The collective oscillations of charge density (plasmons) in conductive solids are basic excitations that determine the dynamic response of the system. In infinite two-dimensional (2D) electron systems, plasmons have gapless dispersion covering a broad spectral range from subterahertz to infrared, which is promising in light-matter applications. We discuss the state-of-the-art physics of 2D plasmons, especially in confined 2D electron systems in stripe and disk geometry, using the simplest approach for conductivity. When the metal gate is placed in the vicinity of the 2D electron system, an analytical description of the plasmon frequency and damping can be easily obtained. We also analyze gated plasmons in the disk when it was situated at various distances from the gate, and discuss in detail the nontrivial behavior of the damping. We predict that it is not a simple sum of the radiative and collisional dampings, but has a nonmonotonic dependence on the system parameters. For high-mobility 2D systems, this opens the way to achieve the maximal quality factor of plasma resonances. Lastly, we discuss the recently discovered near-gate 2D plasmons propagating along the laterally confined gate, even without applied bias voltage and having gapless dispersion when the gate has the form of a stripe, and discrete spectrum when the gate is in the form of disk. It allows for one to drive the frequency and spatial propagation of such plasmons. In this article, we review and analyze the properties of the plasma oscillations or plasmons in two-dimensional (2D) electron systems (ESs) in which carriers, electrons or holes, are localized in a very thin layer or plane and are free to move in two spatial dimensions. Though they have already been studied for more than half a century , scientiThe spectrum of 2D plasmons in infinite 2DESs was first predicted theoretically ,2. Then,To utilize 2D plasmons, it is necessary to clearly understand their properties, especially in profiled nanostructures, which are used ubiquitously for effective light-plasmon interaction. Although the main features of 2D plasmons are generally well-known, in recent years, a number of important fundamental properties have been recognized, especially in practically essential laterally confined 2DESs, which we review. The best-quality plasmons have been obtained in high-mobility quantum wells and heterostructures such as GaAs/AlGaAs structures in which the electron relaxation time due to collisions with impurities and phonons reaches record values . NeverthWe describe plasmons in the simplest classical manner using Maxwell’s equations and the dynamical Drude conductivity for the constitutive relation between the current density and electric field in 2DES. The dynamics of confined 2D plasmons is controlled by partial differential equations, which can be reduced to a complex integrodifferential equation. Of particular interest are the analytical solutions of this integral equation under conditions close to the experimental situations. We pay special attention to the damping of 2D plasmons because it determines the range of existence of the plasmons and the feasibility of their utilization in applications. First, in d above the gate, which was assumed to be an ideal infinite metal plane. The system was placed into a perpendicular constant magnetic field Before considering the confined structures, it is instructive to discuss an infinite 2DES, because its plasmon spectra can be easily derived analytically, which helps to understand qualitatively many features of plasmons in confined 2DESs. We considered a 2DES situated at a distance We considered the propagation of 2D plasma excitations in the form of plane waves, i.e., the solutions for  charge density and other deviations from their average values being proportional to c is the speed of light in vacuum, and parameter In an isotropic 2DES, the conductivity tensor is antisymmetric, i.e., ing form ,39,40,41t, Reβ≥0 , describLet us consider several well-known cases. If the external magnetic field is absent, then Equation  splits igraphene ,44 and ographene ,46. The n, m are the 2D electron concentration, charge, and effective mass, respectively, ħ) and the interband transition frequencies, and the wavelength of the plasmon is much greater than the Fermi wavelength and the electron mean free path. In practice, this approximation works well for a typical 2DES, based on quantum well or graphene structures, at least up to terahertz frequencies ..75]. TheIf a partially gated 2DES with an ideal metal gate is placed in the weak perpendicular magnetic field plasmons :(30)ω(B)Above, we did not take into account collisional decay rate  as well .Lastly, let us emphasize once again that, in the considered partially gated 2DESs, there was no bias voltage applied to the gate, so the conductivity of the 2DES was homogeneous. The existence and (quasi)localization of near-gate plasmons were entirely due to the different Coulomb interactions between 2D electrons inside and outside the gated area of the 2DES.In summary, we considered and reviewed the recent theoretical studies of plasma waves in confined 2DESs on the basis of quantum wells and heterostructures. We assumed that an ideal metal electrode (gate) could be situated parallel to the 2DES, and/or a constant external magnetic field could be applied perpendicular to 2DES plane. In this paper, we focused on plasmons in 2DES in the form of a stripe or a disk, or an infinite 2DES with laterally restricted gate.Concerning 2DESs in the form of a stripe or a disk, we found that electromagnetic retardation effects significantly modify the plasmon frequency and the lifetime. The latter was contributed by the so-called collisional damping appearing due to electron scattering on impurities and phonons, and the radiative damping that occurred due to the radiation of electromagnetic waves during plasmon oscillations. Although the frequency of plasma waves could be qualitatively estimated from the plasmon dispersion law for an infinite 2DES, the damping required much more accurate analysis. In particular, the damping is not a simple sum of collisional and radiative dampings; instead, it has a nonmonotonic dependence on system parameters. For plasmons in gated 2DESs, the damping can have prominent part oscillating as a function of the distance between the 2DES and the gate, which can significantly affect the plasmon lifetime even if this distance is large compared to the lateral size of 2DES and the plasmon wave length.We also briefly discussed the recently discovered so-called near-gate 2D plasmons that appear in infinite homogeneous 2DES with a laterally restricted gate situated in its vicinity. For the stripe-shaped gate, the fundamental mode of such plasmons possesses gapless dispersion low  and shows unexpected properties, combining the features of gated and ungated plasmons. In the case of a disk-shaped gate, near-gate plasmons had a discrete spectrum and manifested a strong interaction with the ”bulk” of ungated 2D plasmons, which resulted in the finite lifetimes of such modes due to the decay in the continuum of the 2D plasmons existing far from the gate.


Laparoscopic hernia repair involves a risk of adhesion between coated mesh and viscera. Plant polysaccharides such as starch and carboxymethylcellulose (SC) make up a product that acts as a barrier and prevents intraperitoneal adhesions. This study aimed to evaluate whether topical SC can also reduce adhesions between mesh and intra-abdominal organs.Forty rats each received placement of two intraperitoneal mesh fragments, one on each side of the abdominal wall. Randomly, 20 animals received SC on the right and other 20 on the left, leaving the contralateral side as a control. Fourteen days after the surgery, the animals underwent an additional laparotomy in which macroscopic analysis was performed.As for the percentage of the mesh area affected by adhesion, one (2.6%) animal had > 75% adhesion on the experimental side, and 11 animals (28.9%) on the control side. The adhesion intensity score showed firm adhesions in three (7.9%) animals on the experimental side and nine (23.7%) on the control side.The use of SC decreased the intensity of adhesions and the surface area of the mesh affected by adhesions. There was no negative interference of the product in the incorporation of the mesh into the abdominal wall. The exact global incidence of incisional hernias is uncertain, with 2–20% of all laparotomies developing incisional hernias, especially midline laparotomiesLaparoscopic surgeries are associated with a lower rate of early complications, such as surgical site infection, seroma, and bleedingDespite these advantages, laparoscopic repairs using the intraperitoneal onlay mesh (IPOM) technique expose the patient to the risks of mesh in direct contact with intra-abdominal organs and structures. Even when using meshes which supposedly provide a protective barrier, there are reports of complications secondary to ileus, adhesions, mesh infections, abscesses, fibrosis, chronic pain, and even intestinal obstruction, and enteric fistulasAdhesions that increase these potential risks occur due to foreign body reaction secondary to the inflammatory reaction generated by the presence of a prosthesis inside the abdominal cavity and in contact with intracavitary organsThe objective of this study was to evaluate whether topical SC can reduce adhesions between the mesh and intra-abdominal organs after IPOM hernia repair in an experimental model, in addition to the already known effect of preventing intraperitoneal adhesions.This research project complied with the rules of the National Council for Animal Experimentation and was approved by the Animal Ethics Committee of Universidade Tiradentes (no. 011120).The Symbotex mesh is a synthetic, nonabsorbable mesh made of three-dimensional