diagnosis as training data for machine learning in future studies.


However, accurately assessing the contributions of an individual or multiple amino acid mutations to overall protein stability to select the most promising mutants remains a challenge. Knowing the specific types of amino acid interactions that improve energetic stability is crucial for finding favorable combinations of mutations and deciding which mutants to test experimentally. In this work, we present an interactive workflow for assessing the energetic contributions of single and multi-mutant designs of proteins. The energy breakdown guided protein design (ENDURE) workflow includes several key algorithms, including per-residue energy analysis and the sum of interaction energies calculations, which are performed using the Rosetta energy function, as well as a residue depth analysis, which enables tracking the energetic contributions of mutations occurring in different spatial layers of the protein structure. ENDURE is available as a web application that integrates easy-to-read summary reports and interactive visualizations of the automated energy calculations and helps users selecting protein mutants for further experimental characterization. We demonstrate the effectiveness of the tool in identifying the mutations in a designed polyethylene terephthalate (PET)-degrading enzyme that add up to an improved thermodynamic stability. We expect that ENDURE can be a valuable resource for researchers and practitioners working in the field of protein design and optimization. ENDURE is freely available for academic use at:  The design of proteins with improved stability and activity is a critical aspect of research in biotechnology and related fields. It holds the potential to revolutionize a wide range of applications , from deTwo widely used protein design approaches are directed evolution and computer-aided protein design. The former approach mimics the natural gene diversification and selection process and involves iterative rounds of mutagenesis, which create a library of mutants, and selection of mutants with desired functions . ComputeMachine learning algorithms have revolutionized the field of protein design, enabling researchers to generate novel proteins with improved properties more efficiently . Two curde novo protein design, DE-STRESS , called DuraPETase , a web application framework for Python. Starting from the File Upload page, the user uploads the PDB files of the designed protein and the reference protein structure. Alternatively, users can choose to provide amino acid sequences of the reference and mutant protein, and ENDURE will automatically predict their structures using ESMFold , which includes the welcome page, file upload section, and interactive visualizations. The UI is designed to be user-friendly and easy to navigate, allowing users to upload their protein structure file, prepare the structure, and run the energy breakdown and residue depth calculations. Since Streamlit is our web development framework, the front and backend are managed under the hood. We do include several analysis modules, which are either pure Python functions or Python functions that call other auxiliary executables. The names of important internal functions in the ENDURE app are written in The protocol consists of two main stages: 1) structure pre-processing actions and 2) structure analysis actions. Those actions are run on the File Upload page.The pre-processing is an important step in the ENDURE web tool as it ensures that the uploaded protein structure is in the correct format and ready for analysis. The pre-processing actions include cleaning of the PDB files to remove any ligands, ions, or water molecules, relaxing of the protein structures to remove any steric clashes or unfavorable interactions, and determining the mutations for the designed protein relative to the reference protein. Additionally, the PDB file is renumbered in this step so that the first residue in the file is at position 1. Relaxing the protein structures is the second important action in preparing the protein structures for analysis. This ensures that the protein structure is in a low energy state according to the Rosetta energy function , which crun function is launched with four parameters as input: the input PDB file name, the location to save the result file, the location to save the log file, and the file path of the Rosetta executable. The output of the protocol is converted to a downloadable CSV file using the convert_outfile function, which saves the CSV file as a dictionary in the current session state.The analysis actions include the energy breakdown (EB) calculations, which provide information about the energetics of each residue’s interaction in the two analyzed protein structures, and the residue depth (RD) calculations. These algorithms are powered by the Rosetta energy function  and the calculate_depth function.These actions are followed by the RD calculation, which uses the MSMS algorithm  from BioThe processing and analysis actions launched from the File Upload page are run in the background to prevent the UI from freezing, and their results are integrated into the interactive visualizations in the front end.The Interaction Analysis page allows users carrying out a comprehensive analysis of the energetic changes in pairwise interactions of single- and multi-mutant protein designs. The user can select and analyze interactions from different categories (A to F explained below) and from different physical interaction types  through different control parameters on the side bar. Individual residue pairs, affected directly or indirectly by the mutations, can be selected and displayed in interactive 3D visualizations.We defined six categories of residue pair interactions to identify the regions in the protein structures most affected by the mutations.Category A: residue pairs that are interacting in the reference structure have different interaction energy in the mutant, even though neither of the two residues were mutated.Category B: residue pairs that are interacting in the reference structure have one member replaced, resulting in a different interaction energy in the mutant.Category C: residue pairs that are interacting in the reference structure no longer interact in the mutant, even though neither of the two residues was mutated.Category D: residue pairs that are interacting in the reference structure no longer interact in the mutant because one member was mutated.Category E: residue pairs that are not interacting in the reference structure interact in the mutant, even though neither of the two residues was mutated.Category F: residue pairs that are not interacting in the reference structure interact in the mutant because one member was mutated.In order for ENDURE to detect the different interaction categories A-F and different physical interaction types, there are several functions implemented on the page that users can execute by clicking the Start Calculations button . Such functions perform a post-processing and filtering of the scorefile generated by the Rosetta EB calculations.energy_calc function is used to identify the essential changes in interaction energies between the mutant and the reference protein structure. It takes the outputs of the residue EB computation performed for the mutant and reference structures, the list of mutations between the reference and mutant, and a streamlit progress bar. The function calls several sub-functions to perform various interaction energy comparisons for each interaction category and physical interaction type. The former is managed by the interaction_analysis function and the latter is managed by the following functions: salt_bridges, disulfide_bonds, and hydrogen_bonds. As the names suggest, these functions calculate the energy differences for different types of interactions, such as salt bridges, disulfide bonds, and hydrogen bonds.The interaction_analysis