Regularization with priors is an effective approach to solve the ill-posed inverse problem of electrical tomography. Entropy priors have been proven to be promising in radiation tomography but have received less attention in the literature of electrical tomography. This work aims to investigate the image reconstruction of capacitively coupled electrical resistance tomography (CCERT) with entropy priors. Four types of entropy priors are introduced, including the image entropy, the projection entropy, the image-projection joint entropy, and the cross-entropy between the measurement projection and the forward projection. Correspondingly, objective functions with the four entropy priors are developed, where the first three are implemented under the maximum entropy strategy and the last one is implemented under the minimum cross-entropy strategy. Linear back-projection is adopted to obtain the initial image. The steepest descent method is utilized to optimize the objective function and obtain the final image. Experimental results show that the four entropy priors are effective in regularization of the ill-posed inverse problem of CCERT to obtain a reasonable solution. Compared with the initial image obtained by linear back projection, all the four entropy priors make sense in improving the image quality. Results also indicate that cross-entropy has the best performance among the four entropy priors in the image reconstruction of CCERT. The gas–liquid two-phase flow widely exists in industries such as the petroleum industry, chemical engineering, and refrigeration systems ,2,3. TheElectrical resistance tomography (ERT) is a visualization technique to reconstruct 2D/3D cross-sectional conductivity distributions by a non-invasive electrode-sensing array ,5,6. DueThe image reconstruction of electrical tomography (ET) is a highly underdetermined and ill-posed inverse problem, as is CCERT ,11,12. TEntropy priors have been proven to be promising in reconstructing positive images from limited and noisy data ,21,22,23This work aims to investigate the regularization-based image reconstruction performance of CCERT with entropy priors. Under the maximum entropy (ME) strategy, three entropy priors, including the image entropy, the projection entropy, and the image-projection joint entropy, are introduced. Under the minimum cross-entropy (MCE) principle, the cross-entropy between the measured projection and the forward projection is introduced. The four entropy priors are used as the regularization terms to develop four corresponding objective functions. To solve the optimization problems expressed by the objective functions, linear back projection (LBP) is adopted to obtain the initial image and the steepest descent method is used to obtain the final image. Image reconstruction experiments will be carried out to verify the effectiveness of the four entropy priors in the image reconstruction of CCERT. The imaging performance of CCERT with the four entropy priors will be compared and discussed.The rest of this article is organized as follows. As mentioned, CCERT is a contactless technique. According to the capacitive coupling principle, for each electrode, a capacitance will be formed by the electrode, the insulation pipe, and the conductive fluid. When a measurement electrode pair, including an excitation electrode and a detection electrode, is selected, a measurement path will be formed by two coupling capacitances and the equivalent resistance of the fluid between the two electrodes. According to the Maxwell’s equations, the field of the sensor can be modeled asAccording to the typical measurement strategy of CCERT, two electrodes are selected as the excitation electrode and the detection electrode respectively, and the rest electrodes are at floating potential. The boundary conditions of Equation (1) areCCERT includes two major computational problems, the forward problem and the inverse problem. The forward problem is to determine the inter-electrode resistances from the conductivity distribution in the sensing area satisfying Equations (1) and (2). The inverse problem is to determine the conductivity distribution from the resistance measurements in the form of a visual image, i.e., the image reconstruction. Therefore, the image reconstruction corresponds to solving the following inverse problemIn detail, the The sensitivity matrix is also known as the Jacobian matrix, which is the sensitivity of the resistance measurement to the conductivity change of the sensing area. Here, the sensitivity matrix is calculated by simulation based on the finite element method (FEM). The software ‘COMSOL Multiphysics’ and ‘MATLAB’ are used to implement the simulation. The sensitivity of the As mentioned, the number of unknown variables A common method to solve Equation (3), i.e., Equation (6) in the real case, is to find the Regularization provides an approach to solve the ill-posed problem and determine the solution from a constraint set of solutions using a priori information. By introducing regularization, the objective function becomesEntropy is used to measure the uncertainty of information in Shannon’s theory, which has many properties that agree with the intuitive principles of what a measure of information should be. Generally, higher entropy means more information. Therefore, maximum entropy (ME) is a potential strategy to improve the image quality. Cross-entropy is a measure of the dissimilarity between two data sets. Smaller cross-entropy means higher similarity between two datasets. In this way, minimum cross-entropy (MCE) provides another approach to the search for a better image result. To study the application of entropy regularization in CCERT, the above ME and MCE strategies are introduced to develop the regularization term According to Shannon’s theory, the entropy To maximize entropy (1)Maximum Image Entropy (MIE)Image entropy is a good choice of a priori information for image reconstruction, which is a measure of the amount of information contained in an image. According to the maximum entropy principle, the larger the image entropy is, the more information in the image is predicted. The image entropy is defined asLet (2)Maximum Projection Entropy (MPE)The quality of the reconstructed image also reflects on the quality of its forward projection. Thus, maximizing the projection entropy is also reasonable. Considering the forward process according to Equation (3), each predicted image Let (3)Maximum Joint Entropy (MJE)The joint entropy Referring to the chain principle in entropy, thenThus, the joint entropy of the predicted image and its forward projection can be introduced as a combination of the image entropy and the projection entropy, which can be calculated byLet Cross-entropy evaluates the dissimilarity between two data sets. Larger cross-entropy means a greater degree of dissimilarity between the two data sets. In radiation tomography for biomedical applications, the minimization of the cross-entropy between the current estimate of the reconstructed image and the anatomical a priori images are used to guide the image reconstruction. In this work, for gas–liquid two-phase flow, the dissimilarity between the practical projection set from the resistance measurements Let Similarly, by minimizing the above equation, the estimated solution with minimum cross-entropy constraint can be obtained.With the four objective functions in Equations (12), (14), (18) and (20), an estimated image Let the number of iterations Calculate the gradient Determine the step length by linear searching as Calculate the new image vector Calculate the new gradient Update the iteration direction as Set Optimization problems widely exist in engineering technologies, and finding the optimal solution is always the goal for researchers and engineers. Research works have been undertaken to seek effective optimization methods, and great achievements have been obtained. Currently, there are many useful methods to solve the nonlinear optimization problem ,37, suchHere, the termination conditions are:(1)(2)(3)where the termination coefficients are set as The initial value of the solution is important in optimization. Here, the initial image With the initial image obtained by LBP, the final image is reconstructed by the iterations of the steepest descent method.To evaluate the quality of the reconstructed image, relative image error (RIE) and image correlation coefficient (ICC) are introduced, which are commonly used in the literature of ET ,39,40. Tl2-norm smooth constraint, where the typical form of Tikhonov regularization algorithm is a typical representative in the regularization-based reconstruction family. Therefore, it is used for comparison in this work. Tikhonov regularization includes a As can be seen in Among the three ME priors, the two priors derived from projection entropy (MPE and MJE) are good at obviating the artifact and keeping relative clear boundaries of the targets. Compared with the three ME priors, the MCE prior shows a better trade-off between removing the artifact and recovering the size of targets. The MCE prior performs better than the ME priors in the reconstruction of S1 and S3, as shown in This work investigates the image reconstruction of CCERT by introducing entropy priors as the regularization terms. Four types of entropy priors  are introduced. By developing the objective function for each entropy prior, the combination of LBP and the steepest descent method is adopted to optimize the objective function. Experiments are carried out and the performances of the four entropy priors are compared.Results show that all the images reconstructed by the four entropy priors are in accord with the ground truth. Compared with the initial image obtained by LBP, regularization with the entropy priors is an effective way to improve the image quality. Among the four entropy priors, the MCE prior has the overall best performance in the trade-off between eliminating the artifact and recovering the size of the targets, while the MIE prior has the poorest performance. MPE and MJE behave the best in eliminating artifacts, but struggle with keeping the size of the reconstructed targets. It is found that these two priors have good performance in reconstructing the target close to the low-sensitivity center of the sensing area.New knowledge and experience have been obtained in this investigation which can provide useful references for further research work. Although the research results show the potential of entropy priors in the image reconstruction of CCERT, the imaging performance of the entropy priors have no advantage over that of the classical Tikhonov regularization. There is still much space for progress in future research on seeking more effective a priori information to take advantage of entropy. For industrial multi-phase flow, if other prior information can be incorporated into the entropy prior, such as dynamic modelling data obtained by simulation or good-quality multi-frequency images obtained by the CCERT system, the informatic nature of entropy is thought to make more sense.