polyester monofilaments coated with bioabsorbable collagen film on its visceral side. Polyester is the result of the reaction of alcohol with carboxylic acid and is a strong, durable, and hydrophilic material. It has pores of 2.3 – 3.3 mm and 66 g/mAdhesion STP (ASTP) is a natural product made by the plant polysaccharides SC, which have hemostatic and anti-adhesion properties. Carboxymethylcellulose is a low-molecular-weight and water-soluble cellulose product. It reduces adhesion and fibrosis formation by creating a film that works as a mechanical barrier, acting as a healing reorganization agentA total of 40 Wistar male rats weighing between 250 and 350 g were used. The animals were housed in the bioterium, with a natural light-dark cycle, adjusted environmental temperature and humidity, and fed and watered ad libitum, both before and after surgery.The animals underwent laparotomy with placement of two intraperitoneal mesh fragments, one on each side of the abdominal wall. Randomly, 20 animals received SC in the abdominal cavity on the right, and other 20 animals received SC on the left, leaving the contralateral side as a control (with mesh and without SC). The experiment used two 3-g bottles of the product, totaling 6 g, equally divided among the 40 animals analyzed using a precision scale.Fourteen days after the surgery, the animals underwent an additional laparotomy, in which macroscopic analysis was performed.The animals were anaesthetized with an intraperitoneal injection of 50 mg/kg ketamine hydrochloride and 20 mg/kg xylazine hydrochloride.After shaving and antisepsis, an 8-cm long incision was made in the ventral part of the abdomen, involving the skin, aponeurosis, and peritoneum, reaching the abdominal cavity. Thereafter, two fragments of meshes measuring 1.5 × 1,5 cm were interposed and fixed to the abdominal wall 1 cm from the midline, with four simple stiches using 4-0 polypropylene . RandomlAfter complete post-anesthesia recovery, the animals were placed in appropriate cages, with a maximum of three animals per cage, being offered water and food ad libitum until the next surgical procedure.2 chamber. Then, necroscopy was performed, and the macroscopic aspects related to the mesh were observed. The degree of adhesions between the organs and meshes (adhesion scoring), area of adhesion between the surface of the mesh and intraperitoneal structures (adhesion coverage on the mesh surface), and integration of the mesh into the abdominal wall (tissue integration score) were evaluatedOn the 14th postoperative day (POD), the animals were euthanized using a COThe variables were described as absolute and relative percentage frequencies. The hypothesis of equal location measures was tested using the Mann-Whitney’s test. The rank-biserial correlation effect size was estimated to evaluate the size of the observed differences, which evaluates the percentage of evidence favorable to a given hypothesis. The study considered a 5% significance level and used the R Core Team 2022 software (Version 4.2.0).One animal died on the nineth POD and another on the 12th POD due to undetermined causes. The mesh used with and without topical SC was evaluated regarding the percentage of surface affected by adhesions, the degree of intensity of the adhesions formed, and the degree of incorporation of the mesh into the abdominal wall on the 14th POD .In all cases, the results showed some degree of adhesion with or without SC, even with coated meshes.As for the percentage of the mesh area affected by adhesion, two (5.3%) animals with mesh and SC and one (2.6%) only with mesh had 0% of their surface affected, as they had adhesions only on the mesh edges; 27 (71.1%) animals on the experimental side and 16 (42.1%) on the control side had between 1–25% of their surface affected; four (10.5%) animals on the experimental side and three (7.9%) on the control side had between 25–50% of their surface affected ; four  animals had flimsy adhesions between the mesh and the intra-abdominal structures on the experimental side, and 21 (55.3%) on the control side. Intermediate adhesions were present in six (15.8%) animals on the experimental side and eight (21.1%) on the control side. Firm adhesions were present in three (7.9%) animals on the experimental side and nine (23.7%) on the control side. The intensity of adhesions formed also showed significant results (p = 0.039), with evidence of firmer adhesions in the control group (R = 0.231).SC presented no significant results regarding the integration between the mesh and the abdominal wall (p = 0.579), with 36 (94.7%) animals on the experimental side and 37 (97.4%) on the control side being classified as A; two experimental animals (5.3%) and no control classified as B; and only one (2.6%) control animal classified as C .As mesh adhesions are one of the main complications and cause of concern when using the IPOM technique, surgeons seek ways to reduce or stop these adhesions. Some surgical techniques avoid the use of intraperitoneal meshes and access retromuscular or preperitoneal spacesIn the present study, despite using a coated mesh, all animals showed some degree of adhesion. As for the percentage of the mesh area affected by adhesion, two animals (5.2%) on the experimental side and one (2.6%) on the control had 0% of the surface affected, as they had adhesions only on the mesh edges. The other animals showed adhesions on the mesh surface with or without SC. Some experimental and even clinical studies demonstrated that, even with the protective barrier, these intraperitoneal meshes present different degrees of adhesions with intra-abdominal structuresThe meshes coated with a protective barrier have different materials on their visceral surface that allow contact between the mesh and intra-abdominal organs. These materials include polyvinylidene fluoride, polylactic acid, oxygenated regenerated cellulose, polyglycolic acid, collagen, and chitosanThe product used in the experiment is available in the Brazilian market under the commercial name Adhesion STP. It is marketed in the form of powder or gel, with packages of 1, 3, or 5 g and with the possibility of laparoscopic application. This study used the powder presentation as it can be applied to a larger area and it is easier to use. Another brand like the one used in the study is the 4DryField (4DF), which contains only starch and no carboxymethylcellulose and it is not available in Brazil, but it is used in Europe. This product is also available as powder and in 1-, 3-, 5-, and 9-g packages. Arista is another product containing the plant polysaccharide starch and it is also available as powder and in presentations of 1, 3, and 5 g.This experiment used a total of 6 g of SC (two 3-g bottles), divided equally among 40 rats, totaling 0.15 g of the product in each animal, with the contralateral side of the studied abdomen being the control. Such volume was determined based on the total coverage of half of the abdominal cavity of each animal, with SC being sufficient to cover the contact area between the mesh and the intracavitary organs, respecting the proposed dose of up to 1 g/kgThere are no studies in the literature evaluating the systemic effects of SC in the form of ASTP. There is also no mention of side effects in its instructions for use. 4DF, in turn, brings a package insert warning regarding the possibility of an inflammatory reaction with increased C-reactive protein after its use. However, a retrospective study evaluated systemic inflammatory effects, and this product was considered safe as it did not induce a significant systemic inflammatory response in patients using between 3–5 g of 4DFPlant polysaccharides have been used to avoid intra-abdominal adhesions after conventional surgery. On an experimental basis, compared to other non-adherent agents, it significantly reduced the incidence and severity of adhesions after laparotomiesAnother clinical study evaluated 20 women undergoing re-laparotomies after using 4DF, showing that 18 of them had effective adhesion prevention with topical use of 3–15 g of the productAs for the intensity of the adhesions evaluated in the study, there were mesh adhesions with the intestine and liver on the side of the mesh without SC . A higheAs for the percentage of the surface area of the mesh affected by adhesions, most of the adhesions on the SC side scored 1–25%, and only one animal had adhesions in > 75% of the mesh. In the sided without SC, the number of animals with adhesions decreased in the score between 1–25% and increased in the score between 5–75% and > 75%, demonstrating protective effect of SC in the area affected by adhesions.As for incorporation, the purpose of this study was to assess whether the topical use of SC could interfere in this process, but there was no statistically significant difference, i.e., its use did not interfere with the mesh incorporation into the abdominal wall. Only one animal on the side without SC had < 50% incorporation. This is important because the proper incorporation of the mesh into the abdominal wall is crucial for the outcome of hernia surgeries. Thus, the product could not interfere with the biological process of fibrous tissue formation.Since this is the only study evaluating the effect of ASTP, with another experimental study evaluating the effect of 4DF in preventing intraperitoneal mesh adhesions, different experimental studies with larger samples, different dosages, other meshes, and even comparing the available brands are needed before we can propose the clinical use of this product.The topical use of the product composed of SC experimentally decreased the intensity of adhesions and the surface area of the mesh affected by adhesions with intra-abdominal structures. There was no negative interference of the product in the incorporation of the mesh into the abdominal wall.