function calculates the difference in interaction energies between a mutant and a reference protein structure for a given list of mutations. The interaction_analysis function processes the outputs of the per-residue EB performed on the reference and mutant structures. It calculates the differences in all single-body  and two-body  energies for all categories (A to F) between the two proteins.The In analyzing the interaction energy changes between the wildtype and mutant protein, it is important to distinguish between total energy changes and significant energy changes. The former is the sum of all energy changes, including those with a small value. However, since thousands of small changes can occur, it is possible for insignificant changes to mask chemically important changes. To overcome this issue, the significant energy change is calculated, which is the sum of only those interaction energy changes that exceed a minimum magnitude. In ENDURE changes that are larger than +1.0 Rosetta Energy Units (REU) or smaller than −1.0 REU are considered significant. By focusing only on significant energy changes, the mutations that are likely to have a significant impact can be more easily detected.For the REF2015 scoring function for soluble proteins, there is an approximate 1:1 correspondence of REU and kcal/mol . Howevertotal_energy_changes and significant_changes functions, respectively. These functions operate on a dictionary returned by interaction_analysis and sum all as well as the significant energy changes for each interaction category specified in an interaction list. Interactions from categories A-F can be selected from a list and the change for a given interaction type  can be furthered inspected.The total energy change for all interactions and the sum of the subset of significant changes, is calculated using the Mutation-induced energetic changes can have different effects on different layers of the protein structure. Therefore, we implemented a residue depth analysis and combined it with the per-residue energy breakdown analysis to distinguish changes occurring on the protein surface from those occurring in buried regions of the protein structure.The Residue Depth page of the ENDURE app allows the user to analyze and compare the effect of mutations on the energy and spatial location of residues. Specifically, the user can select a residue pair that displays a strong negative energetic contribution and visualize the interaction in the protein structure. By adjusting the threshold slider, the user can see which residues have a significant impact on stability and select the most promising mutations for further analysis. Once the user selects a particular mutation by clicking on a point in the scatter plot, the app displays a side-by-side 3D visual comparison of the residue in the mutant and reference structures, which allows for a direct comparison of the effect of mutations on the protein structure. This analysis provides valuable insights into the structural and energetic changes resulting from mutations.The Welcome page  is the fIsPETase enzyme (PDB ID: 5XJH) (m) of DuraPETase by 31°C compared the wildtype IsPETase  , which hD: 5XJH) . As can IsPETase . In addiIsPETase  and HotPIsPETase , using EIsPETase . The favIn addition to the overall energy comparison, ENDURE also provides detailed information about the specific amino acid interactions that contribute to the improved stability of the selected mutant. The interaction analysis feature allows focusing on and visualizing specific residue interactions in the protein structure, which help to rationalize the underlying molecular mechanisms contributing to the improved stability of the selected mutant. These features will be described next.The Interaction Analysis page of ENDURE enables performing a detailed examination of the energetic changes for residue pairs of different types see . With thIsPETase. This salt bridge isn’t present in the wildtype protein but is in DuraPETase—i.e., it belongs to interaction category F. IsPETase has an isoleucine (Ile135) at the same position, which cannot form a salt bridge. In addition, as shown in the left-hand table in the screenshot in For example, The different categories of interaction changes (A to F) allow the user to quickly identify the changes in interactions that have occurred and to focus their attention on the most important ones. For example, if a user observes that most changes are of type E or F, this might suggest that new interactions have formed, which could also significantly affect function. By providing this information, the Interaction Analysis page helps the user to quickly understand and prioritize the changes in interactions that have occurred and guide their efforts in protein design.IsPETase, Ile135 is located on the protein surface, indicated by a low residue depth value of ∼2Å , to residues that aren’t interacting in the reference structure but make interactions in the mutant due to a mutation (category F). These different categories of changes provide a useful way for the user to identify which mutations have the strongest impact on the protein structure, and consequently focus design efforts on specific areas of the protein structure.Compared to previous research, our web application offers a user-friendly and accessible solution for analyzing protein structures and interaction changes. Prior research in this field has typically been focused on developing computational tools for protein structure prediction and analysis  or the aIt is important to note that the tool is limited by the accuracy of the underlying computational tools and algorithms used for protein structure prediction and analysis. Additionally, the interaction analysis section is based on a static protein structure analysis. Accuracy in predicting mutation-induced energy changes could benefit from a model ensemble approach , in whicDespite these limitations, it represents a significant advancement in the field of protein structure and interaction analysis. The integration of computational tools into a user-friendly interface makes it possible for scientists outside the field of computational structural biology to quickly and efficiently analyze protein structures and identify potential areas for improvement. In future versions, ENDURE could be expanded to include additional features and improvements, such as the ability to examine other kinds of proteins, including membrane proteins and proteins with noncanonical amino acid modifications, through the incorporation of different energy functions. It could also be enhanced to consider ligand molecules in the design analysis, allowing the identification of designs with improved binding affinity. These features are currently planned for the next version of ENDURE, which will be released in the future. Additionally, the tool could be further developed to incorporate machine learning techniques to improve the accuracy of the analysis. With these advancements, ENDURE could become an even more powerful tool for protein design and analysis.In conclusion, the ENDURE web application provides a unique and accessible solution for analyzing protein structure and interaction changes and, in that way, represents a significant advancement for the field of protein design. Categorizing changes in pairwise interactions for different interaction types provides a straightforward way for the user to guide their protein design strategies. Integrating computational tools into a user-friendly interface makes it possible for a broader audience to quickly and efficiently analyze protein structures. The future direction of the research will focus on further developing the application to incorporate analysis on protein dynamics, support for non-standard amino acid residues, and application of machine learning techniques. Furthermore, a command line interface integrated in the front end is planned, which will help further customize some of the analyses.


