In recent years in medical imaging technology, the advancement for medical diagnosis, the initial assessment of the ailment, and the abnormality have become challenging for radiologists. Magnetic resonance imaging is one such predominant technology used extensively for the initial evaluation of ailments. The primary goal is to mechanizean approach that can accurately assess the damaged region of the human brain throughan automated segmentation process that requires minimal training and can learn by itself from the previous experimental outcomes. It is computationally more efficient than other supervised learning strategies such as CNN deep learning models. As a result, the process of investigation and statistical analysis of the abnormality would be made much more comfortable and convenient. The proposed approach’s performance seems to be much better compared to its counterparts, with an accuracy of 77% with minimal training of the model. Furthermore, the performance of the proposed training model is evaluated through various performance evaluation metrics like sensitivity, specificity, the Jaccard Similarity Index, and the Matthews correlation coefficient, where the proposed model is productive with minimal training. Medical imaging technology has been critical in medical diagnostics for accurately detecting the presence of malignant tissues in the human body. There are divergent imaging technologies that are available for diagnosis of abnormality among various organisms that includes X-ray technology, as stated by Medical imaging technology has upgraded stupendously to elaborate every minute and tiny ailment in the human body that could efficiently diagnosed disease at a significantly earlier stage. The proposed study primarily focused on tumor identification and volumetric estimation of the tumorous region in the human brain. There are numerous machine learning models available for accurately identifying the tumorous regions from MR images. Yet, most of these techniques are imprecise, process thirsty, and particularly semi-automated procedures used in tumor identification. To circumvent the limitations of the above methodologies, several automated techniques, including the conventional models like Genetic Algorithm (GA), as stated by As part of recognizing ailments, several stages, including pre-processing the MR images to address noise in the original MR images, such as Spackle noise, Poisson noise, and Gaussian noise, are introduced into the image at various stages during the process of rendering the image. And the pre-processed step will enhance the contrast and the texture of the image that assist in a faster and convenient way to recognize the malignant tissues. Once the noise in the image is pre-processed, the MR image is fed to remove the skull region. Then the MR image is segmented to recognize the malignant region, followed by the volumetric estimation for analyzing the impact of the damage. The results of the automated segmentation approaches are refined over multiple iterations for the precise outcome.Generally, the medical images are segmented to locate the abnormal regions in the image based on texture-based information. The process of image segmentation plays a vital role in the identification of the malignant areas in the MR image; There are various semi-automated and automated ways of segmenting the MR images that could efficiently segment the images, but there is a considerable tradeoff between the accuracy and the computation efforts put forward by each of those approaches. Supervisory models yield better accuracy, but they need tremendous training data that needs more computational resources.k value is too large, it would lead to over-segmentation, and if the k value is too small, it will lead to under-segmentation of the image.The K-Means algorithm is one such semi-automated approach that segments the MR Image based on the pre-determined number of segments as stated by Segmentation of MR images is indeed possible using completely automated techniques such as thresholding, as stated by The other predominantly used segmentation technique is through the region growing  strategyThe main objective is to formulate a mechanism that can efficiently segment the real-time image into multiple regions based on the available features by minimizing the computation efforts. The proposed approach is a self-trained strategy that upskills the algorithm with some pre-existing real-time scenarios. Previous experimental results show that the proposed SLNS algorithm can differentiate the skull region from the brain tissues in the MR image without any external pre-processing algorithm. It can quickly extricate brain tissues from the non-brain tissues through the available feature set. The proposed model is robust in handling the images with an acceptable noise level, and it needs less computational effort for training the model. The experimentation has been performed to evaluate the accuracy of the proposed approach, and the upshot seems to be promising.Cognitive technology in real-time image segmentation is a multidisciplinary technique that is an intrinsic aspect of fully convolutional neural networks. Fully convolutional neural networks are widely utilized in real-world settings to successfully handle 2D images. The concept of semantic segmentation has been used in coherence with multi-objective function-based algorithms for better results. The weak learning network is based on the partial training of the algorithm and the tuning of the algorithm so that it would be able to differentiate among multiple classes. In addition, the algorithm is capable of training itself for better efficient segmentation of the image. In every stage of execution for evaluating the tumor’s region from the MR image, the proposed method would segment the image based on the trained information. The resultant segmented imaged would be further refined in further network layer’s multi-objective functions.In contrast to its competitors, the suggested methodology is a partly trained strategy that does not need extensive training. As shown by The model is trained to distinguish brain tissues from non-brain tissues such as brain fluids, the skull region, the thalamus, and the brainstem, which must be isolated from brain tissues for improved segmentation and evaluation of the tumor’s extent. However, whenever a new image is fed into the algorithm as input, post segmentation, the image is fed into the network’s self-learning layer as input for further images.In the automated segmentation of the brain MR image, the crucial thing is to set up training sets that are large enough to train and validate the model. As a result, it is challenging to obtain a self-sufficient dataset for both trains and validating with ground facts that are associated with the imaging data concerning to abnormality for cross validation. On the other hand, self-learning models need a relatively smaller training and validation set. Furthermore, the experimental results used in self-training the model ensure better results in future experimentation based on its previous experimental knowledge. The complete flow diagram of the proposed framework can be seen in The layered architecture of the proposed self-learning network-based segmentation (SLNS) approach includes the convolutional layers that would perform various challenging tasks like pre-processing of the image to remove the image’s noise by considering the adaptive bilateral filter for pixels that surround the actual corresponding pixel. The image is then further processed to remove the skull region in the next successive layer in correlation with the other connected layers. Next, the image is segmented based on the pixel’s intensity value, representing the region’s texture. Finally, the classifier is used to dissimilate the non-brain tissues and damaged region in the human brain.The suggested methodology trains the segmentation algorithm using a self-learning module that gets adequate information from the preset segmentation dataset and previous experimental results. Additionally, each convolutional layer consists of a variety of kernels, including an adaptive bilateral filter with sublayers that determine the appropriate number of clusters and cluster centroids, Sobel filter that is used in the edge detection, and other 2D convolution filters that are generally (3 × 3) in size which slides across the original input image. Over numerous epochs, the model is trained over multiple iterations to identify all the key features in the input image. The image is refined at the earlier stages using an adaptive bilateral filter that processes the image that normalizes the noise like Gaussian noise and Poisson noise during image acquisition. The method of noise reduction is carried forward through the following equations α value is determined by the contra harmonic mean of the neighboring pixels determined in pl represents the pixel likeliness. From the above equation, the The values of the pixel belongingness (Pb) have been demonstrated in where cp determines the membership coefficient, and p designates the pixel, and x designates the fuzzier metric of belongings. The value of the pixel likeliness(pl) is designated through From the above equation, the p(s) denotes the probability of likeliness with the segment s, and Heuristic Approach for Real-time Image Segmentation (HARIS) algorithm is used to segment the high dimensional images like the medical MR images to identify the abnormality from the MR images. HARIS approach incorporates two phases in the image segmentation process. In the initial phase, the optimal number of regions in the image are being assessed, which assists in accurately recognizing the regions in the image based on texture, intensity, and boundary region-related pixels. The techniques like the intraclass correlation and interclass variance are being considered for evaluation. The second phase of the HARIS approach is to identify the local best feature within the region following the presumed feature element that is presumed to be the global best. The selected feature is used in assembling the pixels as a region based on the feature identified.The image is segmented based on the intensity level in the later stages by approximating the minimum number of segments to 23 from the previous experimental studies. The number of segments fitness has been evaluated through the formula stated below In the above The maximum interclass variance is determined by the 1,µ2 That determines the means of the intensities of the image segment.The fuzzy entropy-based  thresholμtc, μetc Are the variables representing the fuzzy membership concerning the image segments associated with the tumors class and non-tumors class. However, the equation is formulated concerning Shannon’s entropy formulation. The value of the threshold(FET) would be greater than 0 and