In this study, the canine allogeneic meniscus was drilled first and then decellularized. The drilled tissue-engineered menisci  were transplanted into the knee joints of model dogs. On the basis of ensuring the mechanical properties, the number of the porosity and the cells implanted in allogeneic acellular meniscus was significantly increased. The expression levels of glycosaminoglycans and type II collagen in the drilled tissue-engineered meniscus were also improved. It was determined that the animals in the experimental group recovered well-compared with those in the control group. The graft surface was covered with new cartilage, the retraction degree was small, and the tissue remodeling was good. The surface wear of the femoral condyle and tibial plateau cartilage was light. The results of this study showed that increasing the porosity of allogeneic meniscus by drilling could not only maintain the mechanical properties of the meniscus and increase the number of implanted cells but also promote cell proliferation and differentiation. After transplantation, the drilled tissue-engineered meniscus provided a good remodeling effect  The meniscus is a kind of C-shaped fibrous cartilage tissue. It is located between the femoral condyle and tibial plateau in the knee joint and has important physiological functions, such as protecting and stabilizing the knee joint, transmitting stress, absorbing impact, nourishing and lubricating the tissue, and preventing the degeneration of articular cartilage . StatistRecently, the rapid development of tissue engineering and regenerative medicine has brought new methods to the treatment of meniscal injury. DMECM  retains the bioactive substances and three-dimensional structure of the meniscus with certain characteristics, such as biomechanical properties to similar to those of the natural meniscus, good cell affinity and low immunogenicity , 10. TheA total of 120 medial menisci were collected from the knee joints of 60 deceased dogs provided by Experimental Animal Center of Northwest A&F University. Sixty of the menisci (30 from each side) were drilled perpendicular to the bottom of the meniscus with a medical multifunctional electric drill with a 26-g needle (diameter of 450 μm). According to the preliminary test results, the hole spacing was set to 1 mm . The remAccording to the prescreening results from our laboratory, the menisci in the drill group and the control group, which underwent 3 freeze–thaw cycles, were shaken in a constant temperature shaking bed in decellularization fluid containing 1.0% (w/w) sodium dodecyl sulfate (SDS), 0.1% (w/v) ethylenediaminetetraacetic acid (EDTA) and 0.5% (w/w) peracetic acid. The decellularization fluid was changed every 2 days. According to the prescreening results from our laboratory, the undrilled group took longer to complete the decellularization due to the absence of voids. The drill group was treated for 3 days, and the control group was treated for 6 days. After removal of the decellularization fluid, the samples in both groups were washed with distilled water in an ultrasonic cleaner for 1 h, disinfected with 75% ethanol in a shaker for 1 h, washed with sterile Phosphate Buffer Saline (PBS) in a shaker for 1 day, wrapped with moist filter paper and stored at −20°C.n = 3) from the drill group and the control group were placed in 4% paraformaldehyde phosphate buffer solution at room temperature for 48 h. The samples were dehydrated by gradient alcohol, cleared by xylene and embedded in conventional paraffin wax. The sections were then continuously sliced at a thickness of 5 μM. The sections were stained with HE (hematoxylin and eosin) and Sirius scarlet and then observed under an optical microscope to determine whether the cells had been removed cleanly and the collagen fiber structure was intact.Allogeneic DMECM samples  were obtained from the drill group and the control group, placed into the specific gravity bottles filled with anhydrous ethanol, allowed to stand for 24 h. Next, the samples were degassed with a vacuum pump until no bubbles escaped, and the bottles were filled with anhydrous ethanol and weighed as M2. The meniscus filled with anhydrous ethanol was removed, and the remaining anhydrous ethanol and the specific gravity bottle were weighed as M3. Porosity = (M2-M3-M0)/(M1-M3).The meniscus was placed in an electric drying oven to dry to constant weight. Under constant temperature conditions, the mass of the 5 mL specific gravity bottle filled with anhydrous ethanol was set as Mn = 3) were placed on the loading platform of a Zwick 250 electronic universal testing machine . Each stent sample was preloaded with 1 N vertical pressure, and the compression test was carried out at a strain rate of 1 mm/min. The stress-strain curve is drawn with the deformation as the transverse axis and the pressure as the vertical axis. The compressive modulus of the meniscus was calculated according to the slope of the starting section of the curve and the cross-sectional area of the cylinder.Using a trephine, the meniscus was made into a cylinder with a diameter of 5.5 mm and a thickness of 2 mm. Two groups of allogeneic DMECM samples  on the drilling meniscus (n = 3) and the control meniscus (n = 3). The cells were placed in the incubator for 5 h, and after sufficient adhesion to the meniscus, the cells were transferred to a 12-well plate for coculture with complete α-MEM at 37°C under 5% CO2 with saturated humidity. The medium was changed every 2 days.The identified 4th passage canine BMSCs frozen in the laboratory , 14 weren = 3) and the control meniscus (n = 3) before and after implantation of the cells were placed in 2.5% glutaraldehyde at 4°C overnight, washed with PBS, dehydrated with an alcohol series, dried with CO2 critical point dryer for 4 h, sprayed with gold by an ion plating apparatus, and observed by scanning electron microscopy.The samples of the drilled meniscus .The proliferation of BMSCs on the drilled meniscus and control meniscus was detected by the CCK-8 method. After 1, 4 and 7 days of coculture, the original complete α-MEM was replaced with new complete α-MEM containing 10% CCK-8. The cells were then placed in an incubator for an additional 4 h of culture. The OD6/mL cell suspension, and 500 μL of the cell suspension was added dropwise to the upper surface of the drilled allogeneic DMECM. The meniscus was turned over after cell adhesion was fully achieved, and then 500 μL of cell suspension was evenly added to the underside of the meniscus, which was transferred to a 12-well plate after cell adhesion was fully achieved. After coculture at 37°C under 5% CO2 with saturated humidity, chondrogenic medium  was used for culture on Day 3. The medium was changed every 2 days. The same treatment protocol was performed with undrilled allogeneic DMECM as controls.Sixth passage canine BMSCs were prepared into a 3 × 10n = 3) from two groups induced for 1, 2, 3 and 4 weeks were digested overnight at 65°C with papain extract . After centrifugation of the digestive solution for 10 min at 10,000 × g, the supernatant was removed. According to the instructions of the Blyscan™ Sulfated Glycosaminoglycan Assay kit , the light absorption values were measured at 656 nm using a multifunctional enzyme marker. After subtracting the absorbance value of the empty allogeneic DMECM, the content of GAGs in samples from each group was calculated according to the standard curve.The drilled tissue-engineered meniscus (n = 3) from the two groups induced in vitro for 1, 2, 3 and 4 weeks were cut up in an ice box. Total protein was extracted by RIPA, and the total protein concentration was determined by BCA. After the concentration of total protein in each group was adjusted, loading buffer was added to the samples for denaturation by boiling, SDS–PAGE electrophoresis, membrane transfer, sealing, and incubation with type II collagen antibody  and the corresponding secondary antibody. Finally, chemiluminescent solution was added to analyze the sample bands, and a gel image processing system was used to detect the relative expression level of COL-II in the samples.The drilled tissue-engineered meniscus  were randomly divided into the drill group, control group, defect group and sham operation group, with 4 dogs in each group. According to the ANOVA degrees of freedom (E) and the 3R principle, our E value is 12, which proves that the number of animals is sufficient. For Meniscus repair, we believe that four dogs can demonstrate the short-term transplantation effect of a tissue-engineered meniscus. All of the dogs were reared, obtained, and housed in accordance with our institute's laboratory animal requirements. All procedures and the study design were conducted in accordance with the Guide for the Care and Use of Laboratory Animals  and were approved by the Animal Ethical and Welfare Committee of Northwest Agriculture and Forest University.in vitro. After general anesthesia , the animals were placed in the supine position. Made a 10 cm skin incision along the tibial tuberosity. The subcutaneous fascia was bluntly separated. The joint capsule was cut, the medial collateral ligament was transected, and the medial meniscus was exposed and separated. Then the whole medial meniscus was resected, and the tibial platform graft bed was established. The tissue-engineered meniscus constructed in vitro was placed into the graft bed. The anterior corner of the meniscus was fixed between the tibial condyles with 4-0 PGA line, the posterior corner was fixed in front of the medial intercondylar spine and posterior cruciate ligament insertion, and the body was fixed in the articular capsule. The joint capsule, fascia and skin were routinely closed after suturing the ligaments. After the operation was completed, the surgical site was disinfected. The surgical part was isolated with sterile gauze, and the limbs were wrapped with medical cotton and immobilized by polymer splints. In the control group, the medial meniscus of the right knee was surgically removed and implanted with the undrilled DMECM-BMSC tissue-engineered meniscus after 4 weeks of induction in vitro. In the defect group, the medial meniscus of the right knee was surgically resected, and the incision was sutured directly without repair. In the sham operation group, the joint capsule of the right knee joint was incised, and the surgical incision was sutured directly without cutting the meniscus. After surgery, the right knee joint was wrapped with medical cotton and immobilized with a splint. Synulox RTU  was injected intramuscularly for 3 consecutive days to prevent infection, and carprofen  was injected subcutaneously to control postoperative pain. The splint was removed 7 days later, and the skin sutures were removed 10 days later. The kennel was ventilated and disinfected regularly, and the test dogs exercised regularly.The drill group underwent surgical resection of the medial meniscus of the right knee, and drilled tissue-engineered menisci were implanted after 4 weeks of induction n = 4) based on eight indices, including lameness, support, locking, instability, pain, swelling, stair climbing and squatting , and the width of the tissue-engineered meniscus before transplantation was recorded as W0. Then, the width retraction rate of the transplanted meniscus was calculated as follows: (W0-W1)/W0. Three experienced pathology technicians who were not aware of the group conditions or repair measures were asked to report which symptoms were observed according to the gross evaluation criteria of the International Cartilage Repair Society (ICRS)  . Gross oMeniscal graft samples were cut from the knee joint and fixed with 4% paraformaldehyde for 48 h. Then, paraffin sections were made, and hematoxylin-eosin (HE) staining was performed to observe the tissue structure. Toluidine blue (TB) staining was performed to observe the acid polysaccharide in the matrix. Chondroproteoglycan (ACAN) and COL-II antibodies were used for immunohistochemical staining to observe the