Daily wheelchair ambulation is seen as a risk factor for shoulder problems, which are prevalent in manual wheelchair users. To examine the long-term effect of shoulder load from daily wheelchair ambulation on shoulder problems, quantification is required in real-life settings. In this study, we describe and validate a comprehensive and unobtrusive methodology to derive clinically relevant wheelchair mobility metrics (WCMMs) from inertial measurement systems (IMUs) placed on the wheelchair frame and wheel in real-life settings. The set of WCMMs includes distance covered by the wheelchair, linear velocity of the wheelchair, number and duration of pushes, number and magnitude of turns and inclination of the wheelchair when on a slope. Data are collected from ten able-bodied participants, trained in wheelchair-related activities, who followed a 40 min course over the campus. The IMU-derived WCMMs are validated against accepted reference methods such as Smartwheel and video analysis. Intraclass correlation (ICC) is applied to test the reliability of the IMU method. IMU-derived push duration appeared to be less comparable with Smartwheel estimates, as it measures the effect of all energy applied to the wheelchair (including thorax and upper extremity movements), whereas the Smartwheel only measures forces and torques applied by the hand at the rim. All other WCMMs can be reliably estimated from real-life IMU data, with small errors and high ICCs, which opens the way to further examine real-life behavior in wheelchair ambulation with respect to shoulder loading. Moreover, WCMMs can be applied to other applications, including health tracking for individual interest or in therapy settings. Manual wheelchair users often report persistent shoulder pain and problems. The prevalence of shoulder pain is accordingly high, ranging from 39 to 71% ,3. Not oWheelchair users are 5.8 times more likely to suffer from shoulder pain than able-bodied controls . Due to Wheelchair propulsion as a risk factor for shoulder problems has been the focus of previous investigations. Several studies have been conducted to address the amount of shoulder load in wheelchair propulsion ,11,12 orIMUs are ideal for monitoring wheelchair propulsion unobtrusively over a long period of time. In comparison with measurement wheels, such as the Smartwheel, which have been used to quantify wheelchair propulsion in a laboratory setting ,18,19, IIn addition to quantifying wheelchair propulsion for studying the risk of shoulder overload in research, wheelchair users also wish to use such technologies for self-care. Unlike other chronic health conditions, health-tracking solutions for shoulder health management are not yet commercially available . Li et aSumming up, the methods for quantifying wheelchair propulsion in daily life are still scarce and usually only address some of the features desired by wheelchair users and therapists or some of the features needed for evaluating wheelchair use as a risk factor for shoulder problems. In this study, we aim to describe and validate a comprehensive and unobtrusive methodology to derive a full set of wheelchair mobility metrics (WCMMs) from one or two IMUs placed on the wheelchair while collecting data in a real-life setting. The described WCMMs include distance covered by the wheelchair, linear velocity of the wheelchair, number and duration of pushes, number and magnitude of turns and inclination of the wheelchair when on a slope.Ten able-bodied participants  were invited to participate in the experiment. The participants were first trained in the wheelchair-related tasks of interest for several hours. Such an able-bodied study sample cannot be representative of the manual wheelchair user population in all of its aspects, for instance considering trunk stability, which in the SCI case might be affected by the lesion level but is still available in the able-bodied case. However, as indicated by Vegter et al. , several−3 m/s2. The gyroscope range was set at 2000 degrees/s, at 16-bit resolution, having an RMS noise value of 0.0481 degrees/s.A standard active wheelchair  was equipped on the right side with a 24-inch Smartwheel  and 2 Shimmer IMUs  on the wheelchair frame and the right wheel, as depicted in Distance covered;Linear velocity of the wheelchair;Number of pushes;Duration of pushes;Number of turns;Magnitude of turns;Wheelchair inclination.While following a course around the campus, the participants implemented a variety of speeds, turns and slopes and completed a figure-8 maneuver 3 times. All trials were recorded on a consumer-grade video recorder for the referencing of activities. Data were synchronized by a specific procedure: “the mechanical IMU sync”. For that procedure, all the IMUs were attached to a rigid beam that was rotated around the longitudinal axis 10 times before and after the actual measurements. This delivers a clear recognizable pattern in the gyroscope signals that can be synchronized by cross-correlation. Visual inspection of the peaks of the synchronized signals indicated an accuracy of one to two samples . While using simple and straightforward signal processing and calculations, the next seven WCMMs were derived from the acquired IMU data for comparison with reference methods:The IMU-derived WCMMs were validated against appropriate reference methods  as described below. All data were collected in real-life conditions.We aimed for a minimum of preprocessing for the IMU data; however, besides basic filtering of noise  , two corThe IMU mounted on the frame of the wheelchair was manually aligned with one of the horizontal lateral pointing tubes of the frame; however, vertical alignment with gravity proved to be hard. For that reason, a period of 10 s of complete standstill (on level floor) was selected from the recorded data (both frame and wheel). Averaging the measured acceleration over these 10 s delivered a steady measure of gravity, which was used to align the IMU’s frame of reference with gravity.Similarly, the IMU mounted on the wheel could not be accurately aligned with the wheel axis. Therefore, a period of 10 s of straightforward wheelchair ambulation was selected from the recorded data for every participant. This track of straightforward ambulation was selected from the video recordings and was the same trajectory for all participants. Averaging the measured angular velocity over these 10 s delivered a steady measure of the rotation around (and a definition of the vector of) the wheel axis in the IMU frame of reference. Concurrently, the angular velocity around the wheel axis can be calculated conform Equation (1).IMU_AV_axis = angular velocity around the wheel axis from wheel IMU;α = angle between vector of the wheel axis in IMU reference system and the currently measured angular velocity vector;IMU_AV_tot = total angular velocity as 3D-vector sum.The Smartwheel contains an optical rotary encoder measuring wheel angle (SW_A), accumulated over time. This variable was reset to zero at the start of measurement. Concurrently, the distance covered can be calculated following Equation (2).SW_Dis = distance covered according to Smartwheel;SW_A = Smartwheel angle accumulated;WD = Wheel diameter in meters.From the wheel IMU data, integration over time of the angular velocity around the wheel axis delivers the accumulated wheel angle over time, from which the distance covered can be calculated in the same fashion as for the Smartwheel, following (Equation (2)). ICC was applied to test the reliability of the estimation of the distance covered for