would lie below 255.From the above The value of the intraclass correlation is determined by σs represents the standard deviation in concern to the given image segment, and the variable σi represents the standard deviation concerning the entire image that is being considered.From The adaptive structural similarity index (ASSI) metric is used to classify the pixel among the tumorous and non-tumorous regions. The structural similarity index relay on the likeness among the pixels among tumor regions. The structural similarity index relies on three factors: the structural parameter, luminance parameter, and contrast parameter. The index is determined as the product of the three factors mentioned above. This paper has proposed an adaptive structural similarity index that would assess the membership alongside the similarity index to make the outcome more realistic. The equation of the similarity index is determined through the equation stated below. ω determines the probability that is multiplied by the product of the structural parameter presented in The  _______________________ Algorithm 1 Algorithm_______________________________________________________________________ Date: x←Structural Parameter, y←Luminance Parameter, z← Contrast Parameter Input: pixel where p represents the row and the q represents the column Output: Assess the correlation index pix← initialize the starting pixel while(i<maximum_number_iterations) for each pixel in the input image, do Update x, y, z and Ω Approximate the Correlation Index Select the regions in the image Determine the suitable category to assign If CI > Threshold, then Assign the corresponding pixel to the tumorous Region else Assign the corresponding pixel to the non-tumorous Region end if end for end While____________________________________________________________________________    The flattening layer is the successive layer after the convolution and pooling layers. It is responsible for transferring the data into the 1-dimensional array used in the subsequent layered architecture. The fully connected layer in the proposed architecture uses the intensity features of the regions that are recognized as abnormal and normal in the considered MR images. Gated recurrent unit (GRU) is used in the proposed model to maintain the interpreted data of the previous experimental prediction. The same apprehension is used in the future in abnormality recognition from the MR image. A Heuristic Approach for Real-time Image Segmentation (HARIS) algorithm is used to differentiate the tumors and non-tumors Region by identifying the appropriate pixels as the features for the prediction.The gated recurrent unit is used to maintain the acquired knowledge from the previous outcomes. GRU is efficient, with comparatively fewer parameters needed to maintain the training data, . GRU canw represents the weight associated with layer l and the variable βrepresents the bias, l in the proposed model is determined through the The variable wl is the weight that is associated with layer l and the variable el+1 represents the error associated with layer l + 1. The variable f(xl) is the activation function that is associated with the layer l that is being determined by the rectified linear unit (ReLu) in the proposed model. The The ReLu based activation function is linear for the greater than zero values, and it will be zero for all the negative values.The learning rate of the proposed model is significant in assessing the performance of the model, which generally controls the weights in the network in concern to the loss gradience. The learning rate is presumed to be at an optimal level so that the model will move towards the solution by considering all the significant features in the prediction. The lesser learning rate presents the slower learning ability resulting in a delayed solution. On the other hand, the higher learning rate results in a faster solution that may ignore few features in the learning process. In the proposed self-learning centric segmentation model, the model will acquire knowledge from the earlier experimental outcomes. The learning rate is also dependent on the number of epochs that the model is designed to execute before it is evaluated. As the number of epochs increases, the learning rate of the model will move towards the saturation point, and we can observe the change in the learning rate untill that point. But increasing the number of epochs will result in consuming more computational efforts in the training process.The other hyperparameters associated with the evaluation process include the loss and accuracy functions related to the proposed model’s training and validation phase. The experimentation has been carried forward over the real-time MR images acquired from the open-source repository LGG dataset acquired from The Cancer Genome Atlas (TCGA) captured from patients with acute glioma. The performance of the proposed approach has been evaluated through various metrics like Sensitivity, Specificity, Accuracy, Jaccard Similarity Index, and Matthews Correlation Coefficient that is assessed from the True Positive value that designates how many times does the proposed approach correctly recognize the damaged Region in the human brain as damaged Region and the True Negative that designates the how many times the proposed approach identifies non-damaged Region correctly and False Positive designates the number of times does the proposed approach identifies damaged Region in the brain as non-damaged Region and False Negative designate the count of how many times does the proposed approach mistakenly chosen non- tumors region as tumors region. The performance of the proposed self-learning network-based segmentation (SLNS) approach is evaluated against the other conventional approaches like twin-centric GA with SGO, HARIS approach, and convolutional neural network in concern to the performance evaluation metrics like Sensitivity, Specificity, Accuracy, Jaccard Similarity Index (JSI), Matthews correlation coefficient (MCC). From The performance of the proposed model is assessed through the HARIS algorithm that decides the best possible number of segments to assist in identifying the abnormalities in the image, and it assigns the pixels to the segment by identifying the ideal pixel in the segment. The second objective function of the HARIS algorithm is replaced with the fuzzy membership assessment model, and the performance of the proposed model is being evaluated and presented in vertexpix represents the vertices that are being considered in the image for processing. The variable From vertexpix represents the vertex pixel in the region of the MR image. The variable From The proposed model’s performance is assessed against the various existing algorithms like thresholding, seeded region growing, fuzzy C-means, and the artificial neural network models concerning the evaluation metrics like sensitivity, specificity, and accuracy presented by The self-learning-centric models are recently becoming part of the biomedical and healthcare domain, where the models are expected to work with minimal training. In a few situations where there is no adequate data available for training the model, the self-learning models are proven to perform well. The model also needs lesser training than its counterparts. The proposed model is capable of learning from its previous experimental results. The hyperparameters like the learning rate that are presented in the current study are at an acceptable level after 43 epochs, and other parameters like the training and validation studies state that the model fine-tuned the performance assessment metrics like the accuracy, sensitivity, specificity, the Jaccard Similarity Index (JSI), and the Matthew correlation coefficient (MCC) are assessed by repeated autonomous executions. The obtained values have proven that the model performs reasonably with minimal training of the data. The fuzzy component is added to evaluate the membership for assigning the pixels to the appropriate segment in contrast to the HARIS algorithm for the assignment of the pixels. The statistical analysis of the study has evinced the performance of the HARIS algorithm in the segmentation process.The pivotal object of the current study on mechanizing a self-learning model that is efficient in identifying the tumor from the MR image with minimal training. The model is efficient in working with problems that have minimal training data available. The proposed model efficiently learns from its prior experimental outcomes and utilizes the acquired knowledge for future predictions. It can be observed from the practical implementation of the proposed model that the resulting outcome seems to be very accurate and precise in identifying abnormality in the human brain. In contrast to fully supervised models like convolutional neural networks, deep learning models and various classification algorithms need to be rigorously trained for better accuracy. Still, the proposed model is proven to be efficient in generating equivalently better outcomes with other models. The proposed model itself can normalize the noise in the input image and robust in differentiating the non-brain tissues like the skull from the brain tissues. However, the proposed approach could be further optimized by incorporating the self-correcting convolution layer through an Ancillary kernel.The self-learning models are robust in handling the unusual problem where there is inadequate training data available. But the self-learning models overfit in few cases as the developer may not have control over the level of training to the model. The overfitting may lead to instability in the predictions that are made in few contexts. Moreover, the process of debugging the issues and rectifying them in the self-learning model is challenging. The models learn from their previous experimental outcomes, and there is a possibility that the models might misinterpret the outcome based on previous experimental results.The proposed model based on the self-learning mechanism is suitable for handling uncertain data more effectively through its previous experiences. The model’s performance can be further improvised by incorporating the long short term memory (LSTM) component for efficiently handling the training data for better accurate prediction of the progress in the tumor growth as the LSTM components are efficient in holding the memories for a longer time by preserving the dependencies based on the network’s information. The incorporated memory elements can retain the state information over the specific iterations constructed through multiple gates. The proposed model can also be enhanced by incorporating the feedback component that would help assess tumor growth progress by correlating its previous outcome.10.7717/peerj-cs.654/supp-1Supplemental Information 1Click here for additional data file.


