Based on the database, under uniaxial compressive stress tests and true triaxial compressive stress tests, the mathematic model of constitutive relation and the failure criteria of plastic concrete were investigated. It was observed that the strength of plastic concrete increased with confining stress. The mathematic model of constitutive relation in the form of the quartic polynomial is in good agreement with measured data. The general equations of failure criteria based on the octahedral stress-space under true triaxial compressive stress in the form of quadratic polynomial are well-fitting with experimental data. The mathematic model of constitutive relation and failure criteria of plastic concrete could provide the basis for a numerical simulation analysis of plastic concrete under true triaxial compressive stress, as well as promote the engineering application of plastic concrete.To establish the mathematic model of the constitutive relation and failure criteria of plastic concrete under true triaxial compressive stress, uniaxial compressive strength and true triaxial compressive strength of plastic concrete under three kinds of confining pressures with a size of 150 × 150 × 150 mm Plastic concrete is considered a five-phase construction material composed of cement, water, aggregate, and bentonite, which has great deformation capacity under load, excellent ductility after reaching failure, appropriate impermeability, and desirable shear strength ,2,3. TheThere are considerable loads applied on the dam remediation and cut-off wall, therefore the research on mechanical properties and plastic concrete properties is of great significance. Experiments under confined and triaxial compressive stress have been conducted to investigate the properties of plastic concrete. The researches revealed that uniaxial compressive strength and modulus of elasticity of plastic concrete decreased by the increase of the bentonite or water-to-cement ratio ,7. The wTo investigate the mechanical behavior and hydraulic conductivity of plastic concrete, experimental tests have been done under various confinement conditions. In these studies, the effects of age, confining pressure, and mix proportions on the strength-deformation parameters and elastic deformability under uniaxial and multi-axial compressive stress have been assessed. Plastic concrete strength increased with age and cement strength class increasing ,7. With The failure criteria have been proposed to predict the mechanical properties of different combinations of concrete. The influence of silica fume and fly ash to self-compacting concrete under uniaxial and triaxial compressive stress and combined compression-shear performance has been explored. With the ash substitution rate increasing, the peak stress and peak strain of self-compacting concrete increased first and then decreased. The strength of self-compacting concrete increased with the addition of silica fume. Moreover, the failure criteria of self-compacting concrete based on the theory of Mohr–Coulomb and octahedral stress space have been proposed separately ,21. The The characteristics and failure criterion of the plastic concrete under true triaxial compressive stress were analyzed . To date3 and 33 samples with a size of 150 × 150 × 300 mm3 with 11 groups of mix proportions of plastic concrete were proportioned to study the constitutive model and failure criteria of plastic concrete. The mix proportions of plastic concrete specimens are reported in 3 and a curing age of 540 days had 6 samples that 3 samples were prepared to test the uniaxial compressive strength and 3 samples were proportioned to test true triaxial compressive strength. When the curing age is 540 days, the development of the strength of plastic concrete tends to be stable, and the influence of curing age on strength can be ignored. There were 3 samples in each group with a size of 150 × 150 × 300 mm3 and a curing age of 90 days prepared to test the measured elastic modulus under uniaxial compressive stress. According to the mix proportions in Herein, 66 samples with a size of 150 × 150 × 150 mmThe particle size distribution curves of the sand and gravel aggregates contained in the plastic concrete specimens are presented in 3 steel molds and 150 × 150 × 300 mm3 respectively. After placing the specimens in wet rooms for 48 h, the samples were removed from the molds and kept curing in a standard curing room with the temperature range of 20 ± 3 °C and relative humidity of 95% for 540 days and 90 days respectively.Using a forced mixer with appropriated rotation mixed the determined plastic concrete mix proportion until a homogeneous mixture was obtained. After mixing, the plastic concrete was placed in 150 × 150 × 150 mmThe loading model of the monotonic triaxial compression test is applied confining loads first and then axial load. True triaxial compression test applies confining loads and axial load at the same time.LY-C tension and compressive stress true triaxial apparatus was used in true triaxial compressive strength tests. The loads in three directions of apparatus are vertical-orthogonal and controlled independently. The maximum compressive load in the uniaxial of apparatus is 450 kN and the maximum tensile load is 75 kN with the load precision error less than 5%. LY-C tension and compressive stress true triaxial apparatus can carry out uniaxial, biaxial and triaxial compressive tests. Displacement meters were symmetrically arranged on the side of specimens. Displacement data were collected by the computer automatically.3 was 0.1 MPa/s and the size of 150 × 150 × 300 mm3 was 0.005–0.01MPa/s.A 3000 kN digital pressure testing machine was used in uniaxial compressive tests. Max capacity is 3000 kN and load precision error is less than 1%. A steel plate was adding to top of the specimens and the electronic displacement meter was fixed on the pressure plate under the testing machine. The data of axial load and deformation of specimens was collected through an automatic data acquisition instrument. The loading speed of specimens with the size of 150 × 150 × 150 mmσ1 and σ2, axial pressure value as σ3, and σ1 ≤ σ2 ≤ σ3, true triaxial compressive tests were performed with three confining pressures of ,  and . Remained confining pressure unchanged after reaching the preset value, and axial pressure continues to increase until the specimen was damaged. The peak value of the stress-strain relation of σ3 was the strength of the specimen under true triaxial compressive stress. The test load was applied at a rate of 0.4 MPa per stage.Defining confining pressure values as According to GB/T 50081-2002 , the str3, recording this elastic modulus as E0. The compressive strength of plastic concrete under uniaxial compressive stress, the compressive strength of plastic concrete under true triaxial compressive stress (σ3) and the percentage increase of true triaxial compressive strength relative to uniaxial compressive strength with a size of 150 × 150 × 150 mm3 and a curing age of 540 days are also presented in σ1, σ2). The confining pressure of true triaxial test is noted as , , .Referring to It is presented in The strength of plastic concrete decreases with the increase of water-to-binder ratio, and under different confining pressures and water-to-binder ratios, the triaxial compressive strength of plastic concrete increases by more than 114% compared with uniaxial compressive strength.The effect of sand-to-total mass ratio on the strength of plastic concrete is not obvious. When the sand-to-total mass ratio is constant, the triaxial compressive strength of plastic concrete basically increases with the increase of confining pressure. When the sand-to-total mass ratio is 0.6, the triaxial compressive strength of plastic concrete increases by 181.85% compared with uniaxial compressive strength.The true triaxial compressive strength of plastic concrete increases with the increase of cement mass. Under different confining pressures and cement content, the triaxial compressive strength of plastic concrete increases by more than 70% compared with uniaxial compressive strength.The strength of plastic concrete decreases with the increase of clay mass. Under different confining pressures and clay content, the triaxial compressive strength of plastic concrete increases by more than 95% compared with uniaxial compressive strength.The true triaxial compressive strength of plastic concrete decreases with the increase of bentonite mass. When bentonite mass is constant, the triaxial compressive strength of plastic concrete basically increases with the increase of confining pressure. Under different confining pressures and bentonite mass, the triaxial compressive strength of plastic concrete increases by more than 95% compared with uniaxial compressive strength.At present, the mathematical model of the constitutive relationship of plastic concrete has mathematical models of linear-elastic, non-linear-elastic, and non-elastic constitutive relations. Plastic concrete is a typical nonlinear material. The mathematical model of linear-elastic constitutive relation cannot describe the constitutive relationship of plastic concrete accurately. The mathematical model of non-elastic constitutive relation is not intuitive in mathematical form, complicated in the derivation process, and not convenient for practical engineering. Therefore, this paper put forward a mathematical model of quartic polynomial conformed to the behavior of plastic concrete under true triaxial compressive stress.a1 and a2 can be calculated by Equations (2) and (3) respectively.fE is the peak secant elastic modulus of plastic concrete under triaxial pressure (MPa). Researches have been carried out that the elastic modulus of plastic concrete gradually increased with the increase of strength, but had great discreteness. The results of triaxial compressive tests carried out the relationship between secant elastic modulus and peak stress. Their relationship could be expressed by Equation (1). The value of According to the empirical formula of elastic modulus under uniaxial compressive stress suggesting by ACI318-08 and GB50010-2002 ,27. Fittb1 and b2 can be calculated according to Equations (5) and (6).Parameters c1 and c2 can be calculated according to Equations (8) and (9).Parameters The average values of the ratio of calculated values to test values of Equations (1), (4) and (7) are shown in From the results shown in According to data obtained from the true triaxial compressive stress tests of plastic concrete, a mathematical model of the quartic polynomial was established, which agreed well with the measured values.x and y in Equations (10) and (11) are showing in Equations (12) and (13).The meanings of Both sides of Equation (10) differentiated The finishing equation is available shown as Equation (16).E0′ is the initial tangent elastic modulus of plastic concrete under true triaxial compressive stress. The expression of E0′ is shown in Equation (18).Substituting D of the model is related to E0′/fE. By analogy, the coefficients A, B, C, D are related to E0′/fE. Because the initial tangent elastic modulus E0′ under triaxial compressive stress is difficult to measure in statistical analysis. Therefore, E0′ is replaced by elastic modulus (E0) measured under uniaxial compressive stress with a curing age of 90d.It can be seen from Equation (17) that the coefficient fE calculated by Equation (7). The equation of each plastic concrete specimen is obtained by fitting the measured stress-strain curve, thus 33 A, B, C, D values are obtained. The expression of A, B, C, D can be obtained. The equations are shown in Equations (19)–(22).E0 is the uniaxial compressive elastic modulus of plastic concrete with a curing age of 90 d.Peak secant modulus The peak compressive strength obtained from true triaxial compressive tests under three confining stress is compared with the peak compressive strength obtained from Equations (10) and (11) to verify the reliability of the mathematical model. The results of peak compressive stress and the comparisons of calculated results and test results are shown in σ3/σf3 is 1.0037, the standard deviation is 0.0031 and the coefficient of variation is 0.0030, which fully verifies the reliability of the established theoretical model of the quartic polynomial.It can be seen from The plastic concrete failure criteria are processing a large number of triaxial test data of plastic concrete, drawing the failure envelope surface in principal stress space, and finding the appropriate mathematical expression according to the geometric characteristics of the envelope surface.f1, f2, f3) obtained from the experiment is calibrated to the principal stress coordinate space , then connect the adjacent points with smooth curved surface to obtain failure envelop of plastic concrete.The strength in the triaxial space of each plastic concrete specimens  is a constant which is the sum of the three principal stresses at each point on the same deflection plane [There is a hydrostatic pressure axis in the coordinate space of principal stress, and the stress of each point on the axis is on plane .