expression and distribution of ACAN and COL-II.Samples of the femoral condyle, tibial platform cartilage and subchondral bone were cut from the knee joint and placed in EDTA-2Na solution for decalcification. The decalcification solution was replaced every 3 days. After complete decalcification, paraffin sections were made, and HE and Safranin O-Fast green (SO-FG) staining were performed to observe the changes in cartilage.P < 0.05 was considered a significant difference, and P < 0.01 was considered an extremely significant difference. Bar graphs were constructed using GraphPad Prism 6 software.The experimental data were processed by SPSS 18.0 software, and the results are expressed as the mean ± standard deviation. Comparisons between groups were conducted by One-Way ANOVA. HE-stained sections were observed by optical microscopy. No nuclei were found in the allogeneic DMECM in the drilled group or control group, indicating that the cells had been cleanly removed. The Sirius scarlet staining results showed that the collagen fiber structure in the allogeneic DMECM was complete. An obvious hole-like structure was observed in the meniscus in the drill group, and the collagen fiber structure around the pore wall was complete .P < 0.01). The compression moduli of the drilled DMECM (51.63 ± 0.89) and control DMECM (52.51 ± 1.24) were not significantly different from that of the normal meniscus (54.14 ± 1.39) (P > 0.05), indicating that drilling had no significant effect on the mechanical properties of the meniscus.The results of the porosity and compression modulus assessments of the drilled and control meniscus are shown in As observed by scanning electron microscopy, the surface structure of the control DMECM was dense with no obvious pores , while t450 value of the BMSC-DMECM complex in the drill group and control group after 1, 4 and 7 days of culture showed an increasing trend with time, but the OD value in the drill group was significantly higher than that in the control group after 1 day of culture (P < 0.05) and was extremely significantly higher than that in the control group after 4 and 7 days of culture (P < 0.01). These results indicated that drilling could not only increase the number of cells planted in the meniscus but also facilitate the growth and reproduction of the implanted cells.The results of BMSC proliferation in the DMECM are shown in in vitro are shown in P < 0.05) and was extremely significantly higher than that in the control group after 3 and 4 weeks of induction (P < 0.01).The GAG contents  in the drilled and control tissue-engineered meniscus after 1, 2, 3, and 4 weeks of induction P < 0.01)  . These rOn the second day after surgery, the mental state, appetite and other signs of the dogs in each group returned to normal, although some had slight swelling of the operated limb. After 10 days, the incisions had healed well, except for those in the sham operation group, and the other 3 groups still displayed slight swelling of the knee joint. Two weeks after the operation, the dogs in the drill group and the control group tended to stand, squat, walk and step up and down normally, with no obvious claudication or interlocking phenomena; knee swelling disappeared, and only slight claudication occurred during vigorous running.P < 0.01) and was closest to that of the sham group (97.19 ± 0.95) (P < 0.01). The scores of the drill group and the control group were significantly higher than those of the defect group (24.26 ± 1.77) (P < 0.01).After 4 weeks, all motor functions returned to normal. The test dogs in the defect group showed lameness at all times after surgery, weight loss in the operated limbs, stiff movement of the knee joint, difficulty climbing up and down steps, inability to jump. The dogs in the sham operation group returned to normal standing, squatting, walking and stepping 2 weeks after surgery, and no abnormalities were observed in the operated limbs or knee joints. The anatomical observation results of the meniscal grafts and knee cartilage of the experimental dogs in each group 12 weeks after surgery are shown in In the control group, the joint fluid was clear and yellow in color. The meniscal graft was completely wrapped by hyperplastic tissue, and the graft had an obvious retraction phenomenon. The degree of wear of the femoral condyle and tibial plateau cartilage was more serious than that of the drill group. In the defect group, the joint capsule was hyperplasic and thickened, the joint fluid was thick and yellow, and there were obvious wear and scratches on the surface of the femoral condylar cartilage and the tibial plateau cartilage. In the sham operation group, no obvious abnormalities were observed in the articular cavity, the joint fluid was clear and yellowish in color, no significant changes were observed in the meniscus or surrounding tissues, and the surfaces of the femoral condylar cartilage and tibial plateau cartilage were smooth and complete.P < 0.01). Meniscus width did not change in the sham operation group, and the retraction rate was 0.The results of the width retraction of the meniscal grafts are shown in P < 0.01), close to that in the sham group (0.21 ± 0.32), and significantly lower than that in the defect group (2.49 ± 0.65) (P < 0.01).The ICRS score results of the knee cartilage are shown in Under the microscope, the HE-stained sections of the meniscal grafts in the drilled group showed obvious channels extending from the surface into the interior, and a large number of cells grew along the channels and infiltrated into the surrounding matrix, generally migrating from the surface to the deep layer. In the control group, the HE-stained sections of the meniscal grafts showed cell growth mostly on the surface or superficial layer, and the internal cells were few and scattered. At high magnification, monocytes infiltrated the surface of the implant, new vascular structures were observed in the stroma, and a small number of fibroid and chondroid cells were seen. TB staining showed that the cell matrix around the pores in the drill group was darker with a large number of blue-stained acidic polysaccharides in the matrix, while the cell matrix in the control group was lighter .Immunohistochemical staining of meniscal grafts: ACAN and COL-II were stained brown in the matrix and distributed around the cells in a cell-dependent manner. In the drilled group, there were more cells growing along the meniscus channel and more ACAN and COL-II around the cells, appearing as darker staining. The control group had darker staining on only the surface or superficial layer .Histological analysis of the femoral condyle and tibial plateau cartilage: HE- and SO-FG-stained sections of decalcified femoral condyle and tibial plateau cartilage samples were observed under a microscope. Compared with the control group, the surface of the drilled group was basically smooth and flat with slight wear, a complete and clear tidal line, uniform matrix staining, and more ovate chondrocytes, making it more similar to the sham operation group. In the defect group, the surface of the cartilage was severely damaged, rough and irregular cracks were observed, and the number of chondrocytes and matrix was significantly reduced .The porosity and number of attached cells are important indices for the evaluation of scaffolds used in tissue engineering. Higher porosity of a scaffold is conducive to the migration and proliferation of cells into the deep layer of the scaffold, as it promotes the transport of nutrients and metabolites and communication between cells. The meniscus contains fewer cells and has a high density of collagen fibers in its matrix, so its porosity is low. Low porosity of a scaffold has a direct effect on the number of seed cells implanted and the metabolism and proliferation of seed cells for tissue remodeling. To this end, researchers have adopted a variety of methods to improve the porosity of DMECM scaffolds. Maier used a trypsin/collagenase/protease multistep digestion process to remove cells in the menisci of sheep, and the results showed that the porosity of the prepared DMECM scaffold increased . Chen etThe meniscus plays an important mechanical role in in the knee joint by transferring loads, reducing shock and absorbing stress . Therefoin vitro was implanted into the recipient knee joint to test its repair effect. Meniscus size is specific to the particular individual. A donor graft that is too large can put more pressure on the joint surface, while one that is too small can put more pressure on itself (The meniscus plays an important role in the overall function of the knee joint. When meniscal damage is beyond repair, meniscal transplantation is an excellent alternative solution. Transplantation has been shown to reduce pain and improve knee function, as well as prevent cartilage degeneration and the development of osteoarthritis. Compared with the lateral meniscus of the knee, the medial meniscus is more prone to tear because it is tightly anchored to the tibial plateau by the coronary ligament and has a smaller range of motion. Therefore, in this study, a model of medial meniscus defect in the knee joint was first established, and then the tissue-engineered meniscus constructed n itself . In thisWith the anatomical structure of the meniscus having a concave upper surface and a flat bottom and the histological structure of high-density collagen fibers, the meniscus converts the vertical pressure from the convex femoral condyle into horizontal circumferential stress that is evenly distributed throughout the tibial plateau, which increases the joint contact area and reduces the direct pressure on the joint surface, ultimately protecting the articular cartilage well . As the in vivo. This strategy has positive significance in the recovery of knee joint function and lays a foundation for the extensive application of DMECM stents in the construction of tissue-engineered menisci. At the same time, the results of this study also provide a reference for human clinical tissue engineering meniscus and meniscus repair.In conclusion, the cell implantation rate of DMECM is a difficulty that remains in the development and utilization of tissue engineering. In this study, physical drilling of the meniscus was performed to improve the porosity of the DMECM on the premise of maintaining adequate mechanical properties, which not only shortened the decellularization time when preparing the scaffolds but also improved the implantation rate of the cells in scaffolds and the fluidity of culture medium. These factors were conducive to the deposition, adhesion, proliferation and differentiation of cells in scaffolds, thus promoting tissue remodeling Drilling can not only increase the porosity of DMECM, maintain the mechanical properties of these DMECM and increase the number of implanted cells but also promote the proliferation and differentiation of the cells and allow tissue remodeling after transplantation. The drilled tissue-engineered meniscus graft presented here has a positive effect on repairing meniscus injury, protecting articular cartilage and restoring knee joint function.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.The animal study was approved by Animal Ethical and Welfare Committee of Northwest Agriculture and Forest University. The study was conducted in accordance with the local legislation and institutional requirements.PD: Data curation, Methodology, Supervision, Writing—original draft, Writing—review & editing. TZ: Data curation, Methodology, Validation, Writing—original draft. WZ: Data curation, Methodology, Validation, Writing—original draft. YL: Data curation, Validation, Writing—original draft. DG: Data curation, Validation, Writing—original draft. CR: Data curation, Validation, Writing—original draft. XiaZ: Data curation, Validation, Writing—original draft. XinZ: Data curation, Validation, Writing—original draft. YZ: Funding acquisition, Methodology, Project administration, Writing—original draft, Writing—review & editing.