both systems across participants .The angular velocity can be obtained from the Smartwheel by differentiating the Smartwheel angle accumulated over time. For both the Smartwheel and IMU data, angular velocity around the wheel axis (expressed in °/s) can be used to calculate the linear velocity in the same fashion as distance covered (Equation (2)), by replacing accumulated angle with angular velocity. The linear velocities from both systems were compared by calculating the RMS value over the complete signals.There are several methods for push detection from Smartwheel data, ranging from simply applying a threshold above noise level  at the pFor push detection from IMU data, the following basic assumption was made: in all-day wheelchair propulsion, when propulsive force is exerted at the rim, the angular velocity will increase. When there is no longer a force exerted, the angular velocity will decrease due to resistive forces. A basic peak detection algorithm  was used to first detect the valleys in the signal of angular velocity around the wheel axis (AV-axis) and concurrently the peaks in between the valleys. This was applied for forward propulsion at those time instances where the angular velocity was positive. The difference between the start and end of each push determined the push duration. The same assumption was the basis for push detection from the angular acceleration (AA), where a push-start is detected when the AA is positive and a push-end is detected when the AA is negative.For both systems (Smartwheel and IMU data), a push was counted as a push when it resulted in a more than 30° rotation of the wheel. Furthermore, pushes with a push duration of more than 2 s were excluded.ICC was applied to test the reliability of the estimations of the number of pushes and the average push duration across participants .All participants performed a figure-8 maneuver like those in Bossuyt et al.  and CollFrom the wheelchair frame IMU , the angular velocity around the vertical was time integrated and the continuous angle of turn (either positive or negative depending on left or right turns) accumulated from the start to end of the protocol. The resulting WC_turn from the wheelchair frame IMU was compared with the difference in 2D orientation of the wheelchair obtained from the 2D-DLT method. WC_turn was compared between systems by applying ICC .The continuous angle of turn from the wheelchair frame IMU served as a reference for the number and magnitude of the WC_turn for the whole of the course measured. WC_turn can be derived from the wheel IMU’s angular velocity signal in a simple fashion based on the following two assumptions: (1) daily wheelchair use does not include sidewards tipping of the wheelchair; (2) the number and inclinations of sidewards-oriented slopes are ignorably small compared with the total amount of vertical turn a wheelchair user encounters on a daily base. Any deviation from the actual measured angular velocity from the wheel axis can then be attributed to a rotation around the global vertical (a WC_turn) and can be calculated using Equation (3). However, the direction of turn (left or right) is lost in this way. Time integration of the signal delivers a continuous angle of turn around the global vertical .IMU_AV_turn = angular velocity of wheelchair turning around the global vertical;α = angle between the vector of the wheel axis in IMU reference system and the currently measured angular velocity vector;IMU_AV_tot = total angular velocity as 3D-vector sum.From the continuous angle of turn, the number of turns and the magnitude thereof can be extracted for both IMUs (frame and wheel). To enable comparison of the magnitude, the continuous angle of turn derived from the frame IMU was rectified. Only turns larger than 30° were included. The absolute number of turns was compared with the ICC between the frame- and wheel-IMU-derived values across participants .Comparison of the calculation of the magnitude of WC_turn between the frame and wheel IMUs was performed by calculating the intersection of the two normalized histograms of the turn  accordinThe different inclines of the course were measured with a digital inclinometer (SPI-Tronic Pro 360) at 5 equidistant locations, for which the values were averaged. As the frame IMU was aligned with gravity, the angle between the actual acceleration measured and the vertical axis of the IMU contains information on incline besides horizontal acceleration due to wheelchair propulsion. To separate these two types of information, a 4th-order bidirectional low-pass Butterworth filter with a cut-off frequency of 0.2 Hz was applied to the frame IMU’s acceleration signal. This cut-off frequency was determined by experimentation and considering the average time needed to propel over the inclination. The inclination was calculated from IMU data as the angle between the filtered acceleration signal and the IMU’s vertical axis in the sagittal plane, averaged over the course of the slope. The calculated inclinations from the IMU data were compared with the  measured inclination by ICC .In total, 302 min of wheelchair activities by the 10 participants was analyzed. The summed distance covered on campus was around 6.5 km. The overall qualitative performance of the participants was highly variable. Some participants, even after several hours of wheelchair training, were still careful and slow in propelling their wheelchair on flat surfaces, on slopes and in making turns, whereas other participants were clearly more experienced and showed much more dynamic behavior. This variation in performance is comparable with the variation in propulsion patterns in the target population of wheelchair users when including persons with paraplegia and tetraplegia. As mentioned before, the able-bodied study sample cannot be seen as representative of the manual wheelchair user population in all of its aspects, for instance considering trunk stability. However, the exerted forces at the rim from the current study sample followed very similar patterns to those observed in data obtained from studies with persons with SCI. Furthermore, in the current study, the movements of the wheelchair are measured and compared using two different devices and methodologies. Despite the variation in, for instance, the propulsion patterns observed in the study sample, the two methods showed good comparability.The results of the comparisons of the derived WCMM variables, according to error measures and ICC (where applicable) are summarized in The total distance covered by both the Smartwheel and wheel IMU appeared to be close to equal and cumulated equally over time, as indicated for one of the participants by In a similar fashion, the linear velocity of the wheelchair, as derived from the Smartwheel data, appeared to be close to equal to the linear velocity derived from the wheel IMU data, with an average RMS value of 0.02; a typical example is depicted in Push detection was performed on propulsive (positive) torque from the Smartwheel at positive velocities only, as most studies examine wheelchair propulsion characteristics on forward ambulation. Similarly, push detection from the IMU data was defined for increasing, positive velocities. Push detection from IMU_AV_axis appeared to be the most robust in comparison with the basic threshold-based algorithm on propulsive torque for Smartwheel data, with an average MAND of 4% . A typicPush detection from the IMU_AA_axis signal resulted in around a 20% higher number of pushes than from the Smartwheel data, although it