(23)σ1+Based on 33 test points of plastic concrete measured by true triaxial compressive stress tests and the general equation of failure criteria of octahedral space for ordinary concrete proposed by reference ,30, thisθ is the included angle of the offset plane. The parameters in Equation (24) calculate according to the following equations.a, b, c can be determined by experiment.The values of parameters γ and χ are in Equations (29) and (30).Define Equation (31) is the general expression of Equation (24).In the experiment of plastic concrete under true triaxial pressure, octahedral normal stress, shear stress and Lode’s angle in the stress space are shown in Based on the data of true triaxial compressive tests, the general equation of failure criteria has been studied as the expression of Equation (32).A comparison between the measured values and the calculated values of Equation (32) is shown in (1)According to the data shown in (2)With the increase of confining compressive stress, the lateral compressive stress had a better restraining effect on the transverse deformation of plastic concrete specimens, which delayed the appearance and development of micro-cracks in plastic concrete specimens. Therefore, the strength of plastic concrete increased with the confining compressive stress.(3)σ3/σ3f was 1.0037, the standard deviation was 0.0031, and the coefficient of variation was 0.0030. So, the results of the mathematical model were in good agreement with the data obtained from the experiment.Based on the experimental data and the existing constitutive model of concrete under triaxial compressive stress, a quartic polynomial constitutive model conforming to the constitutive characteristics of plastic concrete was established for the first time. Compared with the measured data, the ensemble average value of the ratio of (4)The failure criteria of plastic concrete under triaxial compressive stress in octahedral stress space was established. The general equation of the failure criteria was established according to the failure criteria. The average value of the ratio of calculated value to the experimental value was 1.002, the coefficient of variation was 0.0444, and the standard deviation was 0.0445, which proved that the calculated values of the failure criteria equation were in good agreement with the experimental values.In this article, the mechanical performance of plastic concrete was tested and theoretically analyzed. Firstly, the results of the strength of plastic concrete under true triaxial and uniaxial compressive stress were obtained through experiments. Secondly, according to the results of the tests, the relationships between materials and confining pressure on strength of plastic concrete were analyzed. Thirdly, the mathematic models of the constitutive relationship and failure criteria based on the strength of plastic concrete under true triaxial tests were established. The following conclusions can be obtained:


E. coli were detected in two subjects. Our work demonstrates the overall clinical safety of SAT and the low rate of the selection of multidrug-resistant bacteria triggered by this therapy. We also describe the composition of intestinal microbiota under the indefinite use of antibiotics for the first time.The aim was to describe the safety of indefinite administration of antibiotics, the so-called suppressive antibiotic therapy (SAT) and to provide insight into their impact on gut microbiota. 17 patients with SAT were recruited, providing a fecal sample. Bacterial composition was determined by 16S rDNA massive sequencing, and their viability was explored by PCR-DGGE with and without propidium monoazide. Presence of antibiotic multirresistant bacteria was explored through the culture of feces in selective media. High intra-individual variability in the genera distribution regardless of the antibiotic or antibiotic administration ingestion period, with few statistically significant differences detected by Bray-Curtis distance-based principle component analysis, permutational multivariate analysis of variance and linear discriminant analysis effect size analysis. However, the microbiota composition of patients treated with both beta-lactams and sulfonamides clustered by a heat map. Curiously, the detection of antibiotic resistant bacteria was almost anecdotic and CTX-M-15-producing  Clostridioides difficile and multidrug-resistant bacteria. The aim of this study was to describe the safety of SAT over extended periods and its ecological impact on gut microbiota. Increased life expectancy with an acceptable quality of life is a relevant characteristic of current society. The rate of joint replacement surgery is increasing worldwide, with estimates of up to 80,000 operations annually in Spain and an incidence of further prosthetic joint infection of 3–4% . ProstheC. difficile infection in the previous 3 months and the consumption of other antibiotics due to a different infectious episode in the previous 30 days. Each patient provided a fecal sample, and their demographic and clinical characteristics were recorded from their clinical charts in an anonymous confidential database. This study was approved by the center’s local ethics committee (27 March 2017 acta 321).We conducted a prospective observational study at our center’s Department of Infectious Diseases from 2016 to 2018 on patients undergoing SAT due to unresolved implant-associated infection managed with implant maintenance. The inclusion criteria were an age over 18 years, regular follow-up in our consultation, signing the written informed consent document and undergoing SAT for at least an entire month. The exclusion criteria were a history of inflammatory bowel disease (IBD), colorectal cancer, After collecting the feces, the samples were divided into two aliquots and immediately frozen at −80 °C. One aliquot was employed to determine the colonization of viable antibiotic multidrug-resistant bacteria by conventional microbiological cultures, whereas the remaining aliquot was reserved to determine the whole bacterial composition by 16S rDNA amplification and massive sequencing. Enterococcus agar plates supplemented with 6 mg/L of vancomycin, mannitol-salt agar plates supplemented with 4 mg/L of oxacillin, MacConkey agar plates supplemented with 1 mg/L of cefotaxime and with 2 mg/L of imipenem. We performed extended incubation at 37 °C for at least 5 days to allow for the growth of fastidious organisms. Colonies were identified by matrix-assisted laser desorption/ionization-time of flight Mass Spectrometry , and their antibiotic susceptibility was determined using the MicroScan WalkAway system . To select multidrug-resistant bacteria, the samples were cultivated in M-To determine the whole microbiota composition, we completely solubilized portions of 0.5 mg of feces in 5 mL of sterile water and employed 0.5 mL of this solution to obtain total DNA using the QIAamp kit , determining their concentration and quality using the Qubit fluorometer . We amplified the V3-4 region of the bacterial 16s rDNA gene by PCR and then used the amplicons to prepare the sequencing library, following the Illumina 16S Metagenomic Sequencing Library Preparation Guide. Lastly, 16S rDNA massive sequencing was performed on a MiSeq platform  at the Foundation for the Promotion of Health and Biomedical Research (FISABIO) in Valencia, Spain. The 16S rDNA sequencing data analysis and statistics were performed using the QIIME2 (version 2018.4) software package . TaxonomAs bacterial viability cannot be inferred from the high-throughput sequencing data, we aimed to evaluate the SAT impact on alive bacteria using propidium monoazide (PMA), a photoreactive DNA dye that does not interact with intact biological membranes, instead targeting free DNA and dead cells. Once PMA is intercalated into a DNA molecule, it prevents its amplification by PCR, obtaining only positive amplification from viable bacteria. Consequently, all fecal samples were processed in parallel with and without PMA in addition to a control group of dead bacteria after boiling for 15 min. The PMA was subsequently activated by incubating in the dark for 5 min and photoactivating for 30 min with blue LED light. We then extracted total DNA using the QIAamp kit  and performed universal bacterial amplification using rDNA 16S primers. Amplicons were further separated and visualized on a gradient of denaturing acrylamide gel (DGGE) to differentiate live and dead bacterial species.Staphylococcus aureus , and Staphylococcus epidermidis . By the sample collection time, the patients had taken antibiotics for a median of 32 months .Of the 20 patients treated in our department who met the inclusion criteria, 17 of them signed the informed consent and provided a fecal sample. Each antibiotic therapy was individually considered based on the patients’ characteristics, tolerability, safety profile, drug-drug interactions, and the antibiotic susceptibility of the infective microorganism. The prescribed oral antibiotics were beta-lactams , cotrimoxazole , fluoroquinolones , tetracyclines (2 patients 11.7%), and clindamycin (1 patient 5.8%). The remaining patient was hospital-admitted with cancer, had a central catheter and was administered intravenous teicoplanin. The patients were questioned as to SAT-related adverse effects, with 5 (29.4%) reporting mild gastrointestinal symptoms. Three patients had asymptomatic bacteriuria, whereas a fourth patient experienced a single episode of urinary tract infection caused by a microorganism resistant to the antibiotic used in the SAT regimen (doxycycline); however, intestinal colonization by the infective microorganism was not demonstrated. Lastly, one of the female patients reported