In this study, we present an IoT-based robot for wrist rehabilitation with a new protocol for determining the state of injured muscles as well as providing dynamic model parameters. In this model, the torque produced by the robot and the torque provided by the patient are determined and updated taking into consideration the constraints of fatigue. Indeed, in the proposed control architecture based on the EMG signal extraction, a fuzzy classifier was designed and implemented to estimate muscle fatigue. Based on this estimation, the patient’s torque is updated during the rehabilitation session. The first step of this protocol consists of calculating the subject-related parameters. This concerns axis offset, inertial parameters, passive stiffness, and passive damping. The second step is to determine the remaining component of the wrist model, including the interaction torque. The subject must perform the desired movements providing the torque necessary to move the robot in the desired direction. In this case, the robot applies a resistive torque to calculate the torque produced by the patient. After that, the protocol considers the patient and the robot as active and all exercises are performed accordingly. The developed robotics-based solution, including the proposed protocol, was tested on three subjects and showed promising results. Stroke is considered to be one of the leading causes of death worldwide, according to the World Health Organization. Indeed, each year, more than 15 million people in the world are victims of a stroke ,3,4,5,6.The mechanical structure was designed by considering the anatomical constraints of the wrist movements presented in The model contains five main blocks. Each block is described with its elementary components in Unlike similar solutions, the robot is powered by a single motor performing the two main degrees of freedom (DOF) of the wrist joint. We offer a new solution providing 2 DOF using a single motor to power the joint instead of double motors. Based on a flexible mechanical transformation, the robot ensures the two fundamental movements of the wrist: abduction/adduction and flexion/extension. In fact, the hand support part can be reconfigured moving from the horizontal position (producing the abduction/adduction derivation) to the vertical position (producing the flexion/extension derivation). Indeed, the current state, presented in In this section, we present a mathematical model of wrist rotation dynamics in the two fundamental DOF, evaluating the torques required for wrist rotations, and determining the relative importance of various model terms and parameters in order to develop a complete model useful for rehabilitation exercises. The model is evaluated using experimentally observed passive wrist movements imposed by a rehabilitation robot to define the dynamics of wrist rotations. It is worth noting that stiffness, not inertia, dominates wrist rotation dynamics and that, unlike the arm, the wrist DOF are linked by stiffness rather than inertia. We show that the equations of motion are accurately approximated as linear for moderately sized wrist rotations, implying that a very basic internal model could offer a sufficiently accurate estimate of the torques required to govern wrist rotations in rehabilitation exercises.β, and radial–ulnar deviation occurs about the rotated x axis and is represented by γ. A number of torques are applied to the hand when the wrist rotates. Muscle contraction produces active torques. Here, we present them as a group and resolve them  along the flexion/extension (FE) and radial/ulnar derivation (RUD) axes  axes . Passiveβ, and radial–ulnar deviation occurs about the rotated x axis and is represented by γ.The body-fixed XYZ frame is fixed in the hand  and rotates with the hand. Flexion–extension occurs about the Z axis and is represented by The equations of motion of a universal joint with non-intersecting axes, subject to the abovementioned torques, are as follows :Tβ=TinerFE and RUD are represented by In each equation, the first term is called the main torque and the second term is called the interaction torque since it depends on the movement of the other degrees of freedom , frequency domain (FD), and time-frequency or timescale (TS) representation are the primary aspects in an EMG signal analysis . Signal Frequency or spectral domain characteristics are commonly utilized to investigate muscle fatigue and MU recruitment. In the frequency domain, power spectral density (PSD) becomes an important analysis. In this part, four frequency-domain feature extraction methods are used as inputs for the fuzzy classifier including the mean frequency, mean power, frequency ratio, and power spectrum ratio. MNF) is an average frequency computed by dividing the whole sum of the spectrum intensity by the product of the EMG power spectrum and the frequency [j, j, and M is length of the frequency bin.Mean frequency (requency . It can MNP) is an average power of the EMG power spectrum. The calculation is defined as:Mean power (FR) is proposed to distinguish between contraction and relaxation of muscle using the ratio between the low frequency components and the high frequency components of the EMG signal [ULC and LLC are the low-frequency band’s upper and lower cutoff frequencies, respectively; and UHC and LHC are the high-frequency band’s upper and lower cutoff frequencies, respectively. There are two techniques to determine the threshold for separating low and high frequencies. The frequency bands are first determined by experiments. The high and low frequency bands can also be set using the MNF feature value [The frequency ratio  is a variation of the PKF and FR characteristics [P0, which is close to the EMG power spectrum’s greatest value, and the energy P, which is the EMG power spectrum’s total energy. Its formula can be expressed as:n is the integral limit. The power spectrum ratio  to evaluate the rehabilitation state level and (2) to extract the main components of the wrist dynamic model.The physiotherapist starts the control procedure by entering the desired settings. The needed parameters are transmitted to the advanced controller block implemented in the LabVIEW-based HMI after the appropriate processing. The wrist robot receives the computed parameters, including the needed torque and desired position, through the MQTT protocol. The sb-RIO board processes the data from the current sensor, EMG sensor, and encoder before sending it back to the control station over the MQTT protocol. Then, the extracted frequential characteristics from the collected EMG rows are used to estimate muscle fatigue using extraction techniques. The EMG characteristics are sent into the fuzzy system, which estimates the patient’s fatigue. The control motion block uses position feedback to make the proper choice. The settings and the results are recorded in the database. The real-time component of the MQTT protocol is the most essential feature that truly differentiates it; a requirement that eliminates delay issues. To avoid disruptions caused by the increased demand for data interchange, network usage must be kept to a minimum. The MQTT protocol reduced the size of data packets, allowing the network to be used more efficiently and avoiding network disruptions caused by heavy data demand. A message dispatcher is the MQTT central server . This server allows IoT devices to subscribe to or publish messages. Topics are subscribed to and published by the devices. As indicated in The designed robot is light, practical, and user-friendly, making it an excellent choice for at-home rehabilitation. The fact that it is managed remotely by a physiotherapist makes it simpler for the patient, who has no involvement in the device’s operation. In reality, the patient is usually unable to accomplish anything after a stroke and is frequently inactive. This newly created device has a user-friendly HMI with two separate control displays. The first display serves as a configuration and supervision tool . The intBefore beginning, the physiotherapist must input the wrist initial parameters of a related patient including hand length, forearm length and hand mass . Noting The next step consists of measuring the wrist passive components a by launAfter finalizing the passive component measurements, the next step consists of measuring the active components of the wrist joint b. In thiThe second screen of the user interface presents the data storage and reporting interface. This screen provides some features that allow the physiotherapist to add a new subject a, to savThree participants, all with a wrist fracture, were tested just one week after their casts were removed. For ten days, the individuals undertook a comprehensive rehabilitation program to recover their abduction/adduction origin. A physiotherapist was in charge of the exercise, which started when the wrist model parameters were extracted. The exercise was performed three times for a total of 12 sets. The physiotherapist’s instructions were followed by the connected robot. The first tests on the three participants revealed that they had lost around 66 percent of their typical wrist RoM.Subject 1 was received on 12 February 2021, as shown in Rehabilitation performances also include reducing passive stiffness and increasing the produced active torque. Patient 1 reduced passive stiffness from 0.26 Nm to 0.21 Nm. on the other hand, and he showed good ability to produce more active torque starting from 0.93 Nm to 1.27 Nm, achieved on the last day. Likewise, Patient 2 was received on 27 February 2021 and he underwent the same protocol. He completed his last session with a RoM of 62 degrees and a RPF of 6.8:10, as shown in The development of rehabilitation robotics has made significant progress over the past few decades. By using technological engineering solutions, specialists hope to promote the recovery of functions. In this context, here, we proposed a remote-controlled wrist rehabilitation robot. A new protocol based on three steps was proposed to identify wrist health status and dynamic parameters of the human–robot interaction. Fatigue during the rehabilitation session has a direct impact on the torque produced by a patient. The proposed approach takes this constraint into account and integrates a fuzzy logic controller to estimate the degree of fatigue and update the estimated torque value accordingly. A human–machine interface was developed to control the robotic solution and to provide database space for storage and reporting. Tests were carried out on three different patients and showed encouraging results. The next steps involve moving to clinical trials by testing the designed platform on more subjects. In the future, the modeling of a human wrist joint will be optimized by integrating machine learning techniques for more reliability of the model parameters.