In addition, gelatin type A (GT)/alpha-tocopherol (α-TOC), PVA/olive oil (OO), PVA/orange essential oil (OEO), and PVA/anise oil (AO) emulsions were used. The experimental diameters of the nanofibers electrospun from the different tested systems were obtained using scanning electron microscopy (SEM) and ranged from 93.52 nm to 352.1 nm. Of the three studied ANNs, the one that displayed the best prediction results was the one with three hidden layers with the flow rate, voltage, viscosity, and conductivity variables. The calculation error between the experimental and calculated diameters was 3.79%. Additionally, the correlation coefficient (R2) was identified as a function of the ANN configuration, obtaining values of 0.96, 0.98, and 0.98 for one, two, and three hidden layer(s), respectively. It was found that an ANN configuration having more than three hidden layers did not improve the prediction of the experimental diameter of synthesized nanofibers.In the present work, different configurations of nt iartificial neural networks (ANNs) were analyzed in order to predict the experimental diameter of nanofibers produced by means of the electrospinning process and employing polyvinyl alcohol (PVA), PVA/chitosan (CS) and PVA/ Currently, the application of electrospun veils covers a wide range of uses in different industries such as pharmaceutical, food, and environmental due to the special physicochemical and microstructural characteristics displayed by these materials . In the 2) of 0.98, concluding that the parameters used in the design of the employed model significantly affected the average diameter of the electrospun nanofibers. Maurya et al. [−5. By employing two hidden layers, the minimal MMSE value was 8.5 × 10−5, which was obtained by using eight hidden neurons. Since the error values were minimal with two hidden layers, the configuration 4-8-8-1 was selected for maximal optimization, reporting R2 values of 0.79 and 0.94 for the training and testing data, respectively. Lakshmi Narayana et al. [2 value of 0.97 was obtained for the training data and 0.98 for the set of test data. Likewise, Premasudha et al. [This study reported a correlation coefficient . For the electrospinning process, a voltage interval ranging from 20 to 30 kV was selected; the apparatus was connected in series, and the injector–collector distance oscillated between 10 and 20 cm.The viscosity of the studied solutions/emulsions was determined by means of a RheolabQC Anton Paar rheometer at 25 ± 1 °C, employing the DG24 concentric cylinder configuration and the Star Rheoplus 3.0x software. The conductivity was measured with a Conductronic piece of equipment (model PC18) at 25 ± 1 °C.The viscosity and conductivity of the PVA emulsions incorporated with the EOs and GT/α-TOC emulsions and PVA/CS and PVA/Av solutions were established prior to the electrospinning process.The structures of the electrospun nanofibers were analyzed by means of scanning electron microscopy (SEM), employing a microscope (model JSM-6610LV). The images were processed with the ImageJ 1.51j8 software, and with it, the experimental diameter of the nanofibers was also determined, which corresponded to the arithmetic mean of 85 measurements of SEM carried out with different nanofibers .In the present work, the multilayer perceptron (MLP) neural network was employed with sigmoid activation (logsing) in the hidden layers, according to Equation (1), and linear in the output layer, as indicated in Equation (2) ,38:(1)f :(3)xn=x−The error percentage was calculated by means of Equation (4):The relative contribution of each input variable was calculated by means of the algorithm proposed by Olden et al. , accordiThe experimental diameters of the nanofibers, reported in the support material , are cloAs for the PVA/OEO nanofibers, a directly proportional relationship between the concentration and experimental diameter of the nanofibers was observed, as shown in On the other hand, a higher concentration of gelatin in the solution of the GT/α-TOC nanofibers allowed the production of thinner nanofibers, as observed in tic acid ,46,47.Regarding the PVA/CS nanofibers, a decrease in the experimental diameter of the nanofibers was observed as the CS concentration increased, as shown in On the other hand, the Av extract consists of aloine (polyhydroxylated anthraquinone glucoside), which is characterized by having a long alkyl structure that explains the high electrical conductivity of the electrospun solution .As observed in w/w), where it is evidenced that the PVA concentration plays a major role in the surface topography and distribution of the nanofiber experimental diameter. It is confirmed that at 10% PVA, larger diameters than those with 8% are produced; also, the presence of a branched microstructure is evidenced. The micrographs in 2 that relates the predicted diameter to the experimental one. For test 1, the R2 value was 0.71, and for test 2, it was 0.70, which indicated that the results of tests 1 and 2 were not satisfactory in the prediction of the experimental nanofiber diameter; for this reason, increasing the number of input variables to four was considered, as shown in The weighing of the input variables  and outpThe configuration with four ANN input variables consisted of one hidden layer with a variable number of neurons from two to fourteen, as shown in 2 of 0.96 and an error percentage of 4.44%; these results are in contrast with the rest of the proposed configurations for predicting the experimental nanofiber diameter, thus confirming that this configuration was the best approach to the experimental values of the nanofiber diameters obtained by SEM. Different configurations of ANN models featuring a single hidden layer have been employed in the prediction of experimental data [2 of 0.99.In order to avoid overparameterization, a variable number of neurons in a hidden layer from 2 to 14 was chosen for this study. Higher test MMSE values were observed in the ANN configurations consisting of 2, 4, 12, and 14 neurons, as observed in tal data ,56, whictal data , who emp2 ≤ 0.7, more training with the concomitant modification of both hidden layers and neurons is necessary [It has been reported that the use of a single hidden layer can favor the prediction of experimental data ; howeverecessary ,60.For this reason, the 8-neuron configuration allowed the establishment of the importance of the variables related to the characteristics of the polymeric solutions/emulsions and of those operation variables associated with the electrospinning process that are implied in the prediction of the experimental diameter of nanofibers. This type of sensitivity analysis was also proposed by Nasouri  and Kala2 closer to unity, which would imply an enhanced relationship between the experimental diameters and those predicted by the ANN. To this end, the 8-n configuration was proposed, which consisted of 8 neurons in the first hidden layer, whereas n  represented the variations of the neurons corresponding to the second hidden layer, with the following configurations shown in 2 of the output results corresponding to the training, test, and validation stages, it was observed that the configurations in 2 of 0.98 and average error percentage of 3.96%. Similar results were presented by Khatti [2 of 0.97. The prediction of the experimental nanofiber diameter by means of this ANN is complex and depends on the studied system and availability and quality of the input data.Once the response of one hidden layer predicting the diameter of nanofibers was analyzed, the study of the effect of two hidden layers was proposed in order to obtain an Ry Khatti , who emp2 through an additional configuration of three hidden layers of 8-16-n neurons, as shown in n varied from three to six. The results revealed that the 8-16-3  was to increase the Re 8-16-3  and 8-16e 8-16-3  presente2 of 0.98  were used for predicting the experimental diameter produced during the electrospinning process of nanofibers from PVA, PVA/CS, and PVA/Av solutions and GT/α-TOC, PVA/OO, PVA/OEO, and PVA/AO emulsions. In addition, the experimentation is related to the theory by means of an ANN model designed for understanding the nonlinear relationship among operative variables of the electrospinning process such as flow and voltage and physical properties of the biopolymer and essential oil solutions/emulsions.An enhanced prediction of the experimental nanofiber diameter was achieved by employing four input variables  in comparison with the use of three variables  in the ANN configuration.2 close to 0.98. Nevertheless, according to the MMSE, the best configuration for predicting the experimental nanofiber diameter with the test data was the one with three hidden layers, with an MMSE value of 0.03, which is in contrast with the MMSE value of 0.06 for two hidden layers (8-16).The ANN configurations that best predicted the experimental nanofiber diameter were those with two and three hidden layers, with an RThe computation error between the experimental nanofiber diameter obtained by SEM and the one predicted by the ANN was 3.79% for the configuration with three hidden layers, whereas for the one with two layers, it was 3.95%, which confirms the reliability of the ANN with three hidden layers, which will allow for narrowing down the combinations of polymers, solvents, and concentrations of solutions/emulsions in earlier stages in order to optimize the experimentation stage before proceeding to the electrospinning process.Additionally, it was confirmed that the most influential variable in the prediction of the experimental nanofiber diameter by employing a one-hidden-layer configuration with eight neurons was the viscosity of the solutions/emulsions to be electrospun.