vaginal candidiasis and weight gain, in clear association with amoxicillin intake .Escherichia coli isolates in patients 7 and 15, which were further characterized as CTX-M-15. Both patients were treated with non-beta-lactams antibiotics: levofloxacin/rifamycin and teicoplanin, respectively.The fecal carriage of antibiotic multidrug-resistant microorganisms was not detected by selective culturomics, with the exception of two extended-spectrum beta-lactamase (ESBL) producing For the gut microbiota characterization, we evaluated the richness and diversity of the gut microbiota using the Shannon and Chao1 alpha diversity indices , detectiFirmicutes , Bacteroidetes , Proteobacteria , Actinobacteria , and Verrucomicrobia . The abundance of the referent genera from the each phyla was compared by the prescribed antibiotic and the intake duration: Faecalibacterium from Firmicutes, Bacteroides from Bacteroidetes, Escherichia/Shigella from Proteobacteria, Akkermansia from Verrucomicrobia, and Bifidobacterium from Actinobacteria , we decided to interconnect the bacterial abundances with the SAT antibiotic using a heat map analysis . The resLastly, we assessed the viability of the fecal bacteria using PCR-denaturing gradient gel electrophoresis (with and without PMA) to inhibit the amplification of non-viable cells, thereby avoiding unspecific DNA amplifications of transient bacteria . We obseThe short and long-term impact of antibiotics on intestinal microbiota has been documented by nonculture-based techniques ,20,21,22C. difficile due to disruption of the commensal microbiota. The protective role of Barnesiella genera and the Lachnospiraceae family has been reported [Barnesiella; and 19.3 ± 15%; range 3.6–72.0% for the Lachnospiraceae family), and that could be the reason of the low C. difficile prevalence among our patients.SAT is not just a therapeutic option but is in fact the last option for treatment for implants-associated infections when the curative surgical approach is not feasible. SAT safety was our first goal, and we observed no serious complications in our cohort except for patient 11, who reported vaginal candidiasis and weight gain after amoxicillin intake. One of the most relevant consequences of prolonged antibiotic therapy is the infection by toxigenic reported , and botThe weight gain and vaginal candidiasis reported by patient 11 (who had taken amoxicillin for 11 months) are related to major changes in gut microbiota. The growth-promoter property of antibiotics is well known because the property has been extensively employed for livestock but at low doses. Although other patients in our study had been treated with beta-lactams, patient 11 was unique in taking amoxicillin, and we cannot rule out that an increase in body mass index was related to the SAT intake, as has been previously published by other authors ,26,27. LE. coli isolates but in two patients who had not been treated with a beta-lactam. Despite the oral intake, most of the antibiotic dose is absorbed in the small intestine, passing to the blood compartment, with only small amounts of the antibiotic reaching the colon. However, non-modified antibiotic molecules could also be reintroduced into the lumen through biliary excretion, particularly the lipophilic antibiotics such as tetracyclines and fluoroquinolones. Available data on the selection process of antibiotic-resistant bacteria are inferred from in vitro experiments, and some discrepancies can occur in vivo [Unexpectedly, antibiotic multidrug-resistant microorganisms were not detected in feces, except for two ESBL producing  in vivo . One fac in vivo . The int in vivo ,30; alth in vivo .Bacteroidetes and Firmicutes phyla, whereas quinolones activity largely varies in different individuals [Despite previous efforts, specific intestinal microbiota targets have not yet been established for each family of antimicrobials. Aminoglycosides appear to select ividuals . Fluoroqividuals ,22, althividuals . The addividuals , and thiividuals ,35. Our Bacteroidetes, Bifidobacterium, strict anaerobes, and minority populations seem to be the most fragile bacterial populations [The long-term antibiotic effects on the entire gut ecosystem have not been extensively studied, and bacterial signaling is probably different when they are excited/stimulated by antimicrobial molecules. ulations ,37,38,39Our study’s main limitations are the small number of patients for each antimicrobial type, the specific clinical features of each individual that prevent an homogeneous comparison and the lack of baseline samples to better determine the long-term impact of the antibiotics. In contrast, the study’s strength was the inclusion of the PMA technique to assure bacterial viability, which was demonstrated as high and comparable in all patients.In summary, our study demonstrates the overall safety of SAT and the low-rate of antibiotic multi-drug resistant bacterial selection triggered by this therapy. We also described the composition of the intestinal microbiota under the indefinite use of antibiotics for the first time. Our data suggest that SAT is safe in a clinical context of specialized clinical follow-up that monitors adverse effects, interactions and toxicity, introducing the necessary modifications in the treatment.


Purpose: The clinical characteristics and prognoses of immunoglobulin G4-positive (IgG4+) and IgG4-negative (IgG4−) lacrimal lymphomas were comparatively analyzed to screen for clinical indicators with differential diagnostic significance.Methods: This was a retrospective and single-center clinical study. From June 2011 to June 2018, clinical data of 39 patients with lacrimal lymphoma, diagnosed by histopathology were collected from the Department of Ophthalmology, Beijing Tongren Hospital, Capital Medical University.Results: According to inclusion and exclusion criteria, 30 (76.9%) were in the IgG4− group and 9 (23.1%) were in the IgG4+ group. In the IgG4+ group, the sex ratio of male to female was 2:1 and the mean age was 56.67 ± 13.29 years old. In the IgG4− group, the sex ratio of male to female was 3.29:1 and the mean age was 61.47 ± 12.87 years old. Statistical analysis of the clinical indicators showed significant differences between the two groups in affected eye, preoperative history of glucocorticoids, ocular nerve thickening, the expression of serum IgG4 and prognosis (P < 0.05). There was no significant statistical difference in laboratory indicators between the two groups, including C3, C4, RF, ASO, CRP, IgA, IgM, IgG, IgG1, IgG2, and IgG3 (P > 0.05). The event-free cumulative percentages at 3 and 5 years for the 39 lacrimal lymphomas were 81.1 and 62.4%, respectively, with recurrence and death as end events. In 34 lacrimal gland MALT lymphoma cases, the event-free cumulative percentages at 3 and 5 years were 84.4 and 69.1%, respectively. In the IgG4+ and IgG4− groups, the event-free cumulative percentages at 3 years were 75.0 and 87.7%, respectively. The event-free cumulative percentage at 5 years was 62.6% in the IgG4-group and insignificant in the IgG4+ group. There was no statistical difference in event-free cumulative percentage between the two groups (P = 0.983).Conclusion: The pathogenesis and disease characteristics of IgG4-positive lacrimal lymphoma may differ from IgG4-negative lacrimal lymphoma, but the positive expression of IgG4 may not have significant influence on the recurrence of lacrimal lymphoma. Ocular adnexal lymphoma can involve multiple tissues, such as the conjunctiva and lacrimal gland, and accounts for 5–15% of extranodal lymphomas . Among tIn this study, the pathological features, laboratory indicators, treatment, and prognosis of patients with IgG4+ and IgG4− lymphomas were compared and analyzed in order to find clinical and laboratory indicators with differential diagnosis significance.The current study is a retrospective, single-center clinical study conducted between June 2011 and June 2018. The medical records of lacrimal lymphoma confirmed by pathology were collected from the medical records database of the Department of Ophthalmology, Beijing Tongren Hospital, Capital Medical University, by professional ophthalmologists. The number of IgG4 positive expression was counted and confirmed by two professional pathologists. Since some patients had a history of IgG4-related ocular disease before the diagnosis of lymphoma and were treated with glucocorticoids, the inclusion criteria for IgG4+ lymphoma in this study were as follows: (1) diagnosed as lymphoma by histopathology; (2) histopathological findings > 10 IgG4+ plasma cells per high power field (HPF) and an IgG4+/IgG+ cell ratio > 30%; (3) a serum IgG4 concentration > 135 mg/dl; and (4) the patient had a history of IgG4-related ocular disease clearly diagnosed by pathology. Inclusion criteria for IgG4− lymphoma were as follows: (1) diagnosed as lymphoma by histopathology; (2) histopathological findings ≤ 10 IgG4+ plasma cells per HPF and an IgG4+/IgG+ cell ratio ≤ 30%; (3) a serum IgG4 concentration ≤ 135 mg/dL; (4) no history of IgG4-related ocular disease. Exclusion criteria: (1) other ocular lymphoproliferative lesions; (2) Other lacrimal tumors, including lacrimal pleomorphic adenoma, adenoid cystic carcinoma, and adenocarcinoma. A total of nine IgG4+ lymphomas (IgG4+ group) and 30 IgG4− lymphomas (IgG4− group) were identified that met two or more inclusion criteria. The study was approved by the Institutional Review Board of Beijing Tongren Hospital and carried out according to the tenets of the Declaration of Helsinki.General information was collected from medical records database, including medical record number, age, gender, affected eye, previous history , clinical manifestations, course, imaging findings, immunohistochemical indicators, and prognosis. Imaging findings, including magnetic resonance imaging (MRI) or computed tomography (CT), were obtained and confirmed by professional radiologists. Course refers to the duration of clinical symptoms. The cases that did not meet the inclusion criteria and had incomplete medical history were excluded by two professional ophthalmologists.Peripheral venous blood samples were collected from the two groups of patients. The enzyme-linked immunosorbent assay was used to test indicators, including complement C3 and C4, rheumatoid factor (RF), c-reactive protein (CRP), hemolysin against streptococcus O (ASO), IgA, IgM, IgG, and IgG-subtypes . Enzyme-linked immuno sorbent assay (ELISA) kits were purchased from eBioscience (USA). The 96-well microplates were coated with captured antibodies. Plasma samples and standards were added and incubated for 2 h. The wells were washed and HRP-conjugated detection antibodies were added into each well. Plates were washed three times, and the reactions were stopped after incubation with the TMB substrate reagent and optical density read at 450 nm using a micro-plate reader .All patients were treated with surgical resection. Lesions were removed via the anterior temporal eyebrow arch skin incision or the double eyelid skin incision depending on the size of the lesion. Adjuvant therapy, including radiotherapy and chemotherapy, were selected depending on the disease. The appropriate radiation range or chemotherapy regimen was chosen according to the pathological type of tumor and the extent of lesion involvement. The common methods used were external gamma radiation therapy and the CHOP regimen, which included