The canals are essential for agricultural irrigation, shipping and industry as important hydraulic infrastructure. In the seasonal freeze regions, the water conveyance canals are damaged due to the effects of freeze–thaw cycles. The freeze depth of soil in the water transfer canal varies considerably due to changes in temperature and water content. This paper compared the relationship of freeze depth, temperature and water content by field tests and numerical calculation methods by incorporating phase change. The results from present study showed that the decrease in temperature causes the water in the soil to freeze, the ice front migrated downwards, and the water in soil below ice front gradually migrated towards the ice front resulting in a large difference in water content of the soil before and after freezing. The Polyurethane insulation board + Concrete board slope structure (PC) as an insulation slope structure was proposed in this paper to mitigate the effect of freezing and thawing on the water conveyance canals. The freeze depth decreased significantly under the protective effect. In addition, this paper compared the anti-frost effect of different thicknesses of polyurethane insulation boards, and the results provided a reference for the anti-frost design of water conveyance canals. Different types of frozen soil cover the territory of China in which the total area of seasonally frozen soil is about 4.76 × 106 km2 accounting for about 49.6% of China’s territory2. Human engineering activities inevitably conduct in seasonal freeze regions as the society develops. For example, to solve the drought problems in northern seasonal freeze regions, water conveyance canals are usually built to transfer water from water-rich areas to arid areas. The soil in seasonal freeze regions shows the characteristics of freezing and thawing under the influence of temperature. The water conveyance canals built in the seasonal freeze regions are damaged by seepage and freeze–thaw as frost heave, hollow and collapse damage , the properties of soil , the groundwater table and the form of canals The aforementioned research focuses on the factors influencing the development of freeze in water conveyance canal projects in seasonal freeze regions, as well as the variation characteristics and preventative measures based on theory, model tests and numerical simulations. Although numerical calculations, as well as laboratory tests, have achieved numerous achievements in the study of hydrothermal characteristics of water conveyance canals, the accuracy of the results is questioned at times due to various assumptions and boundary conditions. The physical model developed in the laboratory is unable to fulfil the temporal and dimensional effects that affect the freeze in the canals. As for the laboratory model tests, although they provide a more realistic reflection of the effects of temperature and water on freeze, using just one method  is inadequate in determining the freezing characteristics of the canals.The present study examined the freezing behavior and anti-frost effects of canals of Hada Mountain Water Conservancy Project to provide information that ensures the stability and operational safety of water conveyance canals in such areas. This method solved the limitations of laboratory model tests that cannot meet the time and space scales of actual engineering. The general change law of the freezing behavior of water conveyance canals was also revealed. Finally, the numerical simulation which adequately considered the effects of ice-water phase changes was proposed to provide the important technical guidance for freeze prevention and the optimization design of anti-frost structures for water conveyance canals in seasonal freeze regions.The Hada mountain water conservancy project is located on the second mainstream of the Songhua River about 20 km from the southeast of Songyuan City, Jilin Province, China ; t0, t1 are the first and last day of the year when the temperature is below 0 °C (d); and T is the average daily temperature which is negative (°C).According to the statistics of meteorological data provided by Songyuan City Meteorological Service from 1971 to 2012 (41 years), the average freeze period is 123 days per year with the longest and shortest frozen periods as 146 days and 102 days respectively. Freezing has occurred from 22 October to 29 November and thawing has begun from 28 February to 31 March. The important index of coldness in a freeze–thaw cycle is the Freezing Index, which is a cumulative of negative daily average temperature (°C) during a freezing period and can be calculated based on Eq. ; t is the time (d); φ the initial phase, φ = 0.9.During 1971–2011, the The main canal length of the Hada mountain water conservancy project is 95.93 km. The canal cross-section is trapezoidal. The frost damage to the water conveyance canal under low temperature conditions is a serious problem, which threatens the safety of the project. The Polyurethane insulation board + Concrete board slope protection (PC) was designed to reduce the impact of frost damage on the water conveyance canal. The soil slope was used for the comparison of tests. The different forms of PC and soil slope are shown in Fig. To determine the characteristics of freeze depth and the effects of groundwater level on the slopes of the canal, 25 m test sections were established at three different locations  in the main canal of the Hada mountain water conservancy project. The freeze depth and groundwater level monitoring devices were installed at the top, middle and bottom of the slope as shown in Fig. The changes in groundwater level in the region and the freeze–thaw lines on the soil slopes between 2011 and 2012 are shown in Fig. 21. The main factor contributing to the difference was the effect of water content on the soil. The soil at the bottom of slope had a higher water content than soil at the top. The temperature at the bottom of the slope was relatively higher than that at the top because of the effect of latent heat of phase change in water and ice. Therefore, the freeze depth at the bottom was shallower than that of the top. The freeze depths were measured at the top of the slope when 5 cm and 6 cm Polyurethane insulation boards + Concrete board were used for slope protection. The freeze depths of the soil became shallower as the insulation boards became thicker as shown in Fig. The difference caused by the effects of temperature, wind speed, wind direction and external loads on the freeze depth for the same locations of soil was slightThe effect of water content on the freeze depth of soil was discussed in “22. Based on this theory, several numerical models of hydrothermal coupling have been proposed, and the problem of hydrothermal coupling of geotechnical engineering in cold regions has been successfully resolved. The study of hydrothermal coupling has been gradually developed and the application of hydrothermal coupling has been increasing recently. The following assumptions are made in the hydrothermal coupling model to improve the efficiency of the calculation23:The soil medium is a homogeneous isotropic pore medium consisting of unfrozen water, ice and soil skeleton which does not deform during the freezing process.Water migration in geotechnical medium without the contribution of air to water migration.The latent heat and heat transfer processes of water ice phase change is calculated.Seasonal freeze regions are affected by temperature and water freeze in soil causing frost damage. Philip and Devries first proposed the theory of hydrothermal coupling and proposed a nonlinear hydrothermal coupling model based on the principle of viscous fluid flow and heat balance in porous mediaThe modelling is carried out by temperature and water fields under the aforementioned assumptions and the different physical field control conditions are as follows:24. The Darcy’s Law interface contains an implementation of Darcy’s law by using the Storage Model node which explicitly includes an option to define the linearized storage S (1/Pa) using the compressibility of the fluid and the porous matrix25:Qm is a mass source representing the additional liquid water due to melting of the ice inclusion; ρ is the density of soil (kg/m3); t is time (s); p is the pressure (kPa); g is the acceleration of gravity (m/s2); μ is the dynamic viscosity (Pa∙s); κ is the hydraulic conductivity (m/s); S is the water transfer model calculated according to Eq. .e0 is the initial porosity ratio.The gravity term in Eq.  is negleSw depends on the phase change and can be calculated as shown in Eq.  is zero for temperature below the melting temperature; Tpc, and is equal to 1 for temperature above Tpc. It is assumed that the mushy ice zone extends from 0 to − 1 °C in the interfrost benchmark. Therefore, Tpc is set to − 0.5 °C and the transition interval of θ2 is defined as 1 K.When considering the ice-water phase change, the saturation of unfrozen water in the soil, n in Eq.  25.7\dock expressed in terms of saturation Sw can be calculated by Eq. (25.ks is the coefficient of permeability of saturated soil (m/s) and I is the impedance factor.The ice clogs porosity in the soil leading to a reduction in the porosity ratio considering the ice-water phase change which leads to a lower permeability of the soil. The d by Eq.  25.9\doc26:ρC)eq is the effective volumetric heat capacity at constant pressure; T is the temperature of the soil at different moments (°C); keq is the effective thermal conductivity (W/m·K); Q is a heat source (W/m3); Cw is the effective fluid’s heat capacity at constant pressure; u is the velocity field, either an analytic expression or computed from a Fluid Flow interface. It should be interpreted as the Darcy velocity i.e., the volume flow rate per unit cross sectional area.The differential equation for heat conduction in frozen soil is24. The temperature boundary condition as shown in Eq.  as shown in Fig. The maximum freeze depth distribution could be computed based on numerical model established in this paper. A thin layer boundary condition was used instead of the insulation board solid mesh for the convenience of modelling. The insulation board, as well as concrete material parameters, are shown in Table The results of the temperature field simulations are shown in Fig. Comparing the effect insulation board of different thicknesses on anti-frost, it showed that 5 cm and 6 cm insulation boards could significantly reduce the freeze depth. The effect of increasing the thickness of insulation boards on reducing the freeze depth did not change significantly. In actual engineering applications, increasing the thickness of the insulation boards is undoubtedly increase the cost of project, but the effect of improving insulation boards is not obvious. According to presented researches, the insulation boards with thicknesses of 5 cm and 6 cm could improve the anti-frost capacity of the slope. Regions with serious frost damage can refer to the research results of this paper and can appropriately increase the thickness of the insulation boards. Comparing the water content at maximum freeze depth showed that at the maximum freeze depth of the unprotected slope, the