In this study, the stability of inhomogeneous nanocomposite cylindrical shells (INCCSs) under hydrostatic pressure in a thermal environment is presented. The effective material properties of the inhomogeneous nanocomposite cylindrical shell are modeled on the basis of the extended mixture rule. Based on the effective material properties, the fundamental relations and stability equations are derived for thermal environments. In this process, the first-order shear deformation theory (FSDT) for the homogeneous orthotropic shell is generalized to the inhomogeneous shell theory. This is accomplished using the modified Donnell-type shell theory. The analytical expressions are obtained for hydrostatic buckling pressure of INCCSs in the framework of FSDT and classical shell theory (CST) by obtaining a solution based on Galerkin’s procedure. The numerical examples presented include both comparisons and original results. The last section shows the influences of carbon nanotube (CNT) models, volume fraction, and shell characteristics on the hydrostatic buckling pressure in the thermal environment. Cylindrical shells are used in a wide variety of fields such as aircraft and spacecraft, submarines, rockets, and nuclear reactors. The properties of the composite materials used for the manufacture of cylindrical shells should be at a level that can meet the requirements of modern technology. At the end of the 20th century, the extraordinary efforts of materials scientists led to successful results, and in 1991, a seminal composite material with extraordinary properties, called carbon nanotubes, was discovered ,4.In recent years, developments in nanotechnology have facilitated the design and production of new-generation advanced functionally graded materials and extended their application areas. Nanocomposites (NCs) are a new class of inhomogeneous materials that are used in the aerospace, aviation, and automotive industries because they allow the production of structural elements that use few raw materials, and they are affordable and lightweight and use less energy. In addition, polymer structural members reinforced with CNTs can exhibit high mechanical properties, high toughness, improved thermal and electrical properties, good optical clarity, high wear resistance, and other outstanding properties, despite the slight increase in weight ,6,7,8,9.After research on nanocomposites revealed that they have extraordinary mechanical, physical, and chemical properties ,11,12, SThe literature review reveals that the stability of INCCSs subjected to hydrostatic pressure in a thermal environment is not sufficiently investigated. In this work, the FSDT proposed by Ambartsumian  for the This paper is structured as follows: the description of the model is presented in The notes on the geometry of the inhomogeneous nanocomposite cylindrical shell subjected to hydrostatic pressure are illustrated in ectively a. The shThe hydrostatic pressure acting on the inhomogeneous nanocomposite cylindrical shell is expressed as follows b 47]:. The SWCNT reinforcement is aligned in the It is assumed that the material properties of the CNTs and the matrix are temperature-dependent. Therefore, the effective material properties of INCCSs, such as Young’s modulus, shear modulus, and thermal expansion coefficients, are functions of temperature and location. Since the effective Poisson’s ratio and density are weakly dependent on temperature change and location, they are considered constant ,15. ConsSince the coefficients of thermal expansion are functions of the thickness coordinate, their mathematical expression in the longitudinal and transverse directions is expressed by the Shapery model as follows :(4)α11 distribution. The volume fraction of these patterns is modeled as follows :(5)Vcnt=In the U-model of CNTs along the thickness, one has The configurations of the homogeneous U-model and three types of INCs are illustrated in The stress–strain relationships of inhomogeneous nanocomposite cylindrical shells in thermal environments within FSDT can be expressed as follows ,39: (6)τThe shear stresses of INCCSs within FSDT change in the thickness direction as follows ,39,43:(9The relations The first column on the right-hand side of Equation (10) shows the strain components at the mid-surface, and the following definitions apply:The stress resultants of INCCSs are determined as follows :(12)Nij,The thermal forces and moments N11=Equation (15) presents the governing equations of INCCSs under hydrostatic pressure in the thermal environment within FSDT.Suppose that the two end edges of the cylindrical shell are simply supported; the corresponding boundary conditions are modeled as follows :At Also, the closed or periodicity condition is expressed asThe approximation functions for the above boundary conditions are searched as follows :(18)Φ=C1Substituting (18) into the system of Equation (15), and also taking into account (1), and then using the Galerkin procedure for the resulting equations in the range To find the analytical expression that determines the hydrostatic buckling pressure of the INCCSs, the determinant of the square matrix of the coefficients of Equation (18), expressed by the cofactors From Equation (20), one obtainsSince the influence of shear stresses is ignored in the basic relations, the following expression for the hydrostatic buckling pressure of INCCSs is obtained within the CST:The numerical values of the hydrostatic buckling pressure of INCCSs in thermal environments are presented in this section. The material used for the matrix is poly (methylmethacrylate), called PMMA, and the material used as the reinforcement element is  armchair SWCNT with length uated as (24)Em=3It should be emphasized that in medium-length cylindrical shells  of cylindrical shells of different sizes made of pure metal and tabulated in   used FEM, and Shen and Noda  used HSDT and the singular perturbation technique. Formula (22) is used in the calculation, taking into account that . Some of the data used in the comparison are given in . The Badthorf shell parameter is presented as  in . The values in parentheses denote the buckling mode in  ,46).Example 2. The magnitudes of the lateral buckling pressure for composite cylindrical shells patterned by CNTs with the U- and X-models based on the FSDT under two thermal environmental conditions are compared with the results of Shen  using HSDT and the singular perturbation technique and are presented in Table 3. From Formula (22), the formula for the lateral buckling pressure is obtained as follows:The material properties are taken from the study of Shen [and can be calculated from (24) and (25) at T = 300 (K). The following geometrical data are used:. Since the number of longitudinal waves corresponding to the lateral buckling pressure is equal to one, it is not included in   at two thermal environmental conditions. of Shen  and can Typical results of the parametric study are presented in T = 300 (K), the influences of shear deformations on the buckling pressure in shells with U-, V-, Λ-, and X-schemes are 12.58%, 9.03%, 8.7%, and 18.43%, respectively, and at T = 750 (K), these effects are 24.46%, 17.28%, 18.75%, and 33.33%. When comparing T = 300 (K) are less by 3.8%, 2%, 3%, and 4.3% in the U-, V-, Λ-, and X-constructs, respectively, while these the effects for T = 750 (K) are less approximately by 6%, 3.8%, 5.2%, and 7.8%, respectively. In all designs, the effect of SDs on hydrostatic buckling pressure values at T = 300 (K) and T = 750 (K). It has been found that as the temperature rises, its influence on the values of hydrostatic buckling pressure rises. In the same models, the increase in temperature significantly changes the values of the hydrostatic buckling pressure, and the effect of temperature is more pronounced in the frame of the FSDT. For example, when comparing the cases T = 300 (K) and 450 (K) in the same Λ-model, the effect of temperature on the buckling pressure values within the FSDT is 15%, 15.31%, and 14.29% for T = 300 (K) and 750 (K), the effects of temperature on the buckling pressure in the same Λ-scheme are 48.33%, 47.96%, and 48.41% for T = 750 (K) and Although the effect of SDs on the hydrostatic buckling pressure reduces as the fect see . For exaT = 750 (K) and T = 750 (K), that effect rises from 12.9% to 20%.The influence of the V- and Λ-models on the hydrostatic buckling pressure decreases compared to that of the U-model, but that effect increases in the X-pattern as the T = 300 (K) and T = 750 (K) temperatures on the buckling pressure load of U-, V-, Λ-, and X-modeled cylinders is around −48%. It is seen that the temperature effect is lower by around 2–12% in the framework of the CST The effects of inhomogeneous models on hydrostatic buckling pressure values generally increase with increasing temperature in the CST, but this effect is weakened when FSDT is used.(b)Although the increase in temperature reduces the hydrostatic buckling pressure values, the effect of the (c)The effect of the X-scheme decreases continuously with the increase in temperature in the FSDT frame for (d)In the same models, the increase in temperature significantly changes the values of the hydrostatic buckling pressure, and the effect of temperature is more pronounced in the frame of the FSDT.(e)The rise in (f)Although the effect of shear strains on the hydrostatic buckling pressure reduces as (g)The influence of the V- and Λ-models on the hydrostatic buckling pressure decreases compared to that of the U-model, but that effect increases in the X-model as the Analysis and comments using a closed-form solution revealed significant quantitative and qualitative changes in the stability of inhomogeneous nanocomposite cylindrical shells in the thermal environment. In order to prevent the damages that may occur in the applications and the accidents that may be caused by them, it is foreseen that the critical values revealed in the current study should be taken into account during the design phase of the structural elements.