cyclophosphamide, doxorubicin, vincristine, and prednisone.The effective follow-up time was from definitive diagnosis of the first biopsy to the death of the patient or June 2020. The observation indicators during follow-up were general condition, including eyesight, eyelid swelling, and proptosis and imaging findings. In order to objectively evaluate the therapeutic effect and observe whether the lesions had recurred, preoperative and postoperative MRI examination was required for each patient. The specific time points were pre-surgery, 6 months, 1–3 years, and 5 years post-surgery. CT scans were done in patients with contraindications to MRI. Criteria for recurrence was as follows: eyelid swelling or lacrimal gland enlargement, accompanied by objective imaging evidence of lacrimal gland involvement, and confirmed by histopathological examination.t test were used to test the data of two groups consistent with normal distribution. Median and non-parametric rank sum test were used for data that did not conform to normal distribution. The chi-square test or Fisher's exact test were used for counting data. Survival curves for events were generated using the Kaplan–Meier method and compared between the two groups using log-rank tests. The influencing factors were analyzed via binary Logistic regression analysis. A P-value < 0.05 was considered statistically significant.GraphPad Prism 8.0 and SPSS 25.0 software were used for analysis. Measurement data were tested by One-sample Kolmogorov-Smirnov test. Mean ± standard deviation and independent sample P = 0.669) or age (P = 0.336) between the two groups. There was one case of right eye, five cases of left eye, and three cases of binocular disease in the IgG4+ group. There were 15 cases of right eye, 11 cases of left eye, and four cases of binocular disease in the IgG4− group. The incidence of monocular disease was more common in both groups and IgG4− group had a higher significantly incidence of monocular disease (P = 0.031). IgG4+ group had a significantly higher incidence of preoperative glucocorticoid therapy (P = 0.003). In the IgG4+ group, three patients had a history of previous surgery and three patients had a history of sinusitis. In the IgG4− group, two patients had a history of sinusitis. There were no statistically significant differences in history of previous surgery or sinusitis between the two groups (P > 0.05).The gender, age, affected eye, and previous histories of the 39 lymphoma patients were retrospectively analyzed. The results  showed tP > 0.05). Imaging findings are shown in P = 0.049); however, there was no statistically significant difference in sinus mucosa or extraocular muscle thickening . The mean course was 26.00 ± 33.99 months in the IgG4+ group and 20.57 ± 25.10 months in the IgG4− group and was not statistically different between the two groups (P = 0.603).The clinical manifestations in the IgG4+ group were eyelid swelling in seven cases (77.8%), proptosis in two cases (22.2%), eyelid mass in one case (11.1%), and tearing in one case (11.1%). The clinical manifestations in the IgG4− group were eyelid swelling in 13 cases (43.3%), proptosis in nine cases (30.0%), eyelid mass in nine cases (30%), tearing in two cases (6.7%), dry eye in one case (3.3%), decreased vision in one case (3.3%), pain in one case (3.3%), and diplopia in one case (3.3%). Eyelid swelling was the main clinical manifestation in both groups and was not statistically significantly different between the two groups (P > 0.05). And the expression of serum IgG4 was higher in IgG4+ lymphoma than IgG4− lymphoma (P = 0.000).Twelve laboratory indicators, including C3, C4, RF, ASO, CRP, IgA, IgM, IgG, IgG1, IgG2, IgG3, and IgG4, were analyzed in the 39 patients via the ELISA method. According to statistical analysis, C3, C4, IgA, IgG, and IgG1 were normal distribution, while IgM, RF, ASO, CRP, IgG2, IgG3, and IgG4 were not normal distribution. The results are shown as shown in P = 0.009), which may have been due to five cases of lymphoma with a high degree of malignancy included in the IgG4− group.There were 39 cases of lymphoma, including two NK/T cell lymphomas, two diffuse large B cell lymphomas, one mantle cell lymphoma, and 34 MALT lymphomas. In the IgG4+ group, one case underwent surgical resection, two cases underwent surgery combined with glucocorticoid therapy, four cases underwent surgery combined with radiotherapy, and two cases underwent surgery combined with chemotherapy. In the IgG4− group, five cases underwent surgery, 10 cases underwent surgery and glucocorticoid therapy, eight cases underwent surgery and radiotherapy, and seven cases underwent surgery and chemotherapy. In the IgG4+ group, the mean follow-up time was 4.03 ± 1.75 years and included two cases of recurrence, six cases of no recurrence, and one case of loss to follow-up. The mean follow-up time in the IgG4− group was 3.48 ± 1.44 years and included three cases of recurrence, 17 cases of no recurrence, four cases of loss to follow-up, and six cases of death . The results showed that there was a significant difference in prognosis between the IgG4+ and the IgG4− groups (P = 0.983).An event-free survival analysis was performed, with recurrence and death as endpoint events, as shown in In recent years, the relationship between lymphoma and IgG4-related disease (IgG4-RD) has garnered extensive attention of researchers at home and abroad. Some patients with lymphoma, especially MALT lymphoma, have previous histories of IgG4-RD or significantly increased expression levels of IgG4, which are found in the serum and when doing histopathology in primary lymphoma. Thus, it is speculated that IgG4-RD can develop into lymphoma and IgG4 may be involved in the pathogenesis of lymphoma. Oleś  et al. cAt present, the pathogenesis of IgG4-RD developing into lymphoma is still unclear. Studies have shown that it may be related to chronic antigenic stimulation that drives lymphoid proliferation, and the residue of reactive lymphoid follicles may provide conditions for malignant development . Yuka 11 et al. Due to insufficient understanding of IgG4+ lymphoma and the low incidence of IgG4-RD developing into lymphoma, a large number IgG4+ lymphoma cases could not be compared with IgG4− lymphoma. The results of this study showed that there were significant differences between the two groups in laterality, preoperative glucocorticoid history, nerve thickening, serum IgG4 and prognosis. These results indicated that IgG4− lymphoma was most common in monocular disease, while IgG4+ lymphoma was more common in binocular disease, which is consistent with reported literature . PreoperKubota  et al. aLee  et al. aIn conclusion, the clinical features and prognosis of IgG4 positive and IgG4 negative lacrimal lymphoma were analyzed contrastively. The results of this study showed that binocular disease, ocular nerve thickening and the higher expression of serum IgG4 were more common in IgG4-positive lacrimal lymphoma than IgG4-negative lacrimal lymphoma. The pathogenesis and disease characteristics of IgG4-positive lacrimal lymphoma may differ from IgG4-negative lacrimal lymphoma, but the positive expression of IgG4 may not have significant influence on the recurrence of lacrimal lymphoma.The original contributions generated for this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.The studies involving human participants were reviewed and approved by Ethics Committee of Beijing Tongren Hospital. The patients/participants provided their written informed consent to participate in this study.All authors read and approved the final manuscript to public.RL analyzed and wrote the manuscript. NW, JW, and JL helped collect data. JM, XG, and JZ read and criticized the manuscript. All authors critically read and edited the manuscript and read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Our findings revealed that gestational dietary methionine could affect maternal and placental H2S concentrations. With the increase of dietary methionine, maternal plasma and placental H2S concentrations changed quadratically, which was consistent with placental vascular density and reproductive performance. The decrease in H2S production caused by an increase in dietary methionine was likely to be the cause for the increase in the rate of low birth weight piglets and needs further study.Hydrogen sulfide  were randomly allocated into five groups, with feed diets comprisingstandardized ileal digestible methionine/lysine (Met/Lys) ratios of 0.27 (nutrient requirements of swine (NRC); 2012 level), 0.32, 0.37, 0.42, and 0.47, respectively. The litter size and weight at birth were measured and recorded. Maternal blood samples were obtained at embryonic day (E) E40 d, E90 d, and E114 d of gestation. The placental samples were collected at parturition. The results showed that maternal plasma H2S concentration was not affected at E40 d. However, the maternal plasma H2S concentration changed quadratically with the dietary Met/Lys ratio at E90 d (p < 0.01) and E114 d (p = 0.03). The maximum maternal plasma H2S concentration was at the dietary Met/Lys ratio of 0.37. Meanwhile, maternal plasma H2S concentration was positively correlated with piglets born alive (p < 0.01) and litter weight (p < 0.01). Consistent with the maternal plasma, the placental H2S concentration also changed quadratically with the dietary Met/Lys ratio (p = 0.03); the Met/Lys ratio of 0.37 showed the maximum H2S concentration. In conclusion, our findings revealed that the gestational dietary Met/Lys ratio could affect maternal and placental H2S concentrations, which may be an important molecular mechanism affecting placental angiogenesis and piglet development.The placenta is a unique bond between the mother and the fetus during pregnancy, and a proper placental angiogenesis is vital for fetal development. H Methionine (Met) is an essential amino acid in the diets of pigs ,2. In ad2S) is a ubiquitous signaling molecule with important functions in many mammalian cells and tissues and is now considered to be the third gas-phase signaling molecule, in addition to carbon monoxide (CO) and nitric oxide (NO) [2S is mainly produced by Met and the cysteine transsulfuration pathway (TSP), via the direct enzymatic action of cystathionine-γ-lyase (CGL) and cystathionine-β-synthase (CBS) [2S production, placental angiogenesis, and blood flow velocity [2S donors significantly attenuated placental vascular dysplasia and IUGR, caused by CGL inhibition [2S produced by trophoblast cells can promote angiogenesis in placental artery endothelial cells [2S production in sow plasma and placenta. The goal of the current study was to investigate the role of the gestational methionine/lysine ratio on maternal and placental H2S production, both in vivo and in vitro. Hydrogen sulfide (Hide (NO) ,8,9. Endse (CBS) ,11. Studvelocity ,13. Howehibition . In vitral cells . Howevern = 65) were randomly allocated into five groups and fed diets with standardized ileal digestible methionine/lysine (Met/Lys) ratios of 0.27 (nutrient requirements of swine (NRC); 2012 level), 0.32, 0.37, 0.42, and 0.47 respectively. The diet was maintained at constant levels of Lys (average SID Lys 0.71%); the ingredients and nutrient compositions of the experimentaldiets are listed in The experimental design and the dietary formula were described previously . In thisThe sample collection of blood and placenta was described previously . Twelve 