water content of the soil remained 11%, i.e. most of the water in soil was frozen. However, although the water content of soil with protective structures decreased, the unfrozen water content of the soil remained around 14.8%. The freezing action reduced and water at the maximum freeze depth cannot freeze sufficiently with the protection of the insulation boards.Under the protection of polyurethane insulation boards in the middle of the slope, the freeze depth was almost negligible and differed considerably from the actual situation. This was due to the simplification of boundary conditions in numerical calculations and the fact that external factors  were not considered in the calculation process. Therefore, the results obtained differed considerably from reality, but they still illustrated the usability of polyurethane boards in the design of anti-frost structures.29. The temperature changes dramatically from the ground surface to the maximum freeze depth—a process that directly affects the direction and intensity of water migration21. In this paper, the trend of soil freeze depth is summarized in Fig. In seasonal freeze regions, the water in soil freezes under the cold temperature30. For example, at different locations on the slopes, the freeze depth varies between shaded and sunny slopes32.The temperature at the surface in seasonal freeze regions varies widely depending on the seasons, resulting in differences in temperature from the surface to the maximum freeze depthThe freeze depth also varies as shown in Fig. The ice front gradually developed downwards as the temperature decreased, causing a decrease in the path of water migration which was beneficial for water migration. The water content of soil below the maximum freeze depth was less than the initial water content after the water froze to the maximum freeze depth which was inseparably related to water migration.The freeze depth of soil decreased significantly when polyurethane material was used for anti-frost protection, which was beneficial for the safety of canals. Comparing the anti-freeze effect of different thicknesses of insulation boards, it could be concluded that 5–6 cm thick insulation boards could significantly reduce the freeze depth by approximately 60 cm. The anti-freeze effect did not increase obviously when the insulation board was thicker than 6 cm.The thickness and temperature distribution of the frozen layer in seasonal frozen soil areas were the important factors influencing the damage of water conveyance canals. The polyurethane insulation boards precisely met the criteria to fulfil the requirements of increasing the heat entering into slope or reducing the heat diffusion of soil and reducing the freezing. Therefore, such materials have broad prospects for application in the prevention of freezing.This paper investigated the characteristics of temperature-freeze depth-water content of slope based on the combination of field tests and numerical simulations, and compared the effect of different thicknesses of polyurethane materials, the following conclusions are drawn:The results presented in this paper has provided important technical guidance for the implementation of frost prevention measures and the optimization design of an anti-frost structure on canals in freeze regions and can be applied to the design of water conveyance in seasonal freeze regions to determine proper insulation board thickness.


The usability of the system was tested by asking participants to fill standard system usability scales. Moreover, the effectiveness of the method was assessed by analyzing the total procedure time and the time spent with the instruments out of the field of view. The average system usability score overcame the threshold usually identified as the limit to assess good usability (average score = 73.25 > 68). The average total procedure time with the autonomous endoscope navigation was comparable with the classic control (p = 0.85 > 0.05), yet it significantly reduced the time out of the field of view (p = 0.022 < 0.05). Based on our findings, the autonomous endoscope improves the usability of the surgical system, and it has the potential to be an additional and customizable tool for the surgeon that can always take control of the endoscope or leave it to move autonomously.Robots for minimally invasive surgery introduce many advantages, but still require the surgeon to alternatively control the surgical instruments and the endoscope. This work aims at providing autonomous navigation of the endoscope during a surgical procedure. The autonomous endoscope motion was based on kinematic tracking of the surgical instruments and integrated with the da Vinci Research Kit. A preclinical usability study was conducted by 10 urologists. They carried out an  While new generations of robot-assisted surgical systems approach the market , robot autonomy is still away from clinical application . Modern Many current research lines are oriented toward increasing the level of robot autonomy to assist surgeons and to help in reducing their workload, especially for trivial but time-consuming tasks. Pandya et al. identified endoscope control as a near-term development for automation in surgical robotics . In a ge®, Computer Motion Inc., Santa Barbara, CA, USA)   autonomoCA, USA) . The Autthe user . In somethe user .ex vivo realistic experiments have been carried out on this topic yet. Animal ex vivo models have been extensively tested and validated through the years for the simulation of various urological procedures  with tracts of either the esophagus or rectum  of the “Shell” technique  Bowel segment selection, distension, and measurement.ii) Segment separation through stapling.iii) Lateral ileal–ileal anastomosis.iv) Anastomosis between the urethra and the middle section of the segment.v) Detubularization of the segment.vi) Neobladder plication and suturing.vii) Ureteroileal anastomosis.Even though this surgical procedure has been proposed in many variants throughout the years, a comprehensive outline can be summarized by the following steps:A video representation of the full “Shell” technique we aimed at reproducing can be found at i) Distension and measurement—Surgeons were asked, as a first step, to manipulate the bowel until maximum distension was reached, and to measure its total length with a standard surgical flexible scale ; particiv) Detubularization—Since electrocautery was not available at the testing facility, participants were asked to mark the distended bowel sample with a dermographic pen moving along the same detubularization path they would have followed with the actual electrocautery. A special custom-made support was realized to allow the da Vinci Large Needle Driver® to firmly hold a dermographic tip . Immediavi) Plication and suturing—Finally, two 15-cm-long Monocryl® 3–0 UR-6 sutures were used to perform a standardized neobladder plication and suturing with eight passages for the posterior plate, three for the neobladder neck, and five for the anterior plate performing a simplified shell-type reconstruction .For the experiment, we selected three of the neobladder reconstruction steps  to be reproduced by using small tracts of pig bowels. The bowel segment selection step  was removed from (i) to reduce the amount of animal tissue wasted during each experiment and the potential variability in the resulting neobladder dimensions due to incorrect measurements. The same logistical and ethical concerns lead to the decision of removing the segment separation (ii) and the ileal–ileal anastomosis (iii) steps to avoid unnecessary use of disposable stapler cartridges. Steps (iv) and (vii) were removed because they would have involved other organs farther than the bowel. As a result, the surgeon was provided directly with a standardized, precut, 30-cm-long pig bowel tract that was mechanically presealed at the two extremities and partially filled with saline solution to simulate the semifull bowel consistency. The presealed pig bowel sample was therefore presented lying in a folded configuration to simulate a random configuration inside the peritoneal cavity .i) DisteA video showing the entire procedure carried out by the surgeons during the experiment can be found in the ® . The platform is composed of a patient side, featuring mainly the robotic arms mounting the surgical instruments, and a surgeon console integrated with interfaces for controlling the patient side. In particular, the patient side is composed of four robotic arms: up to three patient side manipulators (PSMs), mounting the interchangeable surgical instruments used to perform different procedures on the patients, and the endoscopic camera manipulator (ECM), holding the full HD stereo endoscope. All the robotic arms composing the patient side are linked together through a closed kinematic chain composed of the setup joints (SUJs), a series of links and passive joints that allow registration through direct kinematics of all the robotic arms with respect to the same reference frame  both in a virtual reality training scenario  and in di) Single instrument modality—The field of view is constantly maintained centered on the right surgical instrument , and the distance between the endoscope tip and the instrument is maintained constant, resulting in a consistent magnification of the scene. Fixed parameters such as the lateral offset of the tool with respect to the center of the field of view and the amount of magnification can be preoperatively customized depending on the preference of the surgeon.The key design principles of the SCAN were to guarantee an adequate viewpoint throughout the procedure, as well as good usability and intuitiveness of the system. In general, the system can continuously compute the surgical instrument poses and move the endoscope accordingly, resulting in an ongoing adjustment of the field of view. Intraoperatively, the surgeon is able to switch between two different navigation modalities by pressing a foot pedal on the surgeon console, as can be seen in This modality was modeled by the following equations:base). x is the endoscope newly computed focal axis, obtained from RIGHT_INST, i.e., the right surgical instrument end-effector position  and RCM_endo, the position of the endoscope remote center of motion. ENDO is the newly computed desired endoscope tip position, and zmin is the zooming factor, customizable by the user. For this experiment, the value of z was 0.05 m < zmin < 0.15 m (fixed for each surgeon). Note that the newly computed endoscope position always belongs to the segment connecting the instrument end-effector and the endoscope remote center of motion. All the terms composing the equations can be found in ii) Midpoint modality of the intruments—The field of view is centered on the midpoint of the two surgical instruments, and the magnification of the scene is dependent on the relative distance between the m. This is for maintaining both the instruments inside the field of view of the surgeon and for providing the surgeon with the possibility to modify the image magnification intraoperatively. When the tools are closer to each other, the endoscope moves closer to them . When the tools are far away from each other, the endoscope