The current review describes in detail the various membrane-based techniques, such as membrane contactors, for removing dissolved H2S from various wastewater streams. Various types of hydrophobic membranes have been used, with more emphasis placed on PVDF hollow fiber membranes. The hydrophobic membranes do not allow water to pass through, whereas H2S is readily allowed to pass through the membrane at ambient conditions. In addition, the use of monoethanol amine triazine (MEA-Triazine)- based H2S scavengers has also been described in detail, including the possible scavenging mechanism. The possibility of different types of byproducts has also been explained along with the possible routes to get rid of scavenger byproducts, such as apDTZ. The use of peroxy acetic acid has also been explained to oxidize and solubilize apDTZ. Furthermore, the use of vacuum-based dissolved H2S gas has also been described in detail. The application of the Knudsen and bulk diffusion models to the separation of dissolved H2S through the pores of the hollow fibers has also been explained. Finally, the future challenges and possible solutions along with concluding remarks have also been mentioned in the current review.Given the significance of dissolved H Although an anaerobic membrane bioreactor has proven efficient in producing high-quality effluent with a tolerance for variation in feed quality; one of the disadvantages is treating the wastewater rich in sulfates and organic matter. Since the concentration of sulfates and organic matter is higher in the feed, the sulfate-reducing bacteria can use sulfate as a substrate resulting in the production of H2S. Hence, the removal of dissolved H2S is required to reuse the water. Hence, the Silva group designed a modified direct contact membrane distillation (M-DCMD) configuration for removal of dissolved H2S from the real wastewater (2S (166 ± 15 mg/L−1)-containing permeate was generated due to the anaerobic biological digestion of sugarcane vinasse collected from the local company. The following M-DCMD system having a polypropylene (PP) hollow fiber membrane was used for removing H2S. In this M-DCMD system, the dissolved H2S feed was passed through the lumen of the hollow fiber membrane while a cold NaOH-receiving solution was passed on the shell side of the membrane. As PP is a super-hydrophobic material in nature, the entry of water into the membrane pores is not possible. H2S speciation at different pH values affects the solubility of H2S in the feed, which affects the content of S−2 ions in the feed, and hence, the removal of dissolved H2S from water is dependent upon the pH of the feed solution. At pH 4, 100% of H2S is present in a gaseous state, which increases the removal rate of H2S  for removing Hstewater . The reae of H2S b. Howeve2S-containing feed and the NaOH-receiving solution. The PP membrane being hydrophobic does not allow the water to pass through the membrane from either solution while H2S diffuses from the feed to the receiving solution. Moreover, the two solutions move in a counter-current manner, which increases the rate of removal of H2S from the wastewater stream [An elaboration of the structure of the PP hollow fiber membrane is given in the inset in r stream . M-DCMD 2S in addition to dissolved CH4. In the case of the anaerobic digestion of sludge, sulfate-reducing bacteria take over methanogenic bacteria, leading to the production of H2S. Since H2S has high water solubility, it is found in a dissolved form in the permeate, causing a foul smell, corrosion, SOx production, and toxicity. It has been reported that a concentration of 60 mg L−1 of H2S can cause an irreversible process failure of both acetate-fed and propionate-fed chemostats in an anaerobic digester [2S. In one such effort, E. Lee et al. developed a staged vacuum-based degasifier system for removing dissolved gases, including H2S from the permeate of a staged anaerobic fluidized membrane bioreactor (SAF-MBR) as given in the following −1 sequentially. A vacuum of −0.8 bar was applied across the chamber by the vacuum pump.Like other wastewater streams, the permeate of the anaerobic membrane bioreactor has also been identified to possess considerable quantities of dissolved Hdigester . Althoug2S was found to increase while moving from stage 1 to 2 and finally to stage 3. As the pH decreases and moves towards an acidic region, the H2S removal efficiency increases as shown in 2S reached 88% with pH-adjusted samples. This study found that dissolved H2S removal was governed by factors, such as pH, contact time, temperature, turbulence of the liquid phase, and equilibrium constant [The degasifier system resulted in a considerable decrease in the concentration of pollutants as the COD was recorded to decrease as the influent was moved from stage 1 to stage 3. In the case of the pH-regulated stream, the removal was found to be higher than the raw stream. Similarly, the removal efficiency of Hconstant .2S, mathematical modeling has been carried out in the literature. The researchers have used a hollow fiber membrane contactor with liquid–liquid extraction mode using a hydrophobic membrane as has been discussed in the previous sections. The wastewater stream was introduced into the lumen side of the membrane while an extractant solution was passed in a counter-current manner on the shell side of the hollow fiber membrane. The gas is desorbed from the lumen side and passed to the shell side of the membrane where it is instantaneously reacted with the extractant which is either NaOH or ethanolamine solution. The mathematical models were developed based on the radial and axial diffusion of H2S. The mass transfer across the pores of the membrane was explained based on Knudsen and bulk flow. The following assumptions have been made for the mathematical models:Given the dilute nature of the feed solution, the physical and transport conditions for the feed solution remain unchanged during gas the separation experiment;The isothermal operating conditions have no change in liquid density;There is no wetting or swelling of the membrane, and pores are assumed to be filled with air;There is a fully developed laminar flow with parabolic velocity profiles on the lumen side of the membrane. The operational experimental conditions for flow on the lumen side are chosen to be at a very small Reynold number, NRe, which is generally calculated to be 3;2S remains in molecular form;The pH of the feed solution is controlled so that H2S molecules in the lumen of the membrane;Two-dimensional unsteady state flow with axial and radial diffusion of H2S removal are large compared to the volume of membrane contactors;The volumes of feed and extractant solutions used during HAn instantaneous reaction takes place on the shell side as the extractant phase is highly concentrated.For the sake of better understanding and improving the performance of membrane-based separations of dissolved HlC and lD are the concentration (moles m−3) and diffusivity (m2 s−1) of H2S in the feed. The laminar flow condition has been assumed on the lumen side of the membrane, and hence, the resulting parabolic velocity, zν (ms−1), has been assumed as follows:r1 (m) is the inner radius of the lumen, and −1) in the lumen of the fiber. The Q (m3 s−1), and the number of fibers, N, in the membrane contactor.The gas transport on the lumen side is expressed by an unsteady state convective-diffusion equation, which accounts for both radial and axial diffusion components as given below:r < r1 and 0 < z < L is given in the following equation: oC is the initial concentration (moles m−3) of H2S in the feed solution.The initial condition when t = 0 and for all values of r and z where 0 < The boundary conditions are defined below for the transport of gases in a hollow fiber membrane contactor.r = 0, for all values of t (s) and z (m), the axial symmetry condition is applied as given below:At z = 0, for all values of r and t,At z = L, for all values of r and t, the axial diffusion is assumed to be negligible compared to bulk convection flow, which is given by:For r = r1, for all values of z and t, the flux of H2S in aqueous phase is equal to the diffusion of gases through the pores of the hollow fiber hydrophobic membrane as given below:gintp and gbp are the partial pressures (Pa) of H2S gas at the lumen and shell side, respectively, while gk, R is the universal gas constant (J/(mol.K). Pore is the mass transfer co-efficient inside the pore of the hollow fiber membrane, and hence, the above equation becomes the following:For the condition when r = r1, Henry’s law can be applied at the liquid–gas interface.a is the Henry’s law constant (Pa.m3/mol).At The mass transfer coefficient inside the pore can be estimated by the following equation:τ, of pore, porosity, ε, thickness, b (µm), of the membrane, and combined diffusivity, cD, pore.Equation (14) shows that mass transfer coefficient is dependent on the parameters, which include tortuosity, Dk, pore, can be predicted from the kinetic theory by relating the pore diameter, dpore, with a mean free path of the gas.wM is the molecular weight of the gas. The unit of Dk, pore is cm2 S−1. T is the temperature in K while dpore is the pore diameter in nm.It has been assumed that the transfer of the gas through the hydrophobic pores of the membrane occurs through both Knudsen and bulk diffusion. During Knudsen diffusion, pore size is smaller than the mean free path of the gas molecules and gas molecules colloid more with the walls of the pores than with each other. Due to excessive collisions with each other, the transport of the gas is impeded. The Knudsen diffusion coefficient, In the case of bulk diffusion, the pore size is greater than the mean free path of the gas, which allows the gas to rapidly transfer based on the concentration gradient.2S in a membrane contactor through the pores of the membranes is based on both Knudsen and bulk diffusion as given below:2 s−1.Hence, the removal of dissolved H2S at higher initial concentrations of H2S. The percent removal of H2S was found to be higher at the beginning of the operation with high H2S concentrations compared to lower H2S concentrations. However, with the passage of time, the removal efficiency reaches a steady state, and the removal of H2S flattens [The above-mentioned models have been verified through simulations, and the predictions made by these models have been proven to be in complete agreement with the experimental results and observations. The following flattens .2S from gaseous streams, very little attention has been paid to recovering dissolved H2S from wastewater resources. The currently used strategies also need extensive investigation and optimization for the efficient removal of dissolved H2S from wastewater streams. For example, the byproducts generated from the degradation of MEA-triazine are themselves a huge challenge, such as the amorphous polymeric byproduct apDTZ. The apDTZ deposits in the form of scales, which leads to the extensive fouling of the pipes and oil-producing facilities. Further investigations are required to ensure the complete utilization of the triazine scavengers. In addition to triazine-based scavengers, there is a need to search for novel types of scavengers that can eventually generate easily degradable byproducts.Although several methods have evolved over the past few years for removing HThe currently used methods for solubilizing scavenger byproducts are based on harsh oxidants, such as peroxy acids and hydrogen peroxides, which can cause excessive corrosion and damage to pipelines in the wastewater treatment plants. Although peroxy