2PO4 buffer (pH 7.4) and was centrifuged for 5 min at 13,000 rpm. The supernatant wasused for H2S content and production assay. The protein concentration was determined by the bicinchoninic acid (BCA) protein assay kit .The placenta was selected based on the average pig birth weight ± one standard deviation of each group. A total of 100 mg of placental tissue was separated and ground to a fine powder using a porcelain mortar and pestle, chilled with liquid nitrogen. Next, 10% of the tissue homogenate was made with 100 mM of ice cold KH2 incubator. Before the Met treatment, the PIEC cells were seeded in a 12-well plate (2 × 105 cells/well); 80% confluent PIEC cells were placed in serum-free basic medium for 18 h, followed by Met-free RPMI 1640 medium for another 6 h, then treated with different concentrations of Met  for 24 h (n = 4). The supernatant culture medium was collected for H2S content assay.Porcine iliac artery endothelial cells (PIEC) were obtained from the cell bank of the Chinese Academy of Sciences , cultured in Roswell Park memorial institute (RPMI) 1640 medium , and supplemented with 10% fetal bovine serum  and 1% penicillin/streptomycin solution  at 37 °C in a 5% CO2S levels were measured through the formation of methylene blue [2PO4 buffer (pH 7.4) and 250 μL of 1% (w/v) zinc acetate; for the culture medium and placental tissue homogenate, 500 μL samples were mixed with 250 μL of 1% (w/v) zinc acetate. The reaction mixture was incubated at 37 °C for 2.5 h. The protein content in the samples was removed by adding 10% trichloroacetic acid (250 μL) to the reaction mixture, which was pelleted by centrifugation. The supernatant was then mixed with 100 μL of N-dimethyl-p-phenylenediamine sulfate (20 mM in 7.2 M HCl) and 100 μL of FeCl3 (30 mM in 1.2 M HCl) in a test tube. The mixture was incubated at room temperature for 15 min. The absorbance of the resulting solution was measured at 670 nm in a 96-well plate with a microplate reader. The H2S concentration was calculated using a standard (NaHS) calibration curve  .In this study, the Hene blue ,17. For 2S concentrations, as shown in p < 0.05 was considered to indicate statistical significance. Regression analyses were performed to evaluate the quadratic effects of dietary Met/Lys ratio and H2S concentration, as shown in 2S concentration are shown in Statistical analysis was performed using the SAS statistical package . A one-way analysis of variance (ANOVA) followed by a least-significant-difference (LSD) post-hoc test was conducted to explore the impact of the gestational dietary Met/lysine ratio on maternal plasma and placenta H2S concentration, we collected maternal plasma at different stages of pregnancy. We found that by E40 d, increasing the Met/Lys ratio in the diet had no effect on the maternal plasma H2S concentration, as shown in 2S concentration changed quadratically, with an increase in the dietary Met/Lys ratio, as shown in 2 + 1577x −288.7, R2 = 0.19, p < 0.01) and at E114 d , the maximum maternal plasma H2S concentration was at the dietary Met/Lys ratio of 0.37. These results indicated that maternal plasma H2S concentration could be affected by the dietary Met/Lys ratio.To study the effect of the gestation dietary Met/Lys ratio on maternal plasma H2S in the reproductive performance of the sows, we analyzed the correlation between the maternal plasma H2S concentration and the number of piglets born alive, the litter weight, and average pig birth weight at E114 d. We found that the maternal plasma H2S concentration had a positive correlation with the number of piglets born alive and the litter weight, as shown in 2S may have played an important role in the sows’ reproductive performance.To determine the involvement of H2S concentration. The placenta was selected based on the average pig birth weight ± one standard deviation of each group. Similar to the maternal plasma, the placental H2S concentration also changed quadratically with the dietary Met/Lys ratio, as shown in 2 + 105.6x −9.17, R2 = 0.12, p = 0.03), the maximum placental H2S concentration was at the dietary Met/Lys ratio of 0.37.We further examined the effect of the gestation dietary Met/Lys ratio on the placental H2S production in vitro, PIEC cells were treated with variable mediums which were (1) Met-free (0 μM), (2) had a physiological concentration of Met (50 μM), and (3) had a high concentration of Met , respectively. We found that the H2S concentration was highest in the Met-free medium condition and lowest in a physiological concentration of Met (50 μM), as shown in 2S production increased initially (from 50 to 500 μM) and then maintained relative stability (from 500 to 1000 μM).To further confirm the effect of Met on H2S is an endogenous stimulator of angiogenesis that promotes vascular endothelial cell proliferation, migration, and angiogenesis by activating the NO/cGMP pathway, opening KATP channels, and promoting the phosphorylation of PI3K/AKT and MAPK pathways [2S concentration was positively correlated with the sows’ reproductive performance. With an increase in Met/Lys ratio in the sows’ diet, the maternal plasma and the placental H2S concentrations changed quadratically. These results indicated that there was a dose-effect of Met concentration on H2S production.Hpathways ,18,19. I2S production, recent studies have found that dietary restriction (50% restriction) or Met restriction is the most effective way to increase H2S production. Studies have found that limiting the feed intake can increase liver CGL expression, increase endogenous H2S production, and alleviate liver ischemia-reperfusion injury [2S production can increase in the skeletal muscles by up-regulating the GCN2/ATF4 pathway and activating NAD+/SIRT1 signaling, thus triggering skeletal muscle angiogenesis and delaying muscle aging [2S concentrations were highest under Met-free conditions (0 μM), whereas relative to physiological concentrations, high concentrations of Met did not significantly inhibit H2S production in PIEC cells, which suggested that there were some differences between in vitro and in vivo experiments.Although Met is a precursor for Hn injury . Addition injury  and mainn injury . Recentlle aging ,23. We f2S concentrations were consistent with the sows’ reproductive performance. The decrease in H2S production caused by an increase in dietary Met was likely to be the cause for the increase in the rate of low birth weight, along with the failure to further improve the reproductive performance of the sows. Studies of rodents have found that a high concentration of Met can significantly inhibit CGL activity in peritoneal macrophages, reducing serum H2S content and increasing inflammatory reactions [2S could promote mammary epithelial cell proliferation by activating the PI3K/Akt-mTOR pathway in porcine [2S producing enzymes, or increasing the H2S content by using H2S donors, may be an effective way to alleviate the adverse effects of high Met production. Our current results found that H2S donors diallyl trisufide(DATs) could significantly promote PIEC angiogenesis (unpublished data), which suggests that H2S is a potential target for improving the reproductive performance of sows.In modern animal production, gestational restriction feeding is an effective and widely used practice to improve the reproductive performance of sows. Our previous study found that under the restriction feeding conditions, increasing the Met/Lys ratio from 0.27 to 0.37 can significantly increase the average pig birth weight and the litter weight in the pigs that are born alive . Howevereactions . A recen porcine . Therefo2S concentration, which may be an important molecular mechanism affecting placental angiogenesis and piglet development.In conclusion, our findings revealed that gestational dietary Met could affect maternal and placental H


This article describes the comparative analysis of tests on bond strength of hot-dip galvanized and black steel to concrete with and without chlorides. The bond effect was evaluated with six research methods: strength, electrochemical , optical, and 3D scanning. The tests were conducted within a long period of 18 months on 48 test elements reinforced with smooth rebars ϕ8 mm from steel grade S235JR+AR and ribbed rebars ϕ8 mm and ϕ16 mm from steel grade B500SP. The main strength tests on the reinforcement bond to concrete were used to compare forces pulling out galvanized and black steel rebars from concrete. This comparative analysis was performed after 28, 180, and 540 days from the preparation of the elements. The electrochemical tests were performed to evaluate corrosion of steel rebars in concrete, particularly in chloride contaminated concrete. The behaviour of concrete elements while pulling out the rebar was observed using the system of digital cameras during the optical tests. As regards 3D scanning of ribbed rebars ϕ8 mm and ϕ16 mm, this method allowed the detailed identification of their complex geometry in terms of determining the polarization area to evaluate the corrosion rate of reinforcement in concrete. The test results indicated that the presence of zinc coating on rebars had an impact on the parameters of anchorage. In the case of ribbed rebars of 16 mm in diameter, the maximum values of adhesive stress and bond stiffness were reduced over time when compared to black steel rebars. Moreover, it was noticed that the stiffness of rebar anchorage in chloride contaminated concrete was considerably higher than in concrete without chlorides. The bond strength of reinforcing steel to concrete is a key element that determines the desired behaviour of a reinforced concrete composite. The effects observed at the interface between steel and concrete have been generally thoroughly investigated and clearly described ,2,3,4,5.Description of the contact between the rebar and concrete from the electrochemical point of view always requires with analysis of the bond between the metal and liquid filling concrete pores ,13,14,15b generated on the rebar surface  and measured against the reference electrode Cl−/AgCl,Ag are presented in the tabular form in Ecorr were repeated three times, that is, on days 3, 10, and 25 after setting the specimens in concrete. Each of three measuring series was marked with a different colour as seen in The potential was measured each time for three specimens of the same type, and the calculated arithmetic means were inserted into the tables in Ecorr for galvanized and black steel. The potential of galvanized rebars was lower by 159–512 m than rebars without the protective coat placed in the same concrete. This can be attributed to zinc’s position against iron in the electrochemical series of metals. The potential drop was observed along with concrete hardening. It means that the most negative potentials were generally found for the last measurement series on day 25 from setting the specimens in concrete. The specimens G10-Cl–G12-Cl with galvanized rebars in concrete with chlorides were the exception. A reverse trend was observed for them.The measurement results presented in the form of bar charts demonstrate a clear difference between the potentials Zre–Zim plane are illustrated in The impedance spectra in the complex Rc specified the impedance of the whole concrete, the resistance Rt specified the charge transfer resistance through the metal-pore solution interface, and the CPE0 characterized the pseudo-capacity of a double layer on