delivered a shorter push duration than from the IMU_AV_axis signal . HoweverAs the total turn from the figure-8 maneuver from the frame IMU data differed by less than 1% from the 2D-DLT derived total turn, it seemed appropriate to use the frame IMU as a reference for the wheel-IMU-derived amount of turn. The overlap of the normalized histograms on magnitude of turns was, on average, 95.9%; this is shown for one participant in Wheelchair inclination on longer slopes was detected with a small error (0.3°) and high reliability (ICC = 0.975).Despite the high variation in performance of participants, the derivation of most WCMM variables was robust and consistent in comparison with the values from the respective reference systems; all data were collected in real-life conditions. This is a promising result, enabling the future application of the described methodology for collecting WCMMs from IMU data in real-life settings.The distance covered shows a low error of −0.2% between methods and a high reliability, with ICC of 1.00. Therefore, the distance covered derived from an IMU on the wheel of the wheelchair can be considered equal to the distance derived from a Smartwheel. This variable can be used as a primary measure of mobility assessment, a simple but robust variable for life space assessment, as described by Giannouli et al. . AlthougThe linear velocity data from the IMU on the wheel had a low RMS of 0.02 when compared with the values from the reference system. This variable can then be further detailed into bouts of mobility or activity and rest times. Since this method measures continuously, it allows for flexibility in the selection of bout durations for research or treatment purposes.The number of pushes detected from the wheel IMU’s angular velocity differs by about 4% in comparison with the propulsive-torque-based push detection from the Smartwheel. With an ICC of 0.989, the methods can be considered equal. The number of pushes detected from angular acceleration is, however, around 20% higher than from the Smartwheel data and is not recommended. Furthermore, the underlying assumption or application area for the described method is focused on counting pushes during active wheelchair propulsion; being pushed is not discerned and probably needs more complex methods . The numThe push duration values derived from the IMU data are, however, different from the push duration values derived from the Smartwheel; this can be observed in As no clear definitions of a wheelchair push in real-life settings could be found in the literature, we defined a threshold of a minimum of 30° of wheel rotation per push detected, as well as a cut-off of a maximal push duration of 2 s. These thresholds and cut-offs were applied to data from both the Smartwheel and IMUs but are in fact “food for discussion”: what instance should be considered as a push in wheelchair propulsion in daily conditions, in terms of minimal wheel rotation, increase in angular velocity, and/or duration of the push? The cut-off of a maximum 2 s for push duration was based on visual inspection of the data and the corresponding video for the longer pushes detected, which appeared to be caused by acceleration of the wheelchair when going downhill. As the algorithm used defines the end of a push when the angular velocity starts decreasing, the end of the push was, in these instances, detected when braking or reaching the end of the ramp or longer incline. The same discussion should be held regarding the definition of a turn in wheelchair ambulation, in terms of minimal amount of turn or duration. For instance, should a correction in driving direction of 5° count as a turn? It is expected that future monitoring of WCMMs will add to increased knowledge on a clinically significant amount of turn.The turning of the wheelchair can be reliably calculated from IMU data, either from a IMU attached to the wheelchair frame or a wheel mounted IMU, under the assumptions described. WC turning is an immature area of research in manual wheelchair propulsion, where peak forces at the rim can double in comparison with straightforward propulsion . FurtherIn fact, six different push styles were observed in interaction with different turning styles: application of propulsive torque when driving forward, changing driving direction (from forward to backward or vice versa), which is usually the case when making a turn from standstill, or applying propulsive torque when driving backward, which in fact is braking of the wheelchair, or making a turn. The same can be observed for the application of braking torque for the three driving directions described above. The inclination on longer slopes on the campus could be measured accurately, with an error of 0.3°. Only three participants agreed to descend a ramp with an 11° inclination, where two of them tipped the wheelchair backwards to control speed during the descent. For those situations, wheelchair inclination is still measured correctly but is no longer representative of the slope or ramp negotiated. Nevertheless, as propelling uphill usually occurs without tipping for speed control and puts increased loads at the shoulder, wheelchair inclination is an interesting variable to measure; however, this requires an extra IMU on the wheelchair frame.The variation in pushes and braking actions observed from the real-life data collected deserves further research and the development of appropriate calculations or algorithms to detect the variety of pushes. Braking actions or turning by braking can put higher loads on the shoulder, and proper execution of turns and training to do so could help in reducing shoulder problems. Furthermore, detection of the mounting/descending of roadside curbs or maneuvering over irregular surfaces or uneven terrain, as higher shoulder loading activities, could provide additional insight and help to optimize shoulder loading behavior from wheelchair ambulation. The monitoring of daily wheelchair use in terms of the described WCMMs could add valuable insight into daily shoulder load on modifiable variables. For instance, the quantification of the daily distance covered or the number of pushes a day deliver very clear variables on the mobility of MWUs. The number of wheelchair turns in daily conditions and magnitude of them, might shed more light on shoulder load from daily wheelchair ambulation as a potential undervalued risk for shoulder problems. The amount and steepness of inclinations encountered on a daily basis could increase the insight on environmental barriers that the MWU population must deal with. All these variables and factors are suspected to have a certain relationship with shoulder load and shoulder problems. Quantification of these WCMMs in real-life settings for longer durations and their associations with shoulder problems should be examined.One area of interest for future research will be the development of an accurate and easy to use device or app for physical activity screening, health tracking for individuals or meeting activity goals in discussion and agreement with clinicians and therapists.Summarizing the above, most WCMMs can be reliably derived during real-life conditions from one or two IMUs on a wheelchair. The distance covered, linear velocity, number of pushes and number and magnitude of turns can be reliably derived from one IMU on the wheelchair wheel. With an additional IMU on the frame, the inclination of the wheelchair can be reliably obtained. This opens the way to further examine real-life behavior in daily manual wheelchair ambulation.