moves in the opposite direction, resulting in a wide view over the scene . MinimumIn the equations, the vectors are in bold, and they are all expressed with respect to the same reference frame  was computed from RIGT_INST and LEFT_INST, the positions of the right and the left surgical instruments, respectively. ENDO, the endoscope desired position, was a function of zmin = 0.1m, zMAX = 0.1 m, and dMAX = 0.2m, which are the minimum/maximum zoom allowed and the maximum distance between the tools, respectively. These values were set to match the task workspace, but preoperatively, the surgeon had the possibility to customize them. x again is the camera new focal axis. Even in this case, the endoscope position always belongs to the segment connecting the SC and the remote center of motion. All the terms composing the equations can be found in Once again, in the above equations, the vectors are in bold, and they are all expressed with respect to Fendo) were computed as z = [1 0 0]′, y = z × x, and later normalized as z = x × y.In both the modalities, the y and z components of the endoscope frame . The desired autonomous navigation modality can be reactivated by means of another pedal.The user study involved 12 medical doctors see  affiliatConsidering, in general, the high variability in style between surgeons, and specifically the diverse level of expertise in our sampled population, we decided to have each surgeon perform the neobladder reconstruction twice, once using manual and once using autonomous endoscope control. This redundant acquisition allowed us to evaluate the influence of the autonomous control modality  at the individual level and, therefore, independently from the level of expertise of the surgeon. The order in which users performed the task undergoing manual or autonomous endoscope navigation was randomized with permuted block randomization. This adjustment was intended to compensate for the potential learning and fatigue effects connected to repeating the same procedure over a short period of time. Participants were explicitly requested to interrupt the autonomous navigation only if the SCAN was providing a suboptimal viewpoint.System usability scale section) was completed to derive a qualitative assessment and usability estimate of the system.One of the technical investigators played as assistant to constantly monitor the operating field interacting with the surgeon to timely provide the required external tools  or adjustments . Finally, a post-experiment survey , and all the subjects gave informed consent according to the declaration of Helsinki.The user study took place at the Leonardo Robotics Laboratory of Politecnico di Milano in September 2020. All the To evaluate the system for autonomous endoscope navigation, we considered both the performance of the user related to the execution of the experiment and their posterior feedback about the usability of the system. The metrics we investigated were the (i) total execution time (t_tot) spent by each user in performing the experimental version of the orthotopic neobladder reconstruction; (ii) the time out of the field of view (t_out_FoV), which means the cumulative time with at least one of two tools out of the endoscope field of view  while carrying out the procedure ; (iii) tThe total execution time and the time out of the field of view in both the endoscope modalities (classic endoscope manipulation vs. autonomous endoscope navigation) were analyzed by using the Wilcoxon Rank Sum statistical test to assess significant differences.This section reports the results from the 10 users  who completed the study. Their details are shown in the upper part of p = 0.85, average t_tot_M = 34 ± 13min vs. average t_tot_A = 33 ± 12min).The total execution time (t_tot) for the neobladder reconstruction is shown in the second block of If we group the users into three clusters , we can notice how the major benefit in terms of total execution time was gained by the less experienced classes, i.e., the residents and the fellows. In fact, the average time improvement from the manual to the autonomous modality was equal to 1 min and 49 s for the residents and 1 min and 41 s for the fellows. On the other side, the attendings underwent an average time loss of 2 min and 44 s when using the autonomous endoscope.p = 0.022).The time out of the field of view (t_out_FoV) for the neobladder reconstruction is shown in the third block of By considering the specialization groups introduced in the previous section , the average influence of the autonomous endoscope control on the time out of the field of view was more remarkable for the residents .The System Usability Scale (SUS) outcomes of our system for autonomous endoscope navigation are shown in the bottom block of A well-defined trend can be observed if considering the specialization groups . The average SUS score was 91% if considering the residents, 73% if considering the fellows, and 57% if considering the attendings.ex vivo orthotopic neobladder reconstruction.In this study, we investigated the usability and performance of an autonomous endoscope navigation system, the SCAN, during The average time out of the field of view was reduced while undergoing autonomous endoscope motion. This is in line with the functioning principle of the SCAN as well as with the results obtained in our previous works , showingWe also found a reduction in the average total execution time for residents and fellows undergoing autonomous endoscope navigation, yet such a reduction was not statistically significant at the group level. The high variability in the overall total execution time , as well as the small sample size of the population under investigation, could be the major explanation of this lack of statistical significance.This study was designed to primarily investigate the feasibility and the usability of our system in a surgically relevant scenario. The most relevant outcome in this regard is represented by the average score from the system usability scale that overcame the usability threshold (74%) .Some remarkable trends can be derived from the clusterization of users according to their level of expertise . The surgical residents were the ones who benefited the most from the autonomous navigation system of the endoscope and the ones who gave the highest rate to its usability. Such a negative correlation between the operating room experience and our objective and subjective metrics could be related to the existence of a know-how bias. In other words, the habit of using manual navigation of the endoscope in everyday surgical practice plays a relevant role in the acceptance and the effects of a novel control like the autonomous endoscope navigation. To sum up, the results led to a twofold consideration: on the one side, the low usability (SUS) score for the more experienced surgeons can be linked to their already well-accustomed and rooted proficiency with the manual endoscope control, which might make the SCAN system feel as a disruption of the traditional robot-assisted surgery workflow. On the other side, young or early career surgeons, since they are the ones who performed less interventions and received less training in traditional robotic surgery, might be the ones not only adapting more smoothly to the new technology, but also benefiting the most from it.Nevertheless, SCAN represents a proof of concept for the integration of autonomous endoscope navigation in robotic surgery, and the very final goal is not substituting the current navigation modality, but rather proposing an additional aid to the surgeon. This way, autonomous robotics can enter the operating room as a collaborative tool that the surgeon gets the assistance of, just if desired, and always maintaining full supervision over it.Even though this work presented a first feasibility study on a urological scenario, the SCAN technology is still far from the standards required in an operating room. Several limitations of this study and possible future implementations can be highlighted.The autonomous navigation algorithm tested shown a potential for future clinical applications, yet we tested, in a surgically relevant scenario, only two navigation modalities and some basic forms of user parameter customization. A more tailored yet flexible system, based not only on the initial preferences but also on the intraoperative selections of the surgeon, combined with an improved user interface, could bring autonomous surgical assistance to the next level.The surgical procedure was a simplified version of the clinical orthotopic neobladder reconstruction where many steps have been removed in order to optimize the waste of resources and the quick regeneration of the setup in case of subsequent data acquisitions. Future improvement of the setup will involve integrating the procedural missing steps to achieve full consistency with the real procedure.The overall study, exploratory in its nature, aimed at further understanding the potentialities of a semi-autonomous control system and how differently skilled surgeons reacted to a major change in the robotic-assisted surgery teleoperation workflow. We understood that different experience levels have a strong and multifactorial influence on the outcomes of our investigation. Consequently, this highly variable skill level adding up to the relatively small user sample size might have reduced the statistical power of our tests. A larger sample size in parallel to a specific focus on a skill target could be the key ingredients for the success of future investigations. Furthermore, neither a comprehensive quantitative performance assessment nor a full validation of the proposed experimental setup was in the objectives of this work.A more structured data acquisition protocol and further evaluation of the reconstructed neobladders (by one or more experts) can yield more salient insights on the advantages (or disadvantages) introduced by semi-autonomous endoscope navigation systems in the robotic surgery workflow.This work deals with the optimization of the surgical workflow by means of robotic assistance. Specifically, we introduce the SCAN, a system for autonomous endoscope navigation, and we report its testing in a urological scenario (ex-vivo orthotopic neobladder reconstruction). The feedback from 10 urologists (with heterogeneous experience) showed promising results in terms of usability of the system. Performance improved for resident and fellow (but not for attending) surgeons resulting in an average task completion time reduction when undergoing autonomous endoscope control.To conclude, our system for autonomous endoscope navigation can improve the standard framework of manual camera control by optimizing the surgical workflow. Additionally, our framework has the potential to leave freedom to the surgeons about the activation of autonomous navigation in alternative to the classic manual control, leaving them in power over the control modality and giving them the possibility to customize the autonomous navigation as needed. Moving from interviews with clinicians and further usability studies, future work can investigate the addition of novel modalities of autonomous control that can be selected according to the surgical task.