steel. For the scheme illustrated in Rf and the CPEf specified the resistance and the pseudo-capacity of the forming layer of corrosion products of iron or zinc, which locally limited the access of oxygen to metal surface.The above qualitative analysis of experimentally determined 36 spectra was verified with the quantitative analysis based on adjusting theoretical spectra to corresponding electrical equivalent circuits illustrated in Rt, which was a key parameter, was used to calculate the density of corrosion current icorr = B/Rt from the Stern-Geary equation. The parameter B was determined from the slope coefficients of linear sections of the polarization curves (anodic ba and cathodic bc) obtained during the potentiodynamic tests conducted with the LPR technique described in point 4.4.The detailed results for adjusting individual electrochemical parameters of both electrical equivalent circuits using the Simplex method are presented in Rp for each curve and the slope coefficient of a straight section of the anodic ba and cathodic curves, the corrosion current density icorr = B/R, where the parameter B = babc/2.303 (ba + bc), was calculated from the Stern-Geary equation. The densities of corrosion current averaged each time from three specimens are shown as a bar graph in icorr expressed as [µA/cm2], are presented in the tabular form below the bar graph. The potentiodynamic results from the LPR tests for the steel reinforcement in concrete performed after 3, 10, and 25 days from setting the specimens in concrete are shown in icorr = 0.05–0.13 µA/cm2 were obtained from all three measurement cycles for the specimens with black ribbed rebars ϕ8 mm and ϕ16 mm. This could indicate passivation. For the specimens made of smooth steel rebars ϕ8 mm, an increase in icorr = 0.49 µA/cm2 was observed within two consecutive measurement cycles apart from the first one. This increase was not entirely explicable; however, it could suggest partial decomposition of the passive layer on metal. The expected increased values icorr = 0.36–0.63 µA/cm2, indicating the development of corrosion, were found for unprotected ribbed reinforcing steel ϕ16 mm without zinc protection, which was set in concrete with aggressive chloride ions. In the case of the similar specimens but with the galvanized rebar, a dramatic rise in densities of the corrosion current up to icorr = 9.23 µA/cm2 was noticed during the 1st cycle of measurements. This value was gradually falling in consecutive measurements to icorr = 2.91 µA/cm2 on day 10, finally reaching the value icorr = 0.67 µA/cm2 on day 25. It should be emphasized that very close range of corrosion current densities was obtained from the EIS tests, which had been conducted on a part of the specimens prior to the LPR tests. The observed effect of a rapid rise in the density of corrosion current can be attributed to the cumulative impact of chloride ions due to corrosion and high pH of pore solution, which caused partial dilution of the zinc coating at the initial stage of concrete setting. The values of corrosion current density for other specimens with galvanized rebars in concrete without chlorides ranged from 0.05 to 0.42 µA/cm2. These values usually did not exceed icorr = 0.20 µA/cm2 indicating no signs of corrosion.The analysis of corrosion current densities presented that the following values N acting on the rebar and its displacements s against the specimen was very important information used to determine the anchorage stiffness of rebar in concrete. 3 of displaced points is shown in 5 of the displaced points can be noticed. This grid changes into the asymmetrical crack 6 (bursting) of concrete 2 as presented in 4 of the specimen 1 is presented in 3 of the displaced points that is shown in The optical measurements with the Aramis camera system were additionally taken to provide new and detailed information on the strength tests. Their main objective was to record the displacements of points on the surface of the loaded tests element while pulling out the rebars from concrete causing the specimen failure. These measurements were used to catch the moment of fracture and crack formations in the test element, in which the reinforcement was anchored. Finding the connection between the force s [mm] from the concrete block caused by an increment of the pull-out force F [kN]. The measured shift was recorded using the Aramis camera system, whose software interacted with the control system for an increase in force of the strength machine. Due to the limited access to the Aramis system, the tests were reduced to galvanized and black steel ribbed rebars ϕ16 mm, embedded in concrete with and without chlorides. The elements without chlorides were tested after 180 days from the day of their preparation, and the elements containing chlorides were tested after 540 days.F(s) for the load range F = 0–60 kN were quasi-linear for each test element. A further increase in load, that is, for F > 60 kN, the elements containing chlorides B23-Cl, B24-Cl, G22-Cl, G24-Cl maintained their straight-line relationship F(s). On the other hand, the curves representing the elements  without chlorides in concrete had a clear drop in the slope F(s).The test results shown as curves in All 48 test elements were damaged. Fmax,G and Fmax,B were used to differentiate the pull-out forces acting on the galvanized and black steel rebars, respectively. The values of the pull-out forces Fmax determined for all 48 specimens are shown in The bar graphs presented in The highest values of the pull-out forces (73.11–110.17 kN) were determined as expected for the ribbed rebars ϕ16 mm, and the lowest values (7.99–19.69 kN) for the smooth rebars ϕ8 mm. Except for the ribbed rebars ϕ8 mm, an increase in the pull-out force was noticed after 180 or 540 days. The greatest rise expressed in percentage was found for the smooth rebars ϕ8 mm. Considering the mean pull-out forces acting on the same specimens, the values obtained for galvanized rebars were generally lower compared to black steel rebars. Other results were obtained for smooth steel ϕ8 mm after 180 from setting the specimens in concrete and ribbed steel ϕ16 mm after 28 days from setting the specimens in concrete. A significant rise in the pull-out forces acting on the ribbed rebars ϕ16 mm after 540 days from preparing the specimens with chloride ions should be noted. These ions were aggressive for the reinforcement, so the specimens were very deteriorated due to corrosion.1 and galvanized 2 rebars were embedded in concrete with chlorides of 3% concentration of the cement weight for the period of 540 days. It is important that the test elements with chlorides were stored within the last year in a closed chamber over a layer of water to provide the conditions which would intensify the development of reinforcement corrosion due to high relative humidity. Fragments of the rebar in the foreground were embedded in concrete specimens. Two edge rebars 4 were protected by zinc coating, on which the products of zinc corrosion in silver colour were not particularly distinguished. Three middle black steel rebars 3 had clear signs of plentifully deposited rusty products of iron corrosion.Two types of damage to the test elements were observed during the strength tests. The first type consisted in pulling out the anchored rebar from the concrete specimen without breaking the cover. In that case the concrete, in which the rebar was anchored, remained whole when the ultimate resistance of the element was exceeded. All elements reinforced with rebars of 8 mm in diameter were damaged in the above way. This failure occurred for the rebars made of both steel grades S235JR+AR and B500SP. Breaking of the concrete element, in which the rebar was anchored, was the second observed type of failure. It referred to all elements reinforced with rebars ϕ16 (B500SP). It should be emphasized that none of these elements were destroyed by the rupture of the anchored rebar.The described types of failure of the elements are in line with the observations often described in the literature. Considering the smooth rebars, their failure was caused by pulling out the rebar from concrete, in which the rebar was anchored. The anchorage of ribbed rebars was also destroyed by pulling out the rebars from concrete providing that the reinforcement cover had adequate thickness . In a siFy were determined  from 19.56 kN to 22.26 kN, ϕ8 (B500SP) from 21.91 kN to 28.75 kN and ϕ16 (B500SP) from 107.52 kN to 120.52 kN  was opposite, it means the element failure could be attributed to the exceeded critical stress of bond between rebars and concrete. However, if the following relationship would be satisfiedThe values of the adequate quotients (3) and (4) are shown in fb was observed over the anchorage length lb, the stress values could be determined from the equilibrium state of the rebarlb = 70 mm, u—rebar circumference. The maximum values of these stresses  at the resistance loss are compared in Assuming that the uniform distribution of anchorage stress fb,y,mean was determined in the first place which corresponded to the mean force Fy,mean yielding the reinforcement. The values fb,y,mean were: 11.89 MPa for the rebars ϕ8 S235JR+AR, 14.40 MPa for the reinforcement ϕ8, B500SP, and 32.46 MPa for the rebars ϕ8, B500SP :It should be pointed out that the value fb,y, as Fy, was the random variable, the corresponding confidence intervals at the significance level of 0.02 are additionally presented in Assuming that the stress fb,y was the highest possible value of stress fb, which could be generated at the side wall of the rebar in concrete. It can be attributed to the mechanism of transmitting the force from the reinforcement to concrete. In the case of smooth rebars, where stresses fb were caused by adhesion, the yielding force exerted on the rebar resulted in a rapid drop of its diameter, and consequently the adhesion force was eliminated due to the produced stresses perpendicular to the rebar axis. However, the force Fy initiated so significant deformation of anchored ribbed rebar that it could not be transmitted to concrete.The value fb,max was considered the random variable. It means that the value determined from the Equation (7) takes 100% if fb is within the adequate confidence level specified in fb,max was determined from the analysis of the values presented in In this table fb,max that could be found at the rebar surface. For the galvanized smooth rebars, the values fb,max were lower by 4.2% compared to black steel smooth rebars. Similar observations were made for the ribbed rebars ϕ16 mm embedded in concrete without chlorides. The values fb,max for galvanized rebars were lower by 2.5% than in the case of black steel rebars. Considering the rebars in concrete with chlorides, the reverse relationship was found. The values fb,max were greater by 2.2% after 28 days. In the case of ribbed rebars of 8 mm in diameter, the galvanization had no effect on the value fb,max after 28 days because the adhesive stresses in both cases reached the value fb,y.Galvanization of smooth rebars at the beginning, that is, after 28 days from the day of their preparation, practically had no effect on the values fb,max were increasing with the age of the test specimens which could be interpreted as a consequence of the increased strength of concrete. However, this increment was lower for the galvanized rebars with a diameter of 16 mm. The tests on the elements