Most of that work used uniaxial extensometry testing, with narrow strips separated from corneal tissue (and surrounding limbus and anterior sclera) and subjected to tension forces. The tests suffered from fundamental drawbacks arising from the specimen’s non-uniform thickness, straightening an originally curved tissue and the severing of collagen fibrils along specimen edges. Furthermore, the loading applied  was not compatible with the usual loading of the cornea under intraocular pressure.For those of us on the corneal biomechanics bandwagon, the 25-year journey to date has been challenging and yet extremely exciting. Although interest in the field goes back to the 1970s and before, serious interest from renowned researchers like Woo, Wollensak, Nash and Bryant started to make significant contributions in the 1990s. At that time, most, if not all, efforts were focused on the Efforts to improve the testing protocol led to cornea inflation testing, in which the cornea remained intact and loaded with a posterior pressure simulating closely the effects of intraocular pressure. Still, the test method relied on non-physiologic boundary conditions along the specimen edge, which did not represent the actual stiffness of the limbus. In addition, approximations were also introduced in the analysis of the pressure-deformation results to produce estimates of the stress-strain behaviour; this analysis relied first on a form of shell theory that involved necessary approximations of the cornea as a spherical segment with rotational symmetry and uniform thickness. These features inevitably affected the reliability of the resulting stress-strain behaviour and underscored the need for improvements in the test method.Improvements came first in the form of the finite element-based inverse analysis of the cornea inflation test results–removing the need for shell theory. A more substantial improvement followed with whole globe inflation testing, where complete intact eye globes were tested under variable intraocular pressure while suspending the eye and monitoring its deformation response to pressure changes. This technique presented the ultimate solution as the tissue remained intact, loaded with physiologic intraocular pressure, and no approximations were made in the analysis method; however, the drawback was in the complexity of the testing protocol and the associated high chance of analysis mistakes. The protocol was also very time consuming and required the development of highly complex testing apparatus, access to which was limited to a small number of research groups around the world. Despite this, the resulting information on corneal biomechanical behaviour was invaluable in quantifying trends related to stiffness changes with age, disease and rate of loading.ex-vivo testing helped identify corneal behaviour trends, these trends could not simply be applied to individual corneas. Another Research Topic arose with the realisation–or expectation–that ex-vivo tissue may have undergone deterioration post-mortem, and therefore its experimental behaviour cannot be assumed to apply directly to in vivo eyes. For these reasons, it became evident that in vivo testing and measurement of tissue biomechanics was a necessary next step. The first breakthrough here was in 2005 with the Ocular Response Analyzer , a non-contact air-puff-based instrument that provided two measures of corneal biomechanics; these are Corneal Resistance Factor (CRF), which relates to corneal geometric stiffness–in turn, dominated by changes in corneal thickness–and Corneal Hysteresis (CH), which relates to corneal viscoelasticity. This instrument had a significant impact on the field by showing promise in the in vivo measurement of corneal biomechanics, even though the CRF and CH could not be linked directly to standard measures of stiffness such as the tangent modulus.The results also showed that corneas with the same conditions  still experienced different behaviours. This outcome meant that, while A subsequent development took place a few years later, in 2012, with the Corvis ST . This device used similar non-contact, air puff technology and used its much-enhanced monitoring technique to derive several dynamic corneal response (DCR) parameters. Some of the DCRs, most notably the Stiffness Parameter (SP), the Integrated Inverse Radius (IIR), and the Deflection Amplitude (DA) could be related statistically to corneal biomechanical stiffness, even though (like the CRF and CH) no direct links between them and the standard stiffness measures could be established. A further development then took place in 2018 with the Stress Strain Index (SSI), which promised to estimate the stress-strain behaviour of the tissue and, hence, its tangent modulus at any stress or strain. This development was taken further 2 years later when it became possible to turn the SSI from a single value to a map covering the corneal surface. This step was made possible by relying on the evident link between corneal stiffness and the density and orientation of the tissue’s collagen fibrils, as well as our current knowledge of the tissue’s microstructure maps of both healthy and diseased corneas.in vivo behaviour testing methods are under development and expected to become commercially available within a few years. Most notably, Brillouin Microscopy and elastography are among the most detailed and most advanced techniques with strong scientific evidence of their ability to map corneal stiffness in 3D.Other ex-vivo tests, and ‘quantification and mapping’ of the behaviour of individual corneas measured in vivo, is allowing us to move into treatment optimisation for the first time. This area is the ultimate goal of all our previous efforts as a research community over the last 25 years. And it is exciting because now the target is to benefit patients, rather than to develop methods or understand behaviour. Several applications in which clinicians have had to rely on experience can now be optimised on a scientific basis and with reference to accurate measurements of corneal biomechanics in vivo. These applications include the optimisation of the crosslinking treatment used in patients with keratoconus, customisation of the intracorneal ring segment surgeries used to restore the healthy geometry in irregular corneas, and the incisions used in cataract surgeries which may have an effect on corneal astigmatism.As we now move into the second quarter of the 21st century, the wealth of knowledge on ‘trends’ of corneal behaviour identified in These applications and others are expected to provide bright examples of how corneal biomechanics can really benefit clinical practice over the next few years. So, watch the space!


Extracting circle information from images has always been a basic problem in computer vision. Common circle detection algorithms have some defects, such as poor noise resistance and slow computation speed. In this paper, we propose an anti-noise fast circle detection algorithm. In order to improve the anti-noise of the algorithm, we first perform curve thinning and connection on the image after edge extraction, then suppress noise interference by the irregularity of noise edges and extract circular arcs by directional filtering. In order to reduce the invalid fitting and speed up the running speed, we propose a circle fitting algorithm with five quadrants, and improve the efficiency of the algorithm by the idea of “divide and conquer”. We compare the algorithm with RCD, CACD, WANG and AS on two open datasets. The results show that we have the best performance under noise while keeping the speed of the algorithm. Images are the basis of human understanding of the world. Accurate and stable acquisition of image information has always been one of the basic problems of computer vision. As one of the most common graphics in daily life, circles often contain a lot of information. How to detect circles in images quickly and stably has always been a difficult and important point in computer vision. At present, circle detection is widely used in borehole detection , glass bHough transform  (HT) is The first is a circle detection algorithm based on random sampling, which usually obtains the parameters of candidate circles by random sampling. It only needs one correct sampling to find the true circle, and it is often robust. However, this kind of algorithm needs massive iteration and takes a lot of time. The random Hough transform (RHT) algorithm proposed by Xu et al.  is a claAnother is contour-based circle detection algorithm, which usually connects edge points into curves and then obtains circle parameters by analyzing the information of