The neural network method can obtain a higher precision of radar echo extrapolation than the traditional method. However, its application in radar echo extrapolation is still in the initial stage of exploration, and there is still much room for improvement in the extrapolation accuracy. To improve the utilization of radar echo information and extrapolation accuracy, this paper proposes a radar echo extrapolation model (ADC_Net) based on dilated convolution and attention convolution. In this model, dilated convolution, instead of the pooling operation, is used to downsample the feature matrix obtained after the standard convolution operation. In doing so, the internal data structure of the feature matrix is retained, and the spatial features of radar echo data from different scales are extracted as well. Besides, the attention convolution module is integrated in the ADC_Net model to improve its sensitivity to the target features in the feature matrix and suppress the interference information. The proposed model is tested in the extrapolation of radar echo images in the next 90 min from five aspects—extrapolated image, POD index, CSI index, FAR index, and HSS index. The experimental results show that the model can effectively improve the accuracy of radar echo extrapolation. Accurate short-term nowcasting has attracted much attention in the field of meteorological services. Its goal is to accurately and timely predict the local weather in the next 0 to 2 h, enabling weather stations to issue Urban Emergency Disaster Alerts in time. There are three main methods of nowcasting—radar echo extrapolation method, weather situation analysis and forecast method, and comprehensive analysis method, which is the most accurate and widely used method. However, the accuracy of comprehensive analysis method is based on the accuracy of the radar echo extrapolation method. Therefore, the research on the radar echo extrapolation plays a significant role in the forecast and prevention of severe weather.Nowcasting was first proposed by Browning2. The Strom cell identification and tracking (SCIT)3 and optical flow4. TREC divides two consecutive radar echo images at adjacent times into multiple image subsets, calculates the maximum correlation coefficient of different subsets in the two images, and uses the maximum correlation coefficient to determine the optimal matching area, which is the moving position of the image subset. The TREC method is applicable to extrapolation of steadily changing radar echoes, but not for rapidly changing ones, such as radar echoes of convective precipitation clouds5. Based on TREC, Zhang Yaping et al.6 proposed difference image based tracking radar echo by correlations (DITREC), which tracks radar echo motion on the basis of the correlation method of differential images. DITREC can eliminate the disordered vector in the TREC vector field due to the rapid change of echoes, but when using the derived DITREC field to predict the precipitation field, the prediction accuracy depends on the Z-I relationship it adopts8. However, the strong dependence of the Z-I relationship method on a specific climatic background results in the model’s weak generalization ability. Another radar echo extrapolation method, SCIT, calculates the centroid position and volume of the echo monomer, matches the calculated information with the scanned data before and after the echo monomer and track it, and then extrapolates with multiple consecutive moments of the matching and tracking results10. However, SCIT is only applicable to the identification, tracking and nowcasting of thunderstorm monomers11, which limits its application in weather forecasting to a certain extent. The third traditional radar echo extrapolation method, optical flow, finds the corresponding relationship between previous images and the current image by using the change of the target point in the image sequence in the time domain and the correlation between adjacent images. Then the motion information of objects between adjacent images is calculated according to their correspondence. Optical flow obtains the motion vector field of the echo by calculating the optical flow field of the radar echo, and extrapolates the radar echo based on the motion vector field. Different from TREC, the extrapolation of optical flow is based on the changes of radar echoes, rather than the invariant characteristics of the echoes12. As a result, optical flow can better track radar echo movement. The extrapolation ability of optical flow is superior to other extrapolation algorithms, especially in rapidly changing weather conditions. However, natural movement is dynamic, so radar echoes will be split, disappear, merge, etc., which is contradictory to the invariance assumption of the generation and disappearance of radar echoes by optical flow, greatly weakening the extrapolation of optical flow. In general, the traditional radar extrapolation method could only infer the echo position of the next moment according to the extrapolated images of several past radar echoes. It ignores the motion nonlinearity of the small and medium-scale atmospheric systems existing in the radar echoes under actual conditions. Therefore, historical radar echo data have not been used to full advantage.The traditional radar echo extrapolation methods mainly include tracking radar echoes by correlation (TREC)13. The application of neural network in meteorology sheds new light on the radar echo extrapolation method, and some scholars have conducted research in this area. Chen Jiahui et al.14 used BP neural network model to extrapolate radar echoes and demonstrated the effectiveness of neural network in radar echo extrapolation. Guo Hanyang et al.15 used convolutional gated recurrent unit (CGRU) to extrapolate radar echoes and compared them with TREC. The results show that the neural network model has more advantages than traditional methods. Klein16 added a dynamic convolutional layer to the convolutional neural networks (CNNs) structure and achieved accurate prediction of precipitation echoes by generating two prediction probability vectors. Based on Klein’s model17, added recurrent neural network (RNN) to the dynamic convolutional layer and successfully built recurrent dynamic convolutional neural networks (RDCNN). The neural network has achieved good results in both forecast accuracy and forecast timeliness. As traditional long short-term memory (LSTM) cannot extract spatial features, Shi et al.18 replaced the change of LSTM input to state and the change of state to state with convolution in their model and proposed ConvLSTM. To adapt to the spatial–temporal variableness, Shi et al. further improved ConvLSTM in 2017 and proposed TrajGRU19. To adapt to the spatio-temporal dependence of radar echo images, Singh et al.20 added a convolution structure to recurrent neural network and realized the radar-echo-image-sequence-based prediction. Zhang Lei et al.21 proposed an EDP model for sustainable e-agriculture. This weather radar echo prediction method is based on convolution neural network and long short-term memory networks. The results show that the neural network can effectively improve the prediction accuracy and effectiveness. He Liang et al.22 regarded precipitation forecasting as a picture-to-picture conversion problem, and used a U-net-structured convolutional neural network for forecasting. To extrapolate radar echoes, Zhang Dezheng et al.23 improved the model’s ability to represent the details of spatial structure information by deepening the convolutional layers in the neural network, which is composed of CGRUs.With the development of neural network, its powerful modeling ability and unique advantages in big data processing have attracted extensive attention of scholars, and it has been widely used in the field of meteorologyTo sum up, although the application of neural network in radar echo extrapolation is of great significance in utilizing historical radar echo data and improving the accuracy of radar echo extrapolation, the prediction results are still not satisfactory. They could be blurred or distorted, so the prediction accuracy needs to be improved. Therefore, this paper proposes a radar echo prediction model (ADC_Net) based on dilated convolution and attention convolution. To construct small object information and avoid the losing of internal data structure, the model substitutes dilated convolution for pooling in downsampling the feature matrix obtained after convolution. Also, the integration of an attention convolution module with an attention mechanism can improve the model’s sensitivity to target features and suppress interference information, thus enhancing the extrapolation accuracy of radar echoes.The structure of the ADC_Net model based on dilated convolution and attention convolution proposed in this paper is shown in Fig. As elementary building blocks, ADC_Net has nine recurrent convolution modules (RCNN), four dilated convolution (DCNN), four upsampling convolution modules (UPCNN), four attention convolution modules (ACNN), four skip connections, and a 1 * 1 standard convolution layer (cnn). RCNN is the basic module of the model, and its structure is shown in Fig. In the above module, dilated convolution instead of pooling operation is employed to downsample the feature matrix in the model and the attention convolution module is used to improve the model's sensitivity to the target features in the feature matrix and suppress the interference information. As the dilated convolution and the attention convolution module are the two main innovative structures of the ADC_Net model proposed in this paper, they will be illustrated in the following paragraphs.24. To increase the reception field, dilated convolution injects holes on the basis of the convolution map of standard convolution. Therefore, dilation rate, a hyper-parameter, is added to dilated convolution. The hyper-parameter refers to the number of intervals in the kernel, meaning