In order to use the microwave to measure the dielectric constant of the human body and improve the measurement resolution, a small near-field probe working at 915 MHz is designed in this paper.Based on the electric small loop antenna model loaded by the spiral resonator (SR), a small near-field probe was designed. The probe model is designed and optimized by the HFSS (high frequency structure simulator) software. The human tissues were tested by the manufactured probe and the relationship between the S11 parameters of the probe and the human tissues was analyzed.A probe with small size was designed and fabricated, with the overall size of 10.0 mm × 12.0 mm × 0.8 mm. The probe has a good performance with a 30.7 dB return loss, a 20 MHz bandwidth at the resonance point, and a distance resolution of 10 mm. Due to the small size and good resolution of the probe, it can be used in the measurement of human tissues. The human body is composed of a variety of biological tissues, such as skin, fat, muscle, etc. The dielectric properties are inherent property of biological tissues. Physiological changes of the water content, protein content, types and cell structure of biological tissues will lead to changes in its dielectric properties. A large number of studies have shown that the dielectric properties of different types of biological tissues are different, and the dielectric properties between normal tissues and diseased tissues are also quite different , 2.As a new type of physiological signal detection method, microwave has a broad application prospect in the fields of medicine and biology. Researches on dielectric property of tissues is the key to the development of an accurate microwave-based anomaly detection systems . The opeIn general, we cannot directly measure the dielectric properties of human body, but we can use the probes to measure other parameters of the human body to obtain the dielectric properties indirectly . S11 parAt present, there are three main types of dielectric constant measurement methods commonly used: resonance method, short-circuit waveguide method and reflection method. Microwave-resonance method  and shorThe probe design in this paper is based on the reflection method, which is combined with a resonator . Figure In this paper, a high-resolution probe operating at 915 MHz is designed and fabricated, which is based on an electric small loop antenna loaded with a circular spiral resonator. The probe has the following novelties and development prospects: (1) probe’s working frequency can be adjusted by modifying the resonator coil parameters and matching capacitor parameters. Unable elements such as varactor diodes can also be loaded on the structure to make a frequency adjustable probe. (2) In the measurement, the probe can be located at a certain distance above the skin surface, which can avoid direct contact with the human body and the influence of pressure on the measurement results. (3) The probe adopts a planar circuit structure, which is easy to integrate with other planar circuits (such as microstrip lines and coplanar waveguides), and has great application prospects. The human tissues were measured by the designed probe. The HFSS simulation model of the probe is given, and the mediators simulation is carried out. The consistency between the simulated and measured results proves that the designed probe can be applied to the measurement of human tissues.C1 and C2) to match the probe to the feeding 50-Ω line. The capacitance values of C1 and C2 are 10 pF and 25 pF, respectively. Unlike most resonators used for near-field imaging in the past, the probe designed in this article uses only one port to power supply.The fabricated probe is shown in Fig. The experimental system for measuring human tissues is shown in Fig. When the probe is connected to the VNA without placing any objects under it, the S11 parameter of the probe can be obtained on the VNA as shown in Fig. The tissues were measured by the measurement system shown in Fig. It is difficult to directly measure each tissue layer of human body by probe. In order to verify that the probe can be used to measure the dielectric constant change of human tissue, pork was selected as the measurement object, which is similar to human tissue structure. The skin, fat and muscle of pork were measured, respectively, with the probe, and the S11 parameters were obtained as shown in Fig. In order to obtain the relationship between the probe S11 parameter and the dielectric constant of the tissue more intuitively, the resonant frequencies of the probe in each tissue and the dielectric constants of the probe in each resonant frequency  are listed in Table It can be seen from the table that the resonant frequency of the probe decreases with the increase of the dielectric constant of the biological tissue, which verifies that the designed probe can be applied to the measurement of different biological tissues.In order to verify that the probe can be used to measure the thickness change of human tissues and to verify the resolution of the probe, the finger pulp of the human body is selected as the measurement object. Take six points from the edge of the finger pulp to the center of the finger pulp at 1 mm intervals Fig. a.Fig. 6aAn ultrasound probe was used to measure the thickness of the tissue at each point of the finger pulp, and the fabricated probe was used to measure the S11 parameter at each point. In order to obtain more accurate results, three repeated experiments were carried out, and the maximum resonant frequency of each measuring point was selected. The relationship between the resonant frequency of the probe and the thickness of the finger tissue was obtained as shown in Fig. It can be seen from the figure that the resonant frequency of the probe decreases as the thickness of the finger pulp increases, which verifies that the designed probe can be applied to measure the thickness of human tissues.In order to verify that the probe can be used to measure abnormal nodules in human tissues, a nodule on human skin is selected as the measurement object Fig. a. The noIn order to verify the consistency between the experimental results and the theory, a probe for measuring human tissue model is established in HFSS Fig. . The proIn order to obtain the theoretical results of measuring different biological tissues by the probe and compare with the experimental results, the relative permittivity of the human tissue layer was set to 5, 45 and 55 for simulation. The S11 parameters are shown in Fig. It can be seen from the figure that the resonant frequency of the probe decreases as the dielectric constant of the human tissue layer increases, which is consistent with the measurement results in Fig. In order to obtain the theoretical results of measuring different thicknesses of human tissues by the probe and compare with the experimental results, the dielectric constant of the human tissue layer is set to 40 and remains unchanged, and the thickness is set to 1 mm, 2 mm and 3 mm for simulation. The thickness increased from 1 to 5 mm with 1 mm intervals. The S11 parameters are shown in Fig. It can be seen from the figure that the resonant frequency of the probe decreases as the thickness of human tissue increases, which is consistent with the measurement results in Fig. In order to obtain the theoretical results of the probe measuring human nodules and compare them with the experimental results, a hemispherical nodule with a diameter of 9 mm is established in the human tissue layer Fig. a. The diIt can be seen from the figure that when the human body has abnormal nodules with a dielectric constant 30–50% larger than normal tissues, the resonance frequency of the probe is reduced by 10–13 MHz, which is consistent with the measurement results in Fig. According to the experimental and simulation results, when the dielectric properties and thickness of the measured biological tissues change, the S11 parameters of the probe have regular changes; when nodule appears on the surface of the human body, the resonance frequency of the probe changes significantly. The consistency of the simulation and experimental measurement results proves that the designed probe has practical application value. The error is due to the fact that the dielectric constant of the tissue in this paper is a reference value rather than an accurate value. The probe will be calibrated subsequently. After calibration, the dielectric constant will be inversely calculated and the human tissue can be accurately measured.At present, there have been some studies on the electrical characteristics of acupoints . Based oA near-field probe antenna loaded with a circular SR is designed. The resonant frequency of the probe is 915 MHz. In order to verify that the probe can be used to measure the dielectric properties of human tissues, the fabricated probe is used to measure pork, human fingers and special nodules. When the dielectric properties and thickness of the measured object change, the S11 parameters of the antenna have obvious regular changes. The probe model is established by HFSS, and the influence of the change of the dielectric properties of human tissues on its S11 parameters is also simulated and analyzed. The consistency between the simulation and the experimental measurement results proves that the designed probe has practical application value.Due to the small size and good resolution of the probe, it can be used in the measurement of human tissues with different thicknesses and abnormal nodules, and can also be used in the diagnosis of traditional Chinese medicine acupoints. It is worth noting that the designed probe is suitable for flat and relatively uniform human tissues, such as limbs and abdomen. It is not suitable for parts with complex structures or obvious protrusions, such as joints. A flexible and stretchable antenna for bio-integrated electronics  has beenThe probe design in this paper is based on the reflective sensor, which is combined with a resonator. The SR is used