the curves. Such methods tend to detect more accurately and run faster. However, these algorithms rely on the results of edge extraction and often have poor performance for images with a large number of edge curves crossing each other or with noise. Le et al.  used a sIn general, the random sampling-based circle detection algorithm is time-consuming, while the contour-based circle detection algorithm relies on the edge detection results and is sensitive to noise. Aiming at these two problems, this paper proposes an anti-noise fast circle detection method using five-quadrant segmentation. While improving the accuracy and speed of the circle detection algorithm, the algorithm can maintain good performance under the interference of Gaussian noise. We first perform curve thinning and connection on the image after edge extraction, then suppress noise interference by the irregularity of noise edges and propose circular arcs by directional filtering, then we classify and fit the circular arcs using the five-quadrant segmentation method, and the final true circle is obtained according to the coincidence relationship between the circle and the arc and the average sampling result. The experimental results show that our method has the advantages of high speed, strong noise immunity and high accuracy.(1)We propose a noise suppression algorithm and an arc segmentation algorithm, which can suppress the interference of noise while preserving the arc.(2)We use a five-quadrant segmentation least-squares circle fitting algorithm, which avoids many invalid fittings, and is verified by the coincidence ratio.The contributions of this paper are as follows:The structure of the rest of this paper is as follows: Our method mainly includes three steps of image preprocessing, noise suppression and arc segmentation, and circle detection. The function of image preprocessing is mainly to extract edge points and connect them into arcs. The function of suppressing noise interference and arc segmentation is to exclude noise curves and divide the curves into arc segments. The process of circle detection is to fit arcs and find the true circle.First we use a 5 × 5 median filter to reduce interference. Then the adaptive canny  edge extThe thickness of the curve affects arc segmentation and may lead to duplicate detections. First, the method in the literature  is used Then connect all adjacent edge points into curves. Note that curves with a length less than 15 will be deleted. The final extracted curve format is as follows:Under noise interference, the canny algorithm will detect many interference edges. First, we perform a least squares arc fitting on curve L (Equation ) to apprAlthough the curve obtained by the above steps reduces the interference of a part of the noise, there are still some curves that do not belong to the same circle connected together, which leads to an error in fitting, as shown in the In order to reduce the ineffective arc fitting and speed up the fitting, we use the five-quadrant segmentation method to classify the arc. The entire image region is divided into five regions, with the image center as the axis origin. For the arc On the basis of Among them, The spliced arc is then fitted to the circle parameters  using least squares, and the points on the arc are first verified, where one of the following conditions is met. It is considered as an error detection, otherwise it is a candidate circle:According to the method of the Refs. ,20, the We sampled to select true circles in the set of candidate circles. The sampling point coordinates can be calculated using the following formula:Step 1.Input a picture and perform 5 × 5 Median filtering on it;Step 2.Adaptive Canny edge extraction is used to obtain edge point information;Step 3.The edge point information is contoured to remove redundant edge points. The thinned edge points are connected into curves;Step 4.Direction filtering of curves is used to suppress noise;Step 5.A circular arc that divides a curve into segments;Step 6.The arc is divided into five quadrants according to the position relationship between the arc and the center of the circle;Step 7.Least squares circle fitting of circular arcs is performed within five quadrants. The set of candidate circles is found;Step 8.Remove duplicate circles from candidate circles;Step 9.Find the true circle in the candidate circle and mark it.This section shows the flow of our proposed circle detection algorithm. Our proposed circle detection algorithm can be described as follows:In this section, we compare the proposed algorithm with five other algorithms. The first one is the random circle detection algorithm (RCD) proposed by Chen et al. . We set We refer to the verification method ,24,25,26The test images in this paper were mainly from two Internet public datasets:Dataset GH. This complex world dataset from the Ref.  consistsDataset MY. This complex world dataset comes from the Ref. , which cTo test the performance of each algorithm under different levels of noise, we selected an image with a clear background and a circle consisting of strong edge points and weak edge points at the same time. The following We describe the performance of different algorithms under Gaussian noise in It can be seen from To test the stability of the algorithm, we selected two public datasets to test the algorithm. The following The recall rates of RCD and Wang’s algorithms have always been stable, because the random circle detection algorithm will hardly be affected by noise when randomly selecting points to calculate circle parameters. However, with the increase in noise, their accuracy and F-measure decrease rapidly. The CACD and AS algorithms can maintain good performance without noise interference, but when the noise increases, the performance drops rapidly. When the variance is 0.04, their F-measures are reduced to 48% and 44% on GH and 46% and 14% on MY, respectively. Additionally, when the noise of the CACD algorithm increases, the running time of the program will also increase greatly. In contrast, the running time of the AS algorithm decreases as the noise increases, because the AS algorithm cannot detect arcs in the case of high noise. Our algorithm achieves the best results on both data sets. As the noise increases, other algorithms gradually lose their detection ability, while our algorithm can still maintain high performance.The following From the results in Based on our understanding of circle inspection, we will strive to apply this method to industrial practice areas in the future, such as inspection of PCB boards and Borehole detection.


To explore the clinical value of the Gleason score upgrading (GSU) prediction model after radical prostatectomy (RP) based on a Bayesian network.The data of 356 patients who underwent prostate biopsy and RP in our hospital from January 2018 to May 2021 were retrospectively analysed. Fourteen risk factors, including age, body mass index (BMI), total prostate-specific antigen (tPSA), prostate volume, total prostate-specific antigen density (PSAD), the number and proportion of positive biopsy cores, PI-RADS score, clinical stage and postoperative pathological characteristics, were included in the analysis. Data were used to establish a prediction model for Gleason score elevation based on the tree augmented naive (TAN) Bayesian algorithm. Moreover, the Bayesia Lab validation function was used to calculate the importance of polymorphic Birnbaum according to the results of the posterior analysis and to obtain the importance of each risk factor.In the overall cohort, 110 patients (30.89%) had GSU. Based on all of the risk factors that were included in this study, the AUC of the model was 81.06%, and the accuracy was 76.64%. The importance ranking results showed that lymphatic metastasis, the number of positive biopsy cores, ISUP stage and PI-RADS score were the top four influencing factors for GSU after RP.The prediction model of GSU after RP based on a Bayesian network has high accuracy and can more accurately evaluate the Gleason score of prostate biopsy specimens and guide treatment decisions.The online version contains supplementary material available at 10.1186/s12894-023-01330-6. Prostate cancer is one of the most common malignant tumours of the genitourinary system in elderly men. Its incidence ranks second in the global male cancer incidence spectrum, and its incidence in China is increasing yearly , 2. ProsBayesian theory is a statistical theory corresponding to classical statistics that introduces prior information on the basis of sample information and synthetically investigates the two aspects of information to make inferences about