acids have been found useful for such applications, but the reaction is highly exothermic and spontaneous, which needs further investigation and optimizations. Control over the reaction is highly desirable for field applications. Moreover, the use of cosolvents for solubilizing the stubborn scavenger byproducts needs to be further explored to develop an efficient solvent system. The need of the day is to develop a strategy to minimize the generation of apDTZ.Furthermore, the use of membranes for removing unspent scavengers and byproducts is also a potentially viable technique for industrial and large-scale applications. There is a need to develop efficient membranes with suitable surface chemistry to minimize membrane surface fouling. In addition, there is a need to explore different types of membranes, such as ceramic, polymeric, and composite membranes for removing scavenger byproducts from the water streams. In addition, different membrane configurations, such as hollow fiber and flat sheets, should be explored for removing scavenger byproducts from wastewater streams. Different membrane modules should also be designed and applied to remove scavenger byproducts with lower chances of membrane fouling.2S removal are mainly focused on the use of a hydrophobic PVDF membrane and mostly employed in hollow fiber module form. There is a need to develop more hydrophobic membranes to minimize the loss of vapors through the pores of the membrane. The pores’ structure and size both need to be optimized to allow only the diffusion of H2S through the membrane. There is a need to develop an online system where the permeate of an RO plant should be directed towards a membrane contactor where the dissolved H2S can be efficiently removed from the permeate.The membrane contactors used for dissolved H2S depends on the pH of the feed, there is a need to develop and optimize the conditions of the feed leading to less scaling and enhanced recovery of dissolved gas under operating conditions.Since the percentage of dissolved H2S gas. The established Knudsen–Bulk diffusion model needs to be further optimized for a variety of hydrophobic membranes, leading to best performing membranes.Hence, a proper investigation on the available techniques, including a monoethanol amine triazine (MEA-Trizine) scavenger, peroxyacetic acid oxidation, and membrane contactors, can resolve the serious challenge of scavenging the toxic H2S from various feeds and wastewater streams. Among the various techniques that have been used for removing dissolved H2S, membrane contactors have shown huge potential for removing dissolved H2S. The hydrophobic membranes, such as PVDF and PTFE, have shown enormous potential in this regard because these membranes provide passageways to H2S gas while they do not allow water to permeate through them. Various mathematical models have been explored and developed for better understanding of gaseous diffusion through membrane contactors. Like membrane-based separations, triazine scavengers have also shown huge capabilities for treating dissolved H2S from wastewater resources and, hence, have been used for sweetening of sour water. However, the H2S scavengers generate several byproducts that polymerize and become a cause of concern. Hence, the use of some oxidizing agents, such as per(oxy) acids, has been shown to be promising for treating the byproducts generated during the scavenging action of H2S scavengers. Hence, the exploration of viable and commercially scalable dissolved H2S treating technologies is desperately required to mitigate excessive corrosion and lower the risk of acute toxicity caused by dissolved H2S.The current review has described the utilization of several techniques, including membrane-based separations for removing and recovering dissolved H


The paper presents a new model of secondary injuries after traumatic brain injury. The model is based on the cultivation of rat embryonic fibroblasts reprogrammed to a neuronal phenotype in the presence of cerebrospinal fluid from injured rats. The presented model was used to test the therapeutic effect of inducers of the synthesis of chaperones from the classes of pyrrolylazines and indolylazines, which have neuroprotective properties. Traumatic brain injury (TBI) may cause long-term neuronal death delayed for months. This phenomenon is called secondary damage and is traditionally associated with changes in blood supply, ischemia, hypoxia, inflammation, cerebral edema, increased intracranial pressure, etc. . At the Many scientific groups are involved in modeling secondary injuries after TBI in vitro. This is determined by the need to be able to test new therapeutic approaches or potential therapeutic agents without using animal models. Almost always modeling is reduced to simulating the effect of a single factor that causes secondary damage, for example, oxidative stress  or inflaIn our previous studies, we developed and tested a new model for analyzing secondary damage after traumatic brain injury based on cells cultured in the presence of CSF of injured animals . The adv2.Rat embryonic fibroblasts DFK-3 were obtained from the Vertebrate Cell Culture Collection core facility, which was supported by a grant from the Ministry of Education and Science of the Russian Federation (agreement no. 075-15-2021-683). Cells were cultured in DMEM medium  supplemented with 10% fetal bovine serum  and antibiotics penicillin 100 units/mL and streptomycin 0.1 mg/mL  at 37°C and 5% CO2 were dissolved in 600 µL of the ExtractRNA reagent . mRNA was isolated according to the previously described protocol [These cells were reprogrammed into a neuronal phenotype (DFK3-Neu) by incubating them for 5 days in the Neurobasal medium  containing the Neuromax supplement , 3% fetal bovine serum, 100 units/mL penicillin, and 0.1 mg/mL streptomycin. The neuronal phenotype was tested by analyzing the expression of a panel of markers of mature neurons , 10  using qPCRmix-HS SYBR  according to the manufacturer’s protocol. Data were analyzed for fold change in mRNA using Bio-Rad CFX software (version 3.1). Nucleotide sequences of primers are given in We found that the expression level of the genes encoding the main neuronal markers in DFK3-Neu cells  was, on average, 2–4 times higher than their expression level in DFK3 cells . An incrAt the next stage, we studied the effect of the CSF of injured animals on the survival of neuronal cells. For this purpose, we made TBI in rats according to the previously described protocol ; 9 days As part of the development of this model, it was necessary to test it to make sure that DFK-Neu cells are able to respond to drug treatment. For this purpose, we used pyrrolylazine and indolylazine derivatives synthesized by us , 14, whiFig. 4The key stage of this study was the verification of the new model. To do this, we assessed the survival of rat neurons in the presence of CSF of injured animals, as well as neuroprotective compounds from the classes of pyrrolylazines and indolylazines using the MTT assay. We found that PQ-29 and IA-50 effectively prevented neuronal death in the presence of CSF of rats after TBI. At the highest tested concentrations (8 μM), these compounds prevents the death of 14.36% and 10.9% of the cell population .Thus, we have developed a new convenient model for assessing secondary injuries after TBI. The key feature of the presented model is that it makes it possible to evaluate the cytotoxic effect of the CSF of injured rats on cultured rat cells with a neuronal phenotype. To verify the relevance of the new model, we tested the cytoprotective activity of compounds from the classes of pyrrolylazines and indolylazines, which we previously reported as neuroprotectors. Both compounds demonstrated protective activity in our in vitro secondary injury model. Compound IA-50 was tested in the model of secondary injuries after TBI for the first time, and its therapeutic effect was detected. A certain limitation of the possible use of this model is the lack of data on the possibility of using it to test drugs that do not affect the chaperone system.


To investigate the nature and susceptibility of community-acquired pneumonia (CAP) pathogens in drug-dependent patients.Staphylococcus aureus ATCC25923 strain.The susceptibility of community-acquired pneumonia pathogens isolated from sputum was studied in 31 drug-dependent patients. 13 (42%) were women and 18 (58%) were men. The average age of this group was 28.6 ± 1.2 years. The antimicrobial activity of the main groups of antibiotics was studied in comparison with the susceptibility of the archive S. aureus  and fungi of the genus Candida  prevailed, while in 15 cases, bacteria were inoculated in the form of monoculture, and in 16 cases in the form of associations of bacteria and fungi of the genus Candida. When studying the susceptibility of the isolated strains of microorganisms to the main groups of antibiotics, their high (P ≤ 0.05) resistance to the main groups of antimicrobial drugs used in standard treatment regimens for CAP was established.In total, 51 strains of microorganisms were isolated, among which CAP in drug-dependent patients has a severe complicated course due to the combination of highly virulent bacterial and fungal infections. The causative agents of community-acquired pneumonia in drug-dependent patients have low susceptibility to the main groups of antibiotics used in the treatment of this pathology.


Structural, magnetic, and electrical studies have shown that a reduction in CuCr2Se4 single crystals to the nanosize leads to (1) a weakening of ferromagnetic interactions, both long and short range, (2) a lack of saturation of magnetization at 5 K and 70 kOe, (3) a change in the nature of electrical conductivity from metallic to semiconductor, and (4) a reduction in the thermoelectric power factor S2σ by an order of magnitude of 400 K. The above results were considered in terms of the parameters of the band model, derived from the high-temperature expansion of magnetic susceptibility and from the diffusive component of thermoelectric power. Theoretical calculations showed a significant weakening of both the superexchange and double exchange mechanisms, a reduction in the  band width from 0.76 to 0.19 eV, and comparable values of the Fermi energy and the activation energy (0.46 eV) in the intrinsic region of electrical conductivity. The main advantage of high-energy ball milling is the ability to modify the physicochemical properties of already existing compounds for desired applications.CuCr This primarily causes a change in the nature of electrical conductivity from metallic to semi-conductive  a decrease in the thermoelectric power factor to 13 nWcm−1K−2 at 400 K. The parameters of the band model determined from (1) measurements of the diffusive component of the thermoelectric power and calculations based on Mott’s theory showed that the Fermi energy perfectly correlates with the value of the activation energy in the intrinsic region of the electrical conductivity and (2) calculations of the magnetic exchange integrals derived from the high-temperature expansion of magnetic susceptibility showed a reduction in the width of the mixed valence band of chromium ions to the value of 0.19 eV, caused by the appearance of an energy gap between the bottom of this band and the top of the valence band. These studies have shown that the electrical and magnetic properties of solid materials can be modified to obtain desired applications by reducing the size of their grains. The strength and type of chemical bond have a significant impact on this modification.It has been shown that