as the resonant structure of the probe because it could provide a higher miniaturization rate compared to other resonant structures. For example, with the same number of turns and side length, the SR would resonate at lower frequency compared to the SRR . In addiZin is the equivalent impedance of the model, X is the equivalent impedance of the SR loaded loop, C0 represents the stray capacitance between the loop and the SR, L0 represents the inductance of loop, LSR represents the inductance of the SR, R represents the ohmic losses in the loop and SR conductors, the dielectric loss and stray capacitance between the SR loop turns are modeled by the lumped elements R0 and CSR, respectively. By changing the parameters of C1 and C2, the probe can obtain impedance matching at the best operating frequency.According to the principle of loop antenna and spiral resonator theory, the simulation model of loop resonant antenna is established, which reduces the probe size and improves the spatial resolution. The equivalent circuit of the model is shown in Fig. C1 and C2) at the opening of the loop antenna.Based on this, a simulation model is established in HFSS, as shown in Fig. In antenna design, S11 parameters are usually used to reflect the matching characteristics of the antenna. The relationship between S11 and input impedance is:In this paper, S11 is simulated by HFSS. The specific size of the probe and the matching capacitance value are adjusted to make the value of the S11 parameter at the resonance point as small as possible, and finally adjust the probe to the best matching state.According to FCC regulations on the ISM band, 433 MHz, 915 MHz and 2450 MHz can be used in the medical applications. According to the relationship between frequency and wavelength and the relationship between wavelength and penetration depth, electromagnetic waves of different frequencies penetrate human tissues at different depths. According to the principle of microwave propagation, the higher the frequency, the weaker the penetration of the probe. The probe designed in this paper is used for abnormal measurement of subcutaneous tissues and acupoints. Therefore, the working frequency of the probe is set to 915 MHz.According to the application requirements of traditional Chinese medicine (TCM) acupoint detection, the resolution of the probe designed in this paper should not be greater than 10 mm, so the width of the substrate of the probe is set to 10 mm. The diameter of the loop antenna should be smaller than the width of the substrate, so the diameter of the loop antenna in the probe design is set to 8 mm. In order to facilitate the welding of the 0402 capacitance in the matching circuit, the width of the loop antenna w1 is set to 0.5 mm.L and C are the effective inductance and capacitance of SR. Some of the most important parameters that can affect the resonant frequency of the SR are the width and the number of turns [After determining the outer dimensions of the probe and the size of the loop antenna, the parameters of the SR are discussed. The resonant frequency of the SR is given byof turns . These p2 of the SR is increased from 0.1 mm to 0.3 mm at an interval of 0.05 mm. The variation of the S11 parameter of the antenna is shown in Fig. The width wConsidering that the minimum width of the copper wire in actual production is about 8 mil, the width of the SR is selected as 0.2 mm. The number of turns of the SR is selected as seven circles.C1  =  10 pF, C2  =  25 pF, the resonant point of the probe is the most ideal, and the resonant frequency is closest to 915 MHz. The resonant frequency is 914 MHz with the − 10 dB bandwidth of 10 MHz which covers the required 915 MHz operating frequency.In order to make the resonant frequency of the probe reach the required 915 MHz, a matching circuit is added to the probe to optimize the resonant frequency of the probe. Through simulation optimization (Fig. The comparison of S11 parameters between simulation and measurement is shown in Fig.


In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constitutive laws we formulate a general criterion for the existence of infinitely many weak solutions which reflect the turbulent mixing of the two fluids. Our criterion can be verified in the case that initially the fluids are at rest and separated by a flat interface with the heavier one being above the lighter one—the classical configuration giving rise to the Rayleigh–Taylor instability. We construct specific examples when the Atwood number is in the ultra high range, for which the zone in which the mixing occurs grows quadratically in time. We study the mixing of two different density perfect incompressible fluids subject to gravity, when the heavier fluid is on top. In this setting an instability known as the Rayleigh–Taylor instability forms on the interface between the fluids which eventually evolves into turbulent mixing. For an overview of the investigation of this phenomenon originating in the work of Rayleigh  in 1883 T). Here The mathematical model (see for example Section 6.4 of ) is giveMore precisely, we consider  togetherRayleigh  and for entclass1pt{minimaIn the spirit of the results by De Lellis and the 3rd author , 17, forFor (i)(ii)(iii)B contained in for any open ball Let  problem , 1.3) h h\documeFor the precise definition of weak admissible solutions we refer to Definitions t shows similarities to the conservation law appearing in Otto’s relaxation for the incompressible porous media equation [We would like to point out that the infinitely many weak solutions differ only in their turbulent fine structure, while they all have a continuous coarse grained density profile equation . FurtherThe condition that the density ratio A higher Atwood number implies higher turbulence, and compared to the low Atwood regime, one can not use the Boussinesq approximation  We note that up to our knowledge, our result is the first rigorous result leading to existence of weak solutions with quadratic growth in time for the mixing zone. It is also of interest that both numerical simulations and physical experiments predict a growth rate of the mixing zone like t}A see , 18, 25), 25\docuIn future work we plan to further study the possibility of constructing solutions with different mixing zone growth rates, to investigate the optimality of the growth rates Concerning convex integration as a tool in the investigation of unstable interface problems we have already mentioned the papers , 33, 34.Another classical instability in fluid dynamics is the Kelvin–Helmholtz instability generated by vortex sheet initial data. Regarding this instability solutions with linearly growing mixing zone have been constructed in  based onThere have also been some recent convex integration results for the compressible Euler , 20, 21 The paper is organized as follows: in Section x, t) due to the prescribed energy density function.In Section In Section In Section Let equation  on \docuWeak solutions) Let  A weak solution  of  with \doy system  while por system  and the tions to  in the fSubsolutions) Let e and the initial data P is a distribution, z solves (v is weakly divergence-free (including the weak no-flux boundary condition), The second to last two statements justify to call (b) The result carries over to the three- or higher-dimensional case by constructing suitable potentials analoguosly to , which iP is a weak solution of the linear system e.(c) We will see later that the open set tions of  and defiOur second main result addresses the construction of subsolutions associated with the initial data . ClearlyRayleigh–Taylor subsolution) We call a subsolution z of  associated with the original system . . findingn components of We begin with the construction of plane wave-like solutions to  which arution of . In LemmRecall the projection operator fined in .(i)(ii)(iii)There exists )solving  and satiWe will only present the proof in the two-dimensional case, higher dimensions can be handled analogously to .We start by observing that for any smooth functions ) solves .Let Case 1:Note that in this case we also have We then setd, using , one hasle as in , 16). WeCase 2:In this case we are not allowed to oscillate in time. However, we have er hand,  implies tance in , Remark It can be checked through direct calculation that for any smooth function ) solves .S as before, we obtain thatNow, if we consider ows from  that sete, using , we get\If o solves . Therefond using , we get We now turn to the set of pointwise constraints fined in . The \doz′), see  for morex, t) dependence of the sets For the computation of the hull we drop the For any pair (ii)The Muskat directions (iii)t.For (iv)It holds that (i) This basically has been shown in . We noneM(z) is invariant along the line segment in Muskat direction. PluggingM(z) leads us toNext K can be connected with a K).As a corollary, we obtain that any two points in For any In the case Since how that  holds foIf Recall the definition of S0n×n in .e, n and hence compact. Moreover, for every The projection n. Let M(z) can be rewritten toM(z). Therefore M(z) are both uniformly bounded. Consequently We first prove that ualities  imply thNext we show that any If ly as in  a suitabThe same reasoning applies also to the case Now let From now on we consider the remaining case Let us assume M(z) is diagonal with entries Now we need to guarantee that Furthermore, the last condition needed for Now we have all ingredients for the proof of q-component compact set K. The inclusion Lemma ets, cf. , Lemma 4U is contained in a sufficiently long admissible line segment, similarly to Section 4.3 from [In this subsection we prove that any element from 4.3 from . We recafined in . We haved denotes the Euclidian distance on For any Z spanned by K, that is there exist We proceed as in the proof of Lemma 4.7 from . Since \K, and respectively the inequalities in U do not involve the pressure, this can be done such that Furthermore, since we have We now go back to the fined in . We havefined in , given tLet The proof of Lemma for any for any Then Suppose See . \documen.Fix LetWe defineFurthermore, from  it folloDue to the symmetry of this construction, one can similarly prove that for any e is bounded. The boundedness of In this section we conclude the proof of Theorem We introduce the notion of subsolution associated with , 3.6). . 