filling the dilation rate-1 zeros in the convolution kernel. Figure Dilated convolution, also known as convolution kernel expansion operation, is a convolution method commonly used in pixel-wise output models25 takes a 3 * 3 convolution kernel as an example to show the difference between standard convolution and dilated convolution in the reception field and output. The dilation rate of dilated convolution is 2; the red part of the two figures on the left is the eigenvalue of the convolution operation with the convolution kernel, and the red part on the right is the output result after convolution.Dilated convolution expands the convolution kernel to the scale of the dilated scale constraint, and fills the area not occupied by the original convolution kernel with zeros. This ensures the exponential expansion of the reception field by dilated convolution without losing resolution or coverage. Therefore, in dilated convolution, the size of the feature matrix before and after convolution is not only related to the convolution kernel, convolution step size, and padding, but also affected by the dilation rate. For standard convolution, the calculation method of the feature matrix size after the convolution layer is shown in Eq. . Here, h4When using a neural network to process images, features are generally extracted through convolution operations in the neural network, and then the convolutional feature matrix is downsampled by a pooling operation to reduce the image scale and increase the reception field. However, the loss of information caused by downsampling in the pooling operation is irreversible, and this irreversible loss of information will cause the loss of the internal data structure of the feature matrix during the training process of the neural network. Usually only the probability of each class needs to be predicted in the classification model, so there is no need to consider the loss of image details caused by the pooling operation. When doing the pixel-level prediction task of radar echo extrapolation, it is necessary to restore the image to the same size as the input image through the upsampling operation, so the problem of irreversible information loss needs to be reconsidered. Therefore, in order t to keep resolution and still expand the receptive field, in this paper, dilated convolution, instead of the pooling operation, is used to downsample the feature matrix obtained after convolution in the model, and the reception field of the convolution kernel is expanded through dilated convolution without losing resolution or coverage. In this way, dilated convolution, together with standard convolution, can not only perform convolution operation on data and extract spatial features from radar echo data from multiple scales, but also retain internal data structure, making data information reconstruction possible, which cannot be realized by pooling operation. This is useful in radar echo extrapolation tasks. On the one hand, a larger reception field makes it possible to better learn the overall change trend of radar echoes, and on the other hand, a higher resolution makes it possible to accurately locate the pixel information of smaller radar echoes.27. The attention mechanism comes from the human visual attention mechanism. Humans usually observe and pay attention to a specific part of a scene according to the needs instead of seeing a scene throughout. Therefore, the essence of the attention mechanism is to filter out important information from a large amount and focus on them. In the neural network, a hidden vector is generated by the input image through convolution operation, activation function and pooling operation. The value of this hidden vector is calculated by referring to itself and several surrounding pixels. As a result, if standard convolution is employed, local information rather than global information will be used to calculate target pixels, which brings limitations to the training of neural networks, as is shown in Fig. 28. In contrast, low-level feature maps have more accurate target location but poor prediction ability and more virtual target information29.The attention mechanism has gradually become a research hotspot and an important part of the neural network structure in recent years. Initially applied to machine translation, now it has been used in image processing and recommendation systemsIn order to solve the above problems, this paper integrates the advantages of high-level feature maps and low-level feature maps. The attention convolution module is added to the ADC_Net neural network model. Considering each pixel in the feature map as a random variable, calculate the weight values of all pixels in the current prediction task, the pixels with high weights are used and the pixels with low weights are ignored in training and prediction. The use of the attention convolution module can effectively suppress the pixel information irrelevant to the current prediction task and enhance the related pixel information. Figure  in Eqs.  and 5)..\documen by Eqs.  and (5).21, so the prediction results are more accurate.To sum up, the application of the attention convolution module can simultaneously learn the advantages of high-level feature maps and low-level feature maps in the process of model training and prediction to achieve the global reference of feature values. According to the weight matrix obtained by referring to the global feature, each pixel of the feature matrix is given different weights. This allows the neural network to focus on the pixel information most relevant to the current task each time, making the neural network use pixel information more efficiently in the process of training and predictionThe data in the experiment are New generation of Doppler weather radar detection data, which are stored in polar coordinates. For the convenience of research, the radar echo data in polar coordinates are first stored in the three-dimensional Cartesian coordinate system by interpolation method. Considering the height of the representative average guided airflow in the troposphere, we select the CAPPI radar echo image at a vertical height of 3KM as the experimental data. In order to reduce the parameters in the training process and improve the training efficiency, the CAPPI images are grayscaled before the experiment. The processed grayscale image is then cropped, keeping a 256 * 256 size area in the center of the image. Because the echoes with areas too small are generally weak and evolve rapidly, they have little guiding significance for forecasting work. In order to avoid the influence of the sample quality on the training results, each radar echo image is screened during the construction of the sample dataset. The cases with the echo area coverage greater than 1/10 in the effective detection range of the radar are selected into the sample data set, and the radar echo range is controlled within the range of 0–70 DBZ. Figure hit shows the times that both the predicted value fake and the real value label are 1, far is the times that the predicted value fake is 1 while the true value label is 0, miss the times the predicted value fake is 0 but the true value label is 1, and cn is the times that both the predicted value fake and the true value label are 0. The calculation formulas of the experimental evaluation indicators POD, FAR, CSI and HSS are shown in Eqs. , false alarm rate (FAR), critical success index (CSI) and Heidke skill score (HSS). POD represents the probability that convective weather is predicted to occur and the prediction is successful. FAR represents the probability that convective weather is predicted to occur but the prediction fails. CSI is the prediction accuracy after weighing successful predications and wrong predications. HSS is a quantitative evaluation of the model after comprehensively considering various situations. Therefore, the higher the value of POD, CSI and HSS is, and the lower the value of FAR is, the more accurate the predicted result is, and the better the model effect is. Since strong convective weather usually occurs when the radar echo intensity is greater than 35DBZ, the threshold of the radar echo is set to 35DBZ in this experiment. The real label radar echo image and the predicted radar echo image are binarized respectively, with the pixels larger than 35DBZ in the radar echo image binarized to 1, and the pixels smaller than 35DBZ binarized to 0. When evaluating the experimental results, the binarized pixel value of the real image is named label, and the binarized pixel value of the predicted image is named fake,  in Eqs. , 7), , where s and y represent the predicted value and the true value, respectively. In the process of neural network training, the smaller the loss function value is, the more robust the model is. The prediction effect of the model can be measured through the definition and optimization of the loss function. In model training, considering that the use of the MSE loss function alone may cause a small loss value and result in a poor model training effect, the use of MAE alone may lead to the loss of data feature details. Therefore, in this paper, MSE + MAE is used as the loss function, which is conducive to the convergence of the function. Even if the learning factor is fixed, the function can quickly obtain the minimum value. The loss function of the proposed model is shown in Eq. .10\documDuring the training and testing of the neural network, the choice of different optimizers will impact the prediction results differently. In this paper, Adam is used as the optimizer. Integrating the advantages of the two optimization algorithms AdaGrad and RMSProp, Adam calculates the update step size by considering the First Moment Estimation of the gradient (the mean of the gradient) and the Second Moment Estimation (the uncentered variance of the gradient). Its advantages include easy operation, high computational efficiency, and parameter updates immune to the scaling transformation