conducted after 180 days demonstrated that the value fb,max for the galvanized elements was lower by 18.7% compared to the black steel elements. A similar effect was observed for the elements with chlorides tested after 540 days. In that case, the value fb,max was lower by 9.1% which was not favourable to galvanized steel. A similar adverse effect of galvanization on the value fb was found for the ribbed rebars of 8 mm in diameter that were tested after 180 days. In this case the values fb for the galvanized rebars were lower by 9.3% compared to the black steel rebars. On the other hand, the value fb determined for these rebars after 180 days was lower than after 28 days which was contrary to the expectations. It could indicate a serious drop in the resistance of anchorage of galvanized rebars over time. It should be mentioned that it was a single observation which could not be generalized.The values fb,max. Thus, fb,max could be directly compared with the values determined after 28 days of concrete hardening. In the case of black steel rebars of 16 mm in diameter, chlorides reduced fb,max by 18%. This effect was not so significant for the galvanized rebars as the values were reduced by 13.3%. The results determined after 540 days were likely to confirm the observations that the values fb lower by 9.1% were found in the test elements with Cl. The value fb,max was also affected by the process of galvanization.The test results lead to the conclusions that chlorides in concrete had an impact on the values F. These results are presented in the form of graphs in F(s) showed that these graphs were linear for a gradually increasing force F within the range of 0–60 kN. However, the shape of the graph F(s) was changing in the final stage of loading. For the elements without chlorides , a slope of the relationship F(s) was clearly decreasing. In the case of the elements containing chlorides , a slope of the curve with a quasi-linear shape was approximately constant throughout the whole loading cycle. Two phases were identified for each path of the relationship F(s) for the quantitative description of the above observations. The first phase included the loading range from 0 to 60 kN. The second phase was specified as the load contributing from 90% to 100% of the force Fmax. Then, the shift values s were read from k of the adhesive bond between the rebar and concrete were determined for both phases. They were considered as a quotient of an increment in loading ΔF and the corresponding increase in shift Δs.As described in point 4.5, the rebar shift s against the concrete specimen was recorded during the tests performed on the test elements containing the anchored rebars with a diameter of 16 mm and the measurements taken for the pull-out force F(s).The calculated stiffness values are shown in k during the first loading phase for the specimens with no chlorides and with black steel elements (197.7 kN/mm and 193.7 kN/mm) compared to the stiffness of galvanized rebars (166.34 kN/mm and 193.7 kN/mm). The stiffness of the elements was significantly reduced in the final loading phase. However, higher values were still noticed for the anchorage made of black steel (23.54 kN/mm and 17.32 kN/mm) compared to the anchorage of galvanized rebars (11.22 kN/mm and 14.57 kN/mm).All the elements had significant stiffness values during the first phase of loading. The tests performed after 180 days demonstrated higher stiffness Fmax, the stiffness slightly dropped to the level of 96.04–17.85 kN/m. The obtained results cannot be used to prove conclusively that galvanization of the rebars affects the stiffness of their anchorage in concrete after 540 days from the day of the preparation of these elements. However, the chlorides clearly demonstrated their impact on the stiffness in the final phase of loading. Chloride-induced corrosion of the reinforcement increased the anchorage stiffness in that phase by an order of magnitude.The elements with chlorides that were tested after 540 days demonstrated other stiffness values. Their initial stiffness within the loading range from 0 kN to 60 kN was 164.07–200.00 kN/m. In the final loading phase that covered from 90% to 100% fcm in the test elements at the age of 180 days was 47.70 MPa, and 50.16 MPa in the case of the test elements at the age of 540 days  was accompanied by yielding of the reinforcement regardless of the age of the test elements. The presence of zinc coating on the rebars was not significant for the failure.Yielding of the elements reinforced with smooth rebars ϕ8 mm (S235JR+AR) was noticed only in the second stage of the tests, that is, after 180 days from their preparation. This observation also refers to the anchorage of galvanized and black steel rebars.Yielding of the reinforcement was not found in the case of failure of any test element containing galvanized ribbed rebars ϕ16 mm (B500SP). This fact could not be attributed to the age of the test elements or traces of products from zinc corrosion found after the pull-out of the rebars. This means that the zinc coating on the reinforcement inhibited the full use of mechanical properties of the rebars ϕ16 mm made of steel grade B500SP.In the case of the elements with the anchored black steel ribbed rebars ϕ16 mm (B500SP), yielding was observed only for the elements at the age of 180 and 540 days.Generally, zinc coating reduced the stiffness of anchorage of ribbed rebars ϕ16 mm (B500SP) This stiffness was reduced even by 15% when the pull-out force was within the range of 0–60 kN.However, the chloride-induced corrosion clearly demonstrated its impact on the anchorage stiffness in the final phase of loading. For the same content of chlorides in concrete, the development of corrosion of black steel was considerably more intensive and was related to greater volume of corrosion products on the rebar surface. The products from the corrosion of iron and zinc deposited in concrete pores and filled voids, which caused an increase in the anchorage stiffness in that phase by as much as one order of magnitude.


Massive multiple-input multiple-output (MIMO) systems are a main enabler of the excessive throughput requirements in 5G and future generation wireless networks as they can serve many users simultaneously with high spectral and energy efficiency. To achieve this massive MIMO systems require accurate and timely channel state information (CSI), which is acquired by a training process that involves pilot transmission, CSI estimation, and feedback. This training process incurs a training overhead, which scales with the number of antennas, users, and subcarriers. Reducing the training overhead in massive MIMO systems has been a major topic of research since the emergence of the concept. Recently, deep learning (DL)-based approaches have been proposed and shown to provide significant reduction in the CSI acquisition and feedback overhead in massive MIMO systems compared to traditional techniques. In this paper, we present an overview of the state-of-the-art DL architectures and algorithms used for CSI acquisition and feedback, and provide further research directions. Massive multiple-input multiple-output (MIMO) systems are an important component of 5G and future generation wireless networks due to their ability to serve many users simultaneously with high spectral and energy efficiency. The main idea in massive MIMO is to equip base stations (BSs) in wireless networks with large arrays of cooperating antennas to facilitate spatial multiplexing of many user equipments (UEs) within the same time-frequency resources. Since the number of antennas at the BS is typically assumed to be significantly more than the number of users, a large number of degrees of freedom are available in the downlink, which can be used to shape the transmitted signals in a specific direction or to null interference. This yields a beamforming gain that translates into increased energy efficiency, reduced interference, or improved coverage. In the uplink, each single-antenna user in a massive MIMO system can scale down its transmit power proportionally to the number of antennas at the BS while maintaining the same performance as the corresponding single-input single-output (SISO) system. This leads to higher energy efficiency, which is a major benefit in next generation wireless networks, where excessive energy consumption is a growing concern. On the other hand, if adequate transmitting power is available, a massive MIMO system can significantly expand its coverage compared to a single-antenna system.In communication systems, channel state information (CSI) is required at the receiver to be able to decode the information transmitted over a time-varying channel. CSI is acquired by a training process which involves pilot transmission and CSI estimation at the receiver. This imposes a training overhead on the communication system which scales up with the number of antennas, receivers and subcarriers. In massive MIMO systems, to achieve the aforementioned performance gains, accurate and timely CSI is required both at the BS and the UEs. Availability of downlink CSI at a massive MIMO BS is crucial to enable beamforming and achieve spatial multiplexing gains. Reducing the training overhead in massive MIMO has been a major topic of research since the emergence of the concept.Massive MIMO was originally introduced in a time division duplex (TDD) setting where the uplink and downlink channels are separated in timeFor smaller number of BS antennas, simple vector quantization (VQ) along with exhaustive search may work sufficiently well for MIMO CSI compression and feedback. In the fourth generation long term evolution (4G-LTE) advanced standard, a 4-bit channel quality index (CQI) and the pre-coding matrix indicator (PMI) are fed back to the BS to reveal the CSINN-based approaches have recently shown significant improvements over their model-based counterparts in various wireless communication problems L is the number of multi-path components with lth path. Also, d and kth subcarrier in OFDM, K is the total number of subcarriers.Consider the following massive MIMO channel matrix According to , the CSISuccess of data-driven approaches depends critically on the datasets used to train the NN models. Unlike some more popular applications of NNs, rich and standardized datasets of CSI measurements in actual massive MIMO scenarios do not yet exist. However, there exists MIMO channel models that have proved to be very accurate in statistically modeling actual CSI measurements in practical MIMO scenarios. Among these are the third generation partnership project (3GPP) spatial channel model (SCM)This paper provides an overview of how NNs can be used in massive MIMO systems to improve the performance of CSI acquisition and feedback while reducing both the complexity and overhead. In the following sections, we shall review recently proposed data-driven approaches for CSI estimation, compression and feedback, and provide suggestions for future research.P pilot signals, denoted by Consider uplink MIMO training where the user transmits a block of P may even exceed the channel coherence interval. If this assumption does not hold, LMMSE-based channel estimation performance degrades significantly.Standard channel estimation techniques are typically based on linear minimum mean square error (LMMSE) estimation method. A common assumption in LMMSE-based channel estimation techniques is