3.6). TWe say that ution of  associatution of  in the sWe have the following convex integration result:Suppose that there exists a subsolution z:D→Z of  which coThe proof is similar to those in , 33, theThe main building block of the proof is the following perturbation lemma.z such thatSuppose that there exists a subsolution To prove Lemma Let y and z, and some Fix From here on the proof is the same as Step 2 of the proof of Lemma 2.4 from [Using Lemma  solving  such thamentclasspt{minimaX denote the closure of e it follows that X is metrizable, denote its metric by Letution of .X. Indeed, settingX and that We observe that the functional X. We claim that for any I is continuous at J is continuous with respect to the strong It follows from the Baire category theorem that the setX.Since B be an open ball contained in X and has empty interior, since X, as is The proof of the mixing property  follows In order to prove our convex integration result for  we applyNow let ution of  with somution of  with theution of  to a solution of .Furthermore, for a given function fined in  translatfined in . Similarfined in ,2.4). S. S\documWe have now all pieces together to prove our main result.z gives us a weak solution of  i i\documeproperty , as wellOne may then transfer these conclusions to the setting of Theorem Let us now briefly explain how to establish the admissibility of the obtained solutions, provided that rk as in , 17 one initions , 2.7)..\documenHowever this does not yet allow us to conclude the admissibility of the induced solutions, since the differenceu replaced by We now turn to the construction of Rayleigh–Taylor subsolutions. We start by observing that the relaxation inside the mixing zone z)) from  with u rf, it suffices to set Indeed, in order to see this, given a subsolution e, such that  vanishes. In consequence inequality  of (6.6equality  reduces ualities  are autofined in .G is uniformly strictly convex and to assure the admissibility (Therefore, all that remains to do in order to finish the construction of RT-subsolutions is to find sibility  (in a stl energy .e is continuious across Denotingsibility  in the sInspired by the known families of subsolutions for the Muskat problem  or the KDenote by ality in  for any e defined via (We now turn to the perturbation. Let ined via  to be coWe will look for asymptotic expansions of the associated By integration by parts we rewriteFinally, to conclude the proof of Theorem Let us first prove the second statement. The case It remains to compute the precise growth rates of the mixing zone given in . ObserveWe would like to point out that the condition The independence of ion from , 34, wheion from . Our inte across e in each of the three pieces The continuity of Finally, we would like to state further properties than those of the growth rates of the unperturbed “subsolution” associated with e defined in (Furthermore, we summarize the other ansatzes used during our construction and note that they can all be seen as not too restrictive for different reasons:fined in , inside fined in  inside \fined in . Here wefined in  with equ


We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time. An interesting problem in the field of modeling of biological processes  has beenBasically, after a gene is activated at a random time moment, mature mRNA is produced in the nucleus, then it is transported to the cytoplasm, where the protein translation follows. However, it is known that translated mRNA molecules must get through further processing first, before a new protein particle is formed. Besides that, many sources  claim ths (PDMP) . This cls (PDMP)  or 16]..5′ end ts (PDMP)  and for ase (see ), we jusA consequence of the stochastic expression is the diversity of the population in terms of the composition of individual proteins and gene expression profiles . StochasThis work is organized as follows. In In this paper, we investigate a model which is based on IFS with place-dependent probabilities. Compared to the model presented in , we replGene expression is a very complex biological process including multiple essential subprocesses. In the continuous case, Lipniacki et al.  introducLet The difference equation then could be given by equation of the following kind:R, C, and P will be independent of Thus, our approach is based on particular translation rate see . Providef δ, see . Here γ with the values of parameters Please note that this formula is valid for any In the If we assume that Remark 1.We assumed that i is constant, but important is to explain the way our process behaves after the next switch.For the purpose of calculation of If (3) hold and We can extend this formula from Using the formula (7) we denote bysee also . For theAfter substituting f be a function defined on the set of non-negative integers Let ion from  we invesx which means that after small fixed natural time B be a Borel subset of Let For any Please note that Hence, by taking Therefore,(see 1.7 ), but inDefinition 1.We define life-span function by the following formula:where Hence, instead of he paper ), we jusIn this subsection we introduce basic characteristics of the Markov process represented by the system (4) that will be needed for further considerations. Here, we assume that The explicit expressions for the solutions is known  that sucThe technical proof of this fact, which is based on the usage of formulas (7), is omitted. In the fourth chapter, we introduce Iterated Function Systems to investigate the existence of invariant measure and its support.For We can reformulate then the system (12) in the formThe family We can see thatHence the mapping Definition 2.Let K such that The transformation del from . We willRemark 2.In the paper  it was sric, see .Another way to generate some fractal objects was presented by Barnsley in . The setIn this section, similarly to the paper , we provx to B is defined byB. We can define the mappingT is a Markov operator on space of the bounded Borel measurable real-valued functions (which forms the Banach space with the supremum norm). Then If X of the process is transformed in one step. Here, the operators x to Borel subset P provides the following interpretation. We have f is a bounded Borel measurable real-valued function.We define the operator ely  to descHence, X obtained by a family of randomly iterating Lipschitz maps i the probability of choosing map X have compact closure.Sets of finite diameter in i the mappings x and y, (for details see paper [For any ee paper ).i the mappings For every In this section we assume that cal work , BarnsleUnder these assumptions, the Markov process see also , p. 372)Theorem 1.Let Then the Markov process To illustrate this theorem, we will investigate transition probability in the case of the stochastic process i to the state Each jump transformation Please note that Let Please note that Assume now that the initial distribution of the process K such that In this section we assume that tchinson  states tTheorem 2.Consider the stochastic process where d is the Euclidean distance in Proof. K in the Hausdorff metric uniformly when For any set viii) of  it folloK is an invariant set for this process.Moreover, if Remark 3.Let the book , we willAfter time This process evolves with respect to the points obtained by the solution (12) with given value of i until time of the next jump Hence, Also, Hence, Let Therefore, where Now we will gather all the facts about the process Definition of the process1. Denote the state space 2. Outcome (A)Outcome (B)Outcome (A) and (B)t.According to the reaction scheme Consider the simplified version of this system (12) with 3. Let 4. In addition, let 5. From now, by 6. Let 7. Here, 8. 9. With an analogy to the description in the book , we defi10. We say that 11. X again, but with new initial conditions being equal to i till time of the next jump After time 12. From the definition of the process Summary of the properties of the processK independent from the probability distribution. In addition, if K is invariant. It is worth noting that the life-span function of the process is equal to udied in .To visualize the behavior of the stochastic process (4), we performed stochastic simulation of the process . The codWe consider the system which simplifies both systems (1) and (6), namely (12):In the case of Remark 4.Let us observe that if we consider only integer values of t then the attractor generated by the composition of the systems (36) is a discrete set  we getIf ous case , therefoTaking as the initial points Please note that both sets are symmetric to each other with respect to the point i are sufficient to get to any arbitrary point in Now we are going to describe the attractor We will start with description of the set, which we can reach in two changes of We can assume that LetThe set Equivalently using the Equation (46) we get an alternative formula for the set In the light of Equation (43), descriptions (48) and (51) are equivalent. Analogically to the description of (48), we provide a plot of an attractor in the case of description (50).For the geometric reasons two Formulas (48) and (50) describe the same set f is a local diffeomorphism. Hence Now, let he paper  we provei was switched only once. The set (1)after more than two switches the trajectories of the process do not leave (2)we cannot find any invariant subset es as in , (pp. 31Hence set We developed a model of gene expression using IFS with place-dependent probabilities. As a novelty, in this paper, we introduced new formulas for life-span functions, suitable for discrete case. Moreover, we have shown that asymptotic behavior of the model is in line with the results presented in the paper . We have