of gradients. Also, because of the good interpretability of Adam hyperparameters and little or no need for parameter adjustment, it is applicable to large-scale data and parameter scenarios. In this experiment, the initial learning rate of Adam is set to 0.0001.The language used in this experiment is Python, and the Pytorch framework is used for training on NVIDIA 2488 GPU. To evaluate the performance of the ADC_Net model based on dilated convolution and attentional convolution (ADC_Net) proposed in the paper, it is compared with the ADC_Net model based on dilated convolution (ADC_Net2), the ADC_Net model based on attention convolution module (ADC_Net3), the ADC_Net model based neither on dilated convolution nor on attentional convolution module (ADC_Net4), U_Net, EDP model, and ConvLSTM.Figure Tables This part compares the single training time and model parameters of ADC_Net model based on the ADC_Net model based on dilated convolution and attention convolution (ADC_Net), the ADC_Net model based on dilated convolution (ADC_Net2), the ADC_Net model based on attention convolution module (ADC_Net3), the ADC_Net model based neither on dilated convolution nor on attentional convolution module ADC_Net4) and U_Net, EDP model, ConvLSTM. The details are shown in Table  and U_NeThis paper proposes a radar echo extrapolation model (ADC_Net) based on dilated convolution and attention mechanism. Using dilated convolution instead of pooling operation can not only perform spatial feature extraction on radar echo data from multiple scales, but also preserve the internal data structure. It avoids the loss of the internal data structure in pooling and makes reconstruction of small object information possible. Also, by integrating an attention convolution module with attention mechanism into the model, the sensitivity to the target features is improved, and the interference information is suppressed, thereby improving the extrapolation accuracy of radar echoes. The radar echo extrapolation results of the ADC_Net model based on dilated convolution and attentional convolution (ADC_Net) proposed in the paper is compared with that of the ADC_Net model based on dilated convolution (ADC_Net2), the ADC_Net model based on attention convolution module (ADC_Net3), the ADC_Net model based neither on dilated convolution nor on attentional convolution module (ADC_Net4) and U_Net, EDP model, ConvLSTM. The results show that the proposed model has better prediction performance. Through comparative model experiments, it is found that combining dilated convolution with the attention convolution module can not only improve the prediction performance of the model, but also achieve better results than using dilated convolution or the attention convolution module alone. And through the use of the attention convolution module, the parameters and running time added by dilated convolution to the ADC_Net model can be reduced to a certain extent, and the running efficiency can be improved.Supplementary Information.


One major concern regarding multi-material additive manufacturing (MMAM) is the strength at the interface between materials. Based on the observation of how nature puts materials together, this paper hypothesizes that overlapping and interlacing materials with each other enhance the interface bonding strength. To test this hypothesis, this research develops a new slicing framework that can efficiently identify the multi-material regions and develop interlaced infills. Based on a ray-tracing technology, we develop layered depth material images (LDMI) to process the material information of digital models for toolpath planning. Each sample point in the LDMI has an associated material and geometric properties that are used to recover the material distribution in each slice. With this material distribution, this work generates an interlocking joint and an interlacing infill in the regions with multiple materials. The experiments include comparisons between similar materials and different materials. Tensile tests have shown that our proposed infill outperforms the interlocking joint in all cases. Fractures occur even outside the interlacing area, meaning that the joint is at least as strong as the materials. The experimental results verify the enhancement of interface strength by overlapping and interlacing materials. In addition, existing computational tools have limitations in full use of material information. To the best of our knowledge, this is the first time a slicer can process overlapped material regions and create interlacing infills. The interlacing infills improve the bonding strength, making the interface no longer the weakest area. This enables MMAM to fabricate truly functional parts. In addition, the new LDMI framework has rich information on geometry and material, and it allows future research in multi-material modeling. Additive manufacturing (AM) technologies use a layer-by-layer stacking method to produce three-dimensional 3D) structures from input geometry. Since their introduction over 30 years ago, AM systems have become more popular in many applications. These applications have ranged from conventional products to complex design models. The geometric freedom and the freeform manufacturing technology enable the fabrication of complex structures with accurate material deposition capability at the specified positions defined in the design domain or the computer-aided design (CAD) model. Research advances in AM and the availability of new materials have unlocked a new world of endless possibilities with customization and led to complex multi-material structures ,2. A mulD structuPrinting discrete multi-material objects is a technically difficult but economically favorable process, as it provides additional functionality and flexibility . With muWe make an observation that humans often intertwine materials to strengthen a product, e.g., manufacturing of composites  and jute1.Developing a new, complete LDMI framework to generate interlacing infills from a multi-material CAD model. The infills are also interlacing across layers.2.Verifying that the interlacing also works for materials with distinct properties.3.Finding out the required amount of overlapping to achieve the optimal bond strength.This technology gap shows that the current computer-aided manufacturing (CAM) tools cannot make full use of material properties for MMAM. Therefore, we have to develop an advanced computational tool to process multi-material models. This paper employs a ray representation—layered depth images (LDI) , which iThis paper primarily focuses on the FFF technology and generates toolpaths as the result. The experimental results shown that interlacing infills is an effective approach to improve interface bond strength to be as strong as the materials, for both similar and distinct materials.The rest of the paper is as follows. This section reviews the related topics in MMAM, including the processes, process planning, and interface modeling.There are various MMAM technologies , and eacToday, researchers are contributing significantly to the development of CAD strategies for MMAM. One approach used to represent the multi-material model is a multi-CAD system . This syInterface strength is a key concern in the property of a multi-material part. For example, the hardness at the interface differs from the materials of a multi-material part fabricated by selective laser melting  and therH contains different material volumes, we can define it as A and B as H , it extracts the materials defined in H and stores them in a material library (M). It assigns each material  parallel to the ground at the height to intersect with all the rays. This results in a set of nodes (Suppose an object ge (LDI) , which wLDMI represents a solid model by an image, each pixel of which records a set of sample points by shooting a ray to intersect with the model. The rays come out from the image perpendicularly and all of them are parallel to each other. Each sample point stores its coordinates, normal vectors, and material. The coordinates and the normal vectors give the geometry and the local orientation information, and the material information defines the material regions. We can place the image anywhere theoretically, but since the goal of slicing is to capture the changes in the cross-section geometry at different heights, we place the image at the ground and shoot the rays in the build direction. The image should be large enough to cover the entire model, and the image resolution uses the printing resolution of the 3D printer.d), two components of the normal vector (m). The depth value d is the distance from the image, which suffices to retrieve the actual coordinates because we know the ray equation, and we can calculate the third component of the normal vector by the other two: One way to get the sample points is by computing many line-triangle intersections in the ray-tracing process as illustrated in After converting the CAD model to the LDMI representation, we use it in the slicing process, which divides the model as a stack of 2D layers. By intersecting a slice plane with the rays of LDMI, we can form a 2D grid at a particular height. To get all the geometry and material information in each 2D slice, there are two tasks: (1) determining the materials for each grid node, and (2) forming different material regions.z-axis is pointing to the right instead of the top in this figure, so virtually the grid nodes (dots) aligned vertically are from the same slice plane. The sample points (patterned circles) are located arbitrarily on the ray because their positions depend on the shape of the model, but the grid nodes spread uniformly along the ray since all the layers have the same height. The solid-line and the dotted-line circles indicate the Since the grid nodes are on the rays, the sample points of the rays can determine whether a grid node has any material and what materials it has. A as well as the B, then it contains both materials