the population. The structure of the Bayesian network is a directed acyclic graph, which can present the joint probability density between high-dimensional variables. The TAN Bayesian network (Tree-Augmented Nave Bayesian network) is an extension of the classical Bayesian network model that can address correlated variables and has good predictive ability for high-dimensional data. Bayesian networks have been widely used in medicine, such as in survival models, infectious disease models, decision analysis and gene network analysis –8. ThereA total of 573 patients with prostate cancer underwent radical prostatectomy (RP) in our centre from January 2018 to May 2021.The inclusion criteria were as follows: (1) both prostate biopsy and RP were performed in our centre; (2) the interval between biopsy and RP was less than 60 days; and (3) detailed clinical and pathological data were available.The exclusion criteria were as follows: (1) patients who had a history of radiotherapy and endocrine therapy before RP; and (2) patients who had a history of prostate surgery before RP.A total of 356 patients were included in this study.All patients underwent transperineal standard systematic 12-core biopsy and cognitive MRI/US fusion targeted biopsy. A minimum of two cores were taken for each targeted lesion, followed by a standard 12-core biopsy. The biopsy was performed by senior urologists who had passed the learning curve of the procedure, and the examinations and diagnoses of postoperative pathological specimens were completed by two pathologists with senior professional titles. The Gleason score was scored according to the 2014 International Society of Urological Pathology (ISUP) consensus conference on Gleason grading of prostate cancer. The mpMRI protocol followed the Prostate Imaging Reporting & Data System (PI-RADS) guidelines with T2-weighted, diffusion-weighted, and dynamic contrast-enhanced sequences. The PI-RADS score was assigned by senior radiologists with subspecialist experience in prostate MRI.We defined the GSU as follows: (1) the total GS score of the specimen after RP was greater than that of the biopsy specimen; and (2) the Gleason score changed from 3 + 4 at biopsy to 4 + 3 after RP.We analysed clinical data, including age, body mass index (BMI), total prostate-specific antigen (tPSA), prostate volume, total prostate-specific antigen density (PSAD), clinical stage, pathological characteristics of the biopsy specimen, PI-RADS score and pathological characteristics after RP. The abovementioned indicators were selected with reference to a previous study on the analysis of risk factors for GSU –12. All To evaluate the performance of the model more accurately, a stratified sampling strategy was used to split the dataset into a training dataset and a test dataset. 70%  of the patients were used as the training dataset to establish the model by using the tree-augmented naive Bayes (TAN) algorithm, and the remaining 30% (107 cases) of the patients were used as the test dataset to test the model. The reliability and precision in the confusion matrix were expressed as percentages, and the receiver operating characteristic curve (ROC curve) was plotted by locking the target. All of the abovementioned variables were included, and Bayesia Lab software was used to establish a prediction model based on the TAN algorithm. The confusion matrix, ROC curve and area under the curve (AUC) were used to evaluate the quality of the model. A larger confusion matrix corresponded to a higher accuracy of the model. Moreover, a larger AUC value corresponded to a higher accuracy of the model. After evaluating the accuracy of the model, the Bayesia Lab software was used to perform a priori analysis of 14 variables and a posterior analysis with GSU as the target variable and the remaining factors as the attribute variables. The results of the posterior analysis combined with the polymorphic Birnbaum importance calculation were used to calculate the importance ranking of the attribute variables.A total of 110 patients (30.89%) had Gleason score upgrades. All of the factors in Table The confusion matrix is shown in Table Based on the Bayesian network model, the Bayesia Lab analysis verification function was used to perform prior probability statistics, posterior analysis, importance calculation and ranking of the influencing factors of the GSU Table . The resThe Gleason score that was obtained via prostate biopsy is an important basis for evaluating cancer risk before surgery and making treatment plans. When considering patients who choose active surveillance, the pathological information obtained by biopsy is an important method to assist clinical decision-making . Needle In recent years, prediction models based on big data and artificial intelligence have become a hot spot in clinical research. Previous prediction models for GSU are mostly constructed by using nomogram models; however, due to different risk factors included in different studies, the AUC and accuracy of the prediction models can vary considerably. The accuracy of the nomogram model constructed by Wang  based onIn addition, with the progress of clinical research in recent years, an increasing number of factors have been confirmed to be related to GSU, such as the ratio of positive puncture cores, PSAD and PI-RADS score. The nomogram model only includes independent predictors, and when the nomogram model contains too many predictors, it is easy to fit, which is likely to lead to the failure of the prediction model.Bayesian networks are an effective tool that combines probability theory and graph theory to address uncertainty reasoning and data analysis. It can analyse the problem structure according to the principle of probability theory to reduce the complexity of reasoning and calculation. Moreover, the TAN Bayesian network is an extension of the classical Bayesian network model that can address correlated variables and has good prediction ability for high-dimensional data . In receWe included 14 relevant variables to construct the TAN Bayesian model, thus resulting in an AUC of 82.25%. Moreover, the confusion matrix analysis showed that the accuracy of the Bayesian prediction model was 77.57%, which has a good prediction effect. This reflects the fact that after more variables are included, the accuracy and prediction performance of the Bayesian model is better than that of the previous nomogram model, enabling improved evaluation of the influence of many preoperative variables on Gleason upgrading. Based on this model, we applied importance theory to calculate the importance ranking of GSU risk factors.The results showed that lymph node metastasis, number of positive puncture needles, ISUP grade and PI-RADS score were the top four predictors of GSU. These results suggest that patients with suspected lymph node metastasis on preoperative imaging are at higher risk of GSU. Prostate cancer with lymph node metastasis may be highly malignant, and tumour tissue with high G may be missed at biopsy. In addition, the number of positive needles is often related to the tumour volume, and studies have shown that an adequate number of needles can improve the consistency of the score and reduce the risk of increasing the score . For patIn addition, the TAN Bayesian network model can depict the conditional dependence network between the dependent variable and the predictor variable and display it in the form of a dendrogram, which is simple and intuitive. Our model showed that seminal vesicle invasion was associated with lymph node metastasis and nerve invasion, which was consistent with the clinical characteristics of advanced patients. Clinical stage was associated with positive surgical margins, which is consistent with previous studies in which more advanced tumours had a higher incidence of positive surgical margins . This suThis study is a preliminary attempt to apply Bayesian networks in the field of prostate cancer; however, there were still some limitations. First, due to the limitations of this study being a single-centre study and the lack of external validation, the predictive effect of the model on different populations is still unclear. In addition, Sheridan  found thThe predictive model of Gleason score upgrade after radical prostatectomy based on the Bayesian network has high predictive power, which is better than that of the previous nomogram model. This study can be used to guide clinicians to evaluate the risk of GSU, obtain a more accurate Gleason score before surgery and select the most appropriate treatment plan for patients.Below is the link to the electronic supplementary material.Supplementary Material 1