that the pilot length is larger than the number of transmit antennas, which may be prohibitive in downlink training of massive MIMO systems  to reduce the power consumption and hardware complexity at the BS; and hence, only a coarsely quantized version of With coarsely quantized measurements, the pilot length required for reliable estimation of the channel; and hence, the training overhead increases significantly. Model-based estimation techniques generally minimize a cost function  iteratively subject to sparsity For the extreme case of 1-bit ADCs, reconstruction is possible only up to a scale factor. The initial results reported inWhile fully-connected NNs have been commonly used in previous works and they have the potential to learn and exploit complex joint distributions across all antennas and subcarriers, they do not easily scale with MIMO dimensions and need separate training for different number of antennas, subcarriers, etc. However, as discussed earlier, correlations in typical MIMO channels exhibit locality among antennas and subcarriers, which encourages utilizing convolutional architectures, which can significantly reduce the complexity in both training and inference. This is especially critical in wireless applications, as it is important to acquire an accurate channel estimate within the channel coherence time. Moreover, convolutional kernels, once trained, work for different input dimensions; that is, we do not need to train and use a different NN when the number of antennas in either side of the channel, or the number of subcarriers allocated for communication change.Once the channel matrix However, as we have mentioned earlier, lossy compression is a challenging task even when the underlying source distributions is known perfectly. While we have a relatively good understanding of the fundamental rate-distortion performance for independent and identically distributed sources in the asymptotic limit, lossy compression for practical sources, such as image, audio, or video, has been a research challenge for many decades. Recently, dimensionality reducing autoencoders have shown significant success for lossy compression of such sources with a data-driven approach. Similarly for the CSI, dimensionality reducing autoencoders have recently been used to efficiently reduce the massive MIMO CSI overhead. These autoencoder architectures can be trained to learn a lower dimensional representation of the original CSI matrix to be transmitted over the feedback channel with a reduced overhead. An initial study using this autoencoder approach showed significant improvement in comparison with the best performing sparsity-based techniques These DL-based CSI reduction techniques mainly train an end-to-end auto-encoder structure, assuming ideal feedback of the reduced CSI. However, the estimated CSI (of the downlink channel) is fed back to the transmitter through the uplink channel, which also suffers from noise, interference, and fading. It becomes crucial to design CSI compression and feedback schemes that not only reduce the CSI overhead efficiently, but are also robust against the feedback channel impairments.digital and analog CSI schemes. Digital schemes, which have traditionally received more attention, are based on the separation approach: CSI is first compressed into as few bits as possible and these bits are reliably fed back to the transmitter using a low-rate channel code, which adds redundancy in a way to cope with the channel noise and error in the feedback link. On the other hand, analog CSI follows a joint source-channel coding approach, and directly maps the downlink CSI to the uplink channel input in an unquantized and uncoded manner. Analog approach simplifies the feedback operation as it does not require explicit quantization, coding, and modulation. If the uplink feedback channel is an additive white Gaussian noise channel, and the downlink CSI is Gaussian and perfectly known at the UE, the analog CSI scheme (that incurs zero delay) is optimal in that it achieves the same minimum mean-squared error distortion for the reconstructed CSI at the BS as a scheme that optimally quantizes and encodes the CSI, while incurring infinite delay. The low-latency of the analog CSI scheme makes it a favorable alternative in rapidly changing MIMO channels where the CSI needs to be estimated and fed back to the BS periodically. We shall overview both analog and digital CSI schemes in the presence of feedback channel impairments in the following subsections.There are two main approaches to cope with the limitations in the CSI feedback channel, i.e., the The earlier autoencoder-based CSI reduction techniquesAlthough the authors inInIn the CNN architecture in Fig. entclass1pt{minimaThe training cost for DeepCMC is a weighted sum of the mean square error (MSE) of the CSI reconstruction and the quantizer’s output entropy. A weight parameter We note that, in contrast to the literature on CSI feedback, which has mainly focused on minimizing the reconstruction error, DeepCMC is trained with a rate-distortion cost that takes into account both the compression rate (in terms of bits per channel dimension) and the reconstruction MSE. As we will see below, this additional compression step leads to a significant improvement in the achieved performance. It also allows adapting the CSI quality to the available feedback channel quality.Another important benefit of the DeepCMC architecture is that, it is fully convolutional, and has no densely connected layers, which makes it flexible for a wide range of MIMO scenarios with different number of sub-channels and antennas. As shown by the simulation results, although DeepCMC is trained for a specific number of sub-channels and antennas, it generalizes well to other configurations with different number of sub-channels and antennasIn Fig. For the comparison in Fig. As it can be observed from Fig. Analog CSI feedback follows a joint source-channel coding approach, and directly maps the downlink CSI to the uplink channel input in an unquantized and uncoded fashion. A CNN-based analog CSI feedback scheme, namely AnalogDeepCMC is proposed infeedback overhead. The feedback channel over the j-th uplink subcarrier denoted by j-th subcarrier and Consider CSI feedback from a single-antenna user to a BS with Figure For comparison of the digital and analog feedback performance results, we will assume that the digital feedback can be provided at the instantaneous capacity of the feedback channel. As we have discussed above, this would require the UE to know the uplink channel state. However, during downlink channel training in an FDD MIMO scenario, the UE does not yet know the uplink CSI, and hence, will typically take a cautious channel coding and modulation approach which works at a rate significantly below outage event, and the NMSE will equal 0dB. This is why the NMSE curves all saturate at 0dB for low Figure As observed in Fig. Figure In the previous sections, we have focused on exploiting the joint distribution of CSI matrices to reduce the overhead for CSI estimation and feedback using NNs for lossy CSI compression. In this section, we will explore how we can exploit joint distribution across antennas and subcarriers, or across time and space to further reduce, or even completely remove the amount of required CSI feedback. This is based on the idea of using the available CSI information at the BS at a certain point in time, space or frequency or a subset of antennas as correlated side information to improve the compression efficiency with NNs. This can be considered as implementing Wyner-Ziv lossy compression As an example, consider a FDD massive MIMO scenario, where channel reciprocity does not hold, and separate downlink and uplink training would normally be necessary. Although the uplink and downlink channels are not fully reciprocal, the uplink and downlink signals traverse the same geometrical paths with different frequencies, which imposes some correlation between them. The authors in If the side information proves to be sufficient for predicting the required CSI with an acceptable distortion using a NN, then the NN can characterize a mapping function to predict the required CSI from the available side information with zero overhead. Such mappings can significantly reduce the CSI acquisition overhead and have been considered in Massive MIMO systems are considered as the key technology to enable the excessive throughput requirements in 5G and future generation wireless networks due to their ability to serve many users simultaneously with high spectral and energy efficiency. However, due to the drastic increase in the number of antennas, CSI acquisition and feedback become challenging, requiring excessive time, frequency and computational resources potentially crippling benefits of massive MIMO systems. Many previous works have taken model-driven approaches assuming sparse or low-rank models on the CSI matrix to reduce the overhead. However, these techniques cannot exploit statistical structures that go beyond sparsity. This encouraged data-driven approaches based on training NN architectures over large datasets of CSI matrices, generated using accurate channel models or even from channel measurements, to capture these structures and use them to reduce CSI acquisition and feedback overhead. DL-based approaches have shown significant improvements in comparison with traditional methods for CSI estimation, compression and feedback. Yet, there is still much room for future research.Many NN architectures proposed so far use fully-connected layers for different estimation/compression tasks. While fully-connected NNs have the potential to learn and exploit complex joint distributions across all the antennas and subcarriers, they do not easily scale with MIMO dimensions, and need separate training for different number of antennas, subcarriers, etc. Hence, more insights on the correlation structures of the CSI in practical massive MIMO systems need to be exploited to design more efficient and less complex NNs for the CSI acquisition tasks. On the other hand, many of the existing works focus on a single task  and propose a NN architecture to achieve optimized performance for that specific task. However, the complete CSI training process consists of pilot transmission, CSI estimation, and feedback, and these tasks interact and effect each other . On the other hand, NNs have the capability to model and optimize processes in an end-to-end manner. A NN architecture trained end-to-end for the CSI acquisition task is not yet available. We believe such an end-to-end optimized architecture will not only benefit from the interactions between different tasks, but also can reduce the overall complexity of the NN by avoiding repeated layers that would be required in a task-by-task design process. We also note that, most of the existing results consider a single-user or a single-cell massive MIMO system, and extending these results to more general multi-cell multi-user massive MIMO scenarios is another potential direction for future research. Finally, practical implementation of these NN-based techniques in real environments on real devices has not yet been studied, but may be critical not only to evaluate the performance of the NNs trained on data generated by various channel models in real channel conditions, but also to understand the impact of limited computational resources available at the UEs.