A and B, and so on , which is based on the line distance and applied separately to each material, i.e., Given the material interfaces and regions defined in a 2D plane, this section presents the approach to generate the interlaced infill. The present method can generate the interlaced infills on the fly in the CAM phase, without altering the CAD model. If a region has material, it can have a single material or multiple materials. A single-material region uses a normal infill, and we generate an interlaced infill for the multi-material regions. Without loss of generality, this paper uses triangular infills to explain the generation of interlaced infills, but we can use other types of infills similarly. A triangular infill has three sets of parallel lines inclined at angles of A, B, and C. There are seven different material regions, including three single-material regions, three double-material regions , takes 421 ms to build a With the developed LDMI framework, now we can model the multi-material interface, and this section tests our hypothesis that interlacing infills increases interface strength. To measure the interface strength, we use the ASTM-D638 standard to fabricate a dog-bone shape with two materials touching at the middle of the dog-bone, as shown in 0SLC see  and get E) and the ultimate tensile stress (UTS). Apparently, the PLA is much stiffer than the other two materials and can carry at least two times more loads before fracture, but it fractures at around There are three sets of experiments. The first experiment uses the same material (PLA) but different colors (orange and yellow) to compare the interface strength among various joint configurations. The second experiment further verifies the effectiveness of the interlaced infills in different materials . The last experiment tries to find out if there is a relationship between the interface strength and the overlap size. We have tested all the configurations three times and averaged the values  a butt joint, (2) the interlocking T-joint, and (3) the proposed overlapping joint with interlaced infill. The butt joint joins the materials by simply placing them closely next to each other with no special shaping. The interface strength for this joint purely depends on the material compatibility and the adhesion between the material surfaces introduced in the 3D printing process. It is the baseline to show the improvement achieved by other configurations. The dimension of the T-joint is as follows. The width and height of its flange  are E value is 359 MPa, and the observed UTS is E is around 500 MPa and UTS is around  MPa see . The tesous work  that theThe previous experiment uses two very similar materials, so this experiment tests the interlaced infill on some distinct materials to further confirm its capability. There are three materials and two combinations: PLA-ASA and PLA-PETG. It tests each combination with both the butt joint and the interlaced infill, and the overlap size for the interlaced infill is also 10 mm in this experiment. After knowing that interlacing infills is effective, this experiment wants to find out how critical the size of overlap is to the interface strength and what their relationship is. The experiment is as follows. First, it uses the materials with similar property (orange PLA and yellow PLA) to better observe the changes because of the joint area. Second, it tests four different sizes of overlap: 5 mm, 10 mm, 15 mm, and 20 mm. One major concern of MMAM is the strength at the interface between materials. Particularly, FFF is well-known to have low diffusion between material strands and weak interlayer bonding . ObserviBased on the observation that nature often intertwines materials to increase strength, this paper hypothesizes that overlapping and interlacing infills of different materials enhances the interface strength between the materials of a multi-material part. However, existing slicers cannot generate the interlaced infill. To test the hypothesis, this paper also develops a novel slicer—named layered depth-material images (LDMI)—for multi-material additive manufacturing (MMAM) to process the material information efficiently. The LDMI framework takes a multi-material computer-aided design (CAD) model as an input and applies rendering techniques to encode the material data into the sample points of the model. It then uses the encoded data in the slicing process to identify different material regions in each slice plane and generates the interlaced infills in the multi-material regions.We conducted experiments to compare different joint configurations  and different material combinations . The tensile test results show that the T-joints are better than the butt joints, and the interlaced infills outperform both. The samples of interlaced infill even fracture outside the joint area, meaning that the interlacing leads to a joint at least as strong as the materials. The trend is the same for different material combinations. This verifies the hypothesis, and the approach is promising to create strong multi-material parts. The method can also apply to the reinforcement of a weaker material by interlacing it with a stronger material. We also found that an overlap size of 05-10 mm suffices to have the full interlacing impact on the interface.The major limitations of the present work include being only tested with the triangular infills, the dog-bone shapes, and the fused filament fabrication (FFF) process. Triangular infill is normally the strongest infill pattern because triangles are least likely to deform. It will be interesting to find out whether the interlacing has the same impact on other infill patterns as well. We also plan to extend the present work to functionally graded infills by varying the infill ratio of each individual material, which will require a new way to interlace the materials to achieve the desire mixing ratio. In addition, we will test more complex shapes and loading conditions to further confirm the method’s capability. Finally, will will also test on other MMAM process such as MultiJet printing (MJP) to validate its generality.


With the flood of engineered antibodies, there is a heightened need to elucidate the structural features of antibodies that contribute to specificity, stability, and breadth. While antibody flexibility and interface angle have begun to be explored, design rules have yet to emerge, as their impact on the metrics above remains unclear. Furthermore, the purpose of framework mutations in mature antibodies is highly convoluted.To this end, a case study utilizing molecular dynamics simulations was undertaken to determine the impact framework mutations have on the VH-VL interface. We further sought to elucidate the governing mechanisms by which changes in the VH-VL interface angle impact structural elements of mature antibodies by looking at root mean squared deviations, root mean squared fluctuations, and solvent accessible surface area.Overall, our results suggest framework mutations can significantly shift the distribution of VH-VL interface angles, which leads to local changes in antibody flexibility through local changes in the solvent accessible surface area. The data presented herein highlights the need to reject the dogma of static antibody crystal structures and exemplifies the dynamic nature of these proteins in solution. Findings from this work further demonstrate the importance of framework mutations on antibody structure and lay the foundation for establishing design principles to create antibodies with increased specificity, stability, and breadth. As sequHV) and light chain (LV), and its impact on germline (GL) structure macrostates. We recently explored the impact of common framework mutations in baseline human Ab repertoires with the goal of understanding the effects of these mutations on the developability of monoclonal Abs (mAbs)  . Here, win vivo through a stochastic, Darwinian evolutionary process known as affinity maturation (Abs evolve turation –15. Starturation . It remaH-VLV interface and the complementarity-determining regions (CDRs) to suit the antigen being presented at a given time. Further studies characterizing these dynamic macrostates both in silico and in vitro are needed to deepen our understanding of the diversity of macrostates and the role these states play in Ab stability and breadth. Utilizing the conformational ensemble perspective to better inform Ab engineering efforts could result in more successful clinical trials for therapeutic Abs, more specific sensing technologies, and more effective vaccines against highly mutable pathogens like HIV , we believe the advantage could arise from an increased number of stable macrostates available in the Ab’s conformational ensemble, where macrostates are semi-stable states that the Ab structure visits , 11. Addlike HIV –19, Malalike HIV , and Inflike HIV .in vitro Ab engineering techniques , typically do not capture increases in Ab flexibility, but instead select primarily for mutations that increase the binding affinity, which generally rigidify the protein  region of five mature Abs  both with and without GL-reverting mutations . This allowed us to parse out the effects of key single- and double-point mutations along the evolutionary trajectories of the clinically-relevant Abs of interest. Mutations are annotated throughout the text using the IMGT numbering scheme . The mutations were chosen based upon our previously-published  position2.2Several new simulations were performed in this work and have been analyzed alongside simulations that we performed for a prior study . Here, w2.3We calculated the RMSD of the Abs over the course of the entire MD simulations. This allowed us to determine whether the simulations had converged , and to determine the number of stable Ab macrostates sampled within the simulated timescales. As a special case, the control simulation for Pertuzumab was cut short at 276 ns in subsequent analysis steps due to the large conformational change the Ab was observed to undergo at this time point, which resulted in a shift in the relative orientation between the variable and constant regions of the Ab towards a different macrostate.H-VLV interface. A “shift” was calculated by subtracting the SASA of the control Ab from the mutant.We then calculated the RMSF of the Abs over the last 150 ns of each simulation to determine the per-residue flexibility of the Ab. Since all simulations were deemed to have converged by 150 ns, only the last 150 ns of each simulation were used to compute the RMSF. The RMSF profile of the control Ab was subtracted from that of each mutant Ab to determine how much the flexibility changed as a function of the mutation(s). The residues comprising each CDR loop were identified through an IgBlast  alignmen2.4H-VLV interface angle every 100 frames for each of our simulations , leading to a distribution of H-VLV interface angles for each Ab. Additionally, we performed a two-tailed t-test on the angle distributions to quantify how different the angle distributions of the mutant Abs were from that of the control Ab . These distributions were also fit to a combination of Gaussians and normalized. Finally, we calculated the average RMSD and mean H-VLV interface angle for each Ab over the last 150 ns of each simulation. We then subtracted the results for the control Ab from the mutant Abs to determine how much the mutant Abs “shift” in each of these metrics. After plotting these values, we found correlations by performing a linear regression.Using ABangle , we calc33.1H-VLVinterface angles differ when comparing the crystal structures of the Abs to the ensemble of solution state Ab structures generated over the second half of the production MD simulations. For all five Abs we studied, we observe a shift towards more negative H-VLVinterface angles for the ensemble of solution state structures .Similar to the case for Atezolizumab, introducing key framework mutations into Pertuzumab causes significant shifts in the Introducing the A54S GL-reverting mutation into Trastuzumab leads to a significant right-shift in the ensemble mean interface angle compared to the control , we observe that compared to the control Abs, the mutated Abs sample a narrower distribution of interface angles Table S23.3H-VLV interface angle upon mutation might impact the conformational stability and/or flexibility of the Abs. To this end, we calculated the RMSD of each Ab over the course of the production MD simulation, in reference to its respective starting structure, which is essentially the same as the crystal structure (and so will be referred to as such) since restraints are removed only at the beginning of each production run. We anticipated that changes in the furthest from the crystal structure value, and that of the double-point mutant shifted the least from the crystal structure value, with the values for the single-point mutants falling in-between. If changes in the H-VLV interface angle are driving the observed changes in RMSD, we would expect to see the mutants have a lower overall RMSD than the control, as they prefer an interface orientation similar to that of the crystal structure; however, our findings show the opposite is true. In other words, the increased RMSD of the mutants above the control Ab do not appear to be a direct result of the greater H-VLVorientational shifts of the mutants from the reference  structure used in the RMSD calculations, but are instead a product of a cascade of effects. More specifically, we hypothesized that the mutation-induced changes in the interface angles instead mediate changes in the flexibility of the Abs, which is the key driving force behind the observed increases in RMSD of the mutant Abs above the control. Feeding into this hypothesis, the RMSD is seen to stabilize quickly in each simulation, indicating the overall conformational stability of the Abs is relatively unaffected by the changes in the interface angles. We explore this flexibility hypothesis in detail in the following section.The RMSD results for Atezolizumab contrast those of lower RMSD compared to the control. For Daratumumab  structure, we aimed to eliminate this bias by only comparing the mutant Ab data to the control Ab data, rather than to the crystal structure. RMSD stabilizes quickly in each simulation, indicating the interface angle shifts upon mutation have little impact on the conformational stability of the Abs. This led us to look at the results for Atezolizumab from this perspective, we observe that greater interface angle shifts to the right of the control consistently lead to greater increases in RMSD above the control 2Ai. SimH-VLV interface angle upon mutation  should experience decreased flexibility.From these results, we hypothesized that mutation-induced shifts in the To explore this idea, we calculated the minimum and maximum difference in RMSF between each mutant and its respective control Ab, ignoring the first and last 10 residues of the Abs that are known to be highly flexible and could skew our results. We decided to look specifically at the largest differences in RMSF–both positive and negative— between the mutant and the control because comparing the average RMSF values would likely dampen any overall trends by cancelling out negative and positive fluctuation changes. We also calculated the SASA of each Ab, and then plotted these values separately against the minimum and maximum RMSF changes for each Ab  with the Ab, as has been noted in the literature  are co-crystallized with a ligand. The presence of a ligand can aid in resolving a high-quality crystal structure and reveal critical information about the paratope of the Ab under study, however, it also places structural restraints on the Ab of interest. The impact of these restraints can, of course, be biophysically relevant for the integrity of the complex, but the restraints can also bias our understanding of how the Ab will behave in solution before it meets its cognate antigen.H-VLV interface angle. While not all mutations studied had a significant impact on the H-VLV interface angle, or had the same impact across different Abs, we did see that even mutations distant from the H-VLV interface could impact the relative orientation of the Ab heavy and light chain. These findings highlight the need to more broadly study the effects of mutations on the H-VLV interface angle, in order to use this parameter as a tool to tune and develop Abs with desired properties.Next, we found that framework mutations can significantly impact the H-VLV interface angle also had correlated shifts in their RMSD values, but that these shifts were not due to changes in the overall conformational stability of the Abs, nor simply due to geometric changes in the antibody away from the reference  structure. This, in turn, led us to investigate the impact of the framework mutations on the SASA and RMSF of the Abs.Furthermore, we found that the Ab mutations that impacted the H-VLV interface angle, as these shifts expose more of the Ab to solvent and decrease the contact angle between the Ab heavy and light chains. However, because the H-VLV interface angle can shift either right or left to increase the SASA, it is difficult to discern if this is truly causative and more studies need to be done to fully validate this hypothesis. We also note that with mutations that increase the overall SASA of the Ab, other regions of the Ab may still experience a slight decrease in SASA and thus flexibility due to the angle shift, evidenced by both positive and negative fluctuations (compared to the control) in the RMSF profiles. The reverse holds true for mutations that decrease the overall SASA.We found that when a mutation increases the overall SASA of the Ab, it results in an increase in the flexibility of the newly solvent-exposed regions of the Ab (and vice versa). We believe this is due to the Ab having fewer constraints in a less tightly-packed conformation. Our hypothesis is that increases in SASA are directly due to changes in the H-VLV interface angle can vary in solution, but the reasons behind these shifts have yet to be fully characterized and understood, which is necessary to realize any potential benefits.These findings may have important implications for understanding antibody mechanisms of action and for rational Ab design and offers another parameter to tune when engineering potential Ab therapies. It is clear from our and others’ work that the H-VLV interface has long been shown to influence the orientation of the CDR loops, and in turn, the antigen specificity profile  may indicate that this relationship is not necessarily linear; however, given how close the two coefficient values are, additional simulations are warranted to elucidate the exact nature of the correlations. The ability to precisely tune Ab flexibility could contribute to increasing the number of macrostates the Ab visits, allowing it to sample a wider range of unique conformations and thus bind to more diverse antigens and ligands. In addition, other novel real-world impacts of modulating Ab flexibility could become known through future experimental testing. In particular, prospective studies such as in silico mutagenesis could be performed to either increase or decrease flexibility and observe the effects on affinity maturation, etc., which could then be tested via experimental affinity and kinetics measurements. Current Ab engineering techniques tend to optimize solely for binding affinity; our results imply a new approach might be fruitful where in addition to seeking out strong binders, we also find Abs that utilize flexibility to overcome energy barriers.Looking forward, our work suggests that mutations that shift the The original contributions presented in the study are included in the article/KS, ER, JF, and BP designed research, performed research, analyzed data, and wrote the paper. All authors contributed to the article and approved the submitted version.


The imaging range of traditional plane wave imaging is usually limited by the directivity of the plane wave. In this paper, a multi spherical wave imaging method based on an ultrasonic array is proposed, which radiates both compression and shear waves in a solid medium to form the multi spherical wave. Firstly, excitation characteristics of the multi spherical wave are analyzed theoretically and the calculation method of echo delay of multi spherical wave imaging is derived. Multi spherical wave imaging is compared with conventional ultrasonic plane wave imaging by designing experiments. Compared with ultrasonic plane wave imaging, multi spherical wave imaging is not limited to the size of the transducer and can greatly improve the detection range. In addition, compared with the multi plane wave imaging method, the multi spherical wave imaging algorithm is relatively simple, fast, and has high application value. At present, with the improvement of testing quality and real-time capability standards in the field of industrial nondestructive testing, the requirements of ultrasonic imaging technology are becoming higher and higher . In the All the previous research on plane wave imaging algorithms were carried out around a single longitudinal wave. However, in recent years, the fusion of multiple imaging methods and multi-wave imaging is an important development trend in the field of acoustic imaging. Among them, representative imaging methods include multi-mode full-focus imaging , multi-wThis paper mainly focuses on fast ultrasonic multi spherical wave imaging based on ultrasonic array. Firstly, the acoustic emission and imaging principles about the plane wave are reviewed and the relevant experiments are carried out. The multi spherical wave imaging method using ultrasonic array is proposed based on the idea of plane wave imaging. The implementation process of spherical wave emission is analyzed and the corresponding imaging algorithm is established. Then, based on the idea of ultrasonic multi wave focusing, the composite multi-spherical wave emission and imaging detection is studied, and the algorithm and calculation basis are obtained. Finally, the verification experiments with correlation analysis about imaging quality and speed are carried out.The conventional single plane wave imaging mode controls all the array elements of the ultrasonic transducer to simultaneously apply non-delay pulse excitation , as showx-axis direction is parallel to the ultrasonic phased array, the z-axis represents the direction of the imaging depth, and the plane wave is excited by the phased array for scanning. According to the above plane wave emission mode and the geometric relation, the propagation path x, z) and then reflected to the n-th element of the phased array can be expressed as  and shear wave excited by the second packet [time delay rule given by Equation (17)] are spherical compressional wave and spherical shear wave, respectively. Therefore, two spherical waves are formed and propagate with compressional and shear wave velocities, respectively. They are equivalent to the spherical compressional wave and spherical shear wave that start simultaneously from the virtual point source, respectively. It should be noted that the shear wave excited by the first packet and the compressional wave excited by the second packet are not the spherical waves and they are not considered here and do not affect the final results.According to this method, ultrasonic phased array can simultaneously emit spherical waves propagating with the velocities of the compressional and shear waves to scan the measured block, that is, forming multi spherical wave for scanning. Due to the different ultrasonic characteristics of compressional and shear waves, multi-wave imaging with the multi spherical wave emission mode has good influence on the effective detection range and transverse resolution of imaging detection.z-axis, the deflection spherical wave can be obtained. Similar to m = 1, 2, ..., K), each transducer element needs to be excited twice to form spherical compressional and shear waves, so the whole process of composite multi spherical wave compounding emission has a total of 2K excitations. Where, when the deflection angle of the virtual point source is m = 1, 2, ..., K), the delay time of the first excitation of the n-th element can be expressed as:If the spherical center of the spherical wave is not on the n-th element can be expressed as:The delay time of the second excitation of the x, z) and then reflected to the n-th element of the phased array is the same as that of the spherical shear wave, which can be expressed by Equation (13).According to the geometric relation in the figure above, when the deflection angle is n-th element are defined as M = 1, 2), which can be written as: M = 1 and is the shear wave velocity for M = 2.The image function needs to superimpose echo signals of all array elements according to a certain delay. According to Equation (13), time delays of the echo signal received by the Therefore, coherent multi spherical wave imaging can be obtained as:z axis, multi wave emission is carried out at K different deflection angles. According to Equation (21), all received signals are beam synthesized, and finally, the results of coherent multi spherical wave imaging are obtained.By changing the included angle of the virtual point source relative to the In this section, experimental data are used to conduct imaging in accordance with the above methods. The test block in the experiments is shown in designed  in previIn the experiments, the single plane wave emission is achieved by non-delay excitation and the single spherical wave is achieved by time delay according to Equation (8). Then, the experimental equipment is used to collect and process the data. By comparing According to Equations (3) and (11), the echo data collected by the system are calculated for beam synthesis. Imaging results of the single plane wave and spherical wave without deflection can be obtained, as shown in By comparing the results in In this section, experiments of multi spherical wave imaging and composite multi spherical wave imaging are considered and carried out. First, the transducer controlled the emission of two spherical waves with different wave velocities at 0 deflection angle (without deflection). Then, each element received the defect scattering echo data for beam synthesis according to Equation (21). Where, multi spherical waves are emitted without a deflection angle, image reconstruction of the data after beam synthesis is obtained and shown in By comparing the results in K = 11. The center of the transducer is selected as the coordinate origin of the imaging results, and the data after beam synthesis is reconstructed. The results are shown in Next, in order to verify the imaging effects of coherent spherical wave compounding and the composite multi spherical wave, the experimental system excited the element according to the delay rules analyzed in Compared with single plane wave imaging, the resolution and signal-to-noise ratio of composite spherical wave imaging and composite multi spherical wave imaging are greatly improved. By comparing the imaging results in The above results show that the detection result of composite multi spherical wave ultrasonic imaging based on virtual point source emission is better than that of the composite spherical wave. However, the phased array should be excited twice at each deflection angle for the composite multi spherical wave while excited only once for the composite spherical wave. Therefore, the detection time of composite multi spherical wave imaging is slightly slower than that of the composite spherical wave.K = 5. The center of the transducer was selected as the coordinate origin of the imaging result, and the data after beam synthesis are reconstructed, as shown in In order to further improve the computational speed of composite multi spherical wave imaging, five multi spherical waves with different deflection angles are set up in experiments. That is, in the scanning range of −30°~30°, the value of By comparing the imaging results in In ultrasonic detection and imaging, the transverse and longitudinal resolutions are different. The transverse resolution depends on the effective width of the ultrasonic beam while the longitudinal resolution is mainly determined by the duration of the excitation pulse and the sound speed. Generally speaking, the longitudinal resolution is better than the transverse resolution for ultrasonic array imaging. The defects in the ultrasonic image seem to be oval shaped, not circular. In fact, ultrasonic detection and imaging only proves the existence and approximate size of the defect, not the actual shape of the defect.The imaging region of the undeflected plane wave has been seriously affected by the size of the transducer. Plane wave imaging without deflection can only detect the corresponding defects below the transducer array. However, undeflected spherical wave imaging can detect the defects beyond the vertical range of the transducer array.Compared with spherical wave imaging without deflection, the detection sensitivity of the composite multi spherical wave is slightly improved in the sensitivity of the large angle. However, there is no focusing emission, and the overall imaging effect is relatively poor.Compared with undeflected plane wave and spherical wave imaging, the resolution and SNR of composite spherical wave imaging and composite multi spherical wave imaging are greatly improved. Since the properties of both compressional and shear waves are utilized, multi spherical wave imaging can obtain better images over a larger deflection region.Composite multi spherical wave imaging can improve the speed of echo processing by appropriately reducing the number of transmission deflections, and the imaging effect is better than that of composite spherical wave ultrasonic imaging.In order to improve the resolution and SNR of plane wave imaging detection in traditional ultrasonic imaging algorithms, the multi spherical wave ultrasonic imaging method based on phased array virtual point source emission has been proposed. In this paper, the flow based on spherical wave emission has been introduced in detail and the calculation formula of echo beamforming for multiple spherical wave emission has been derived. Finally, the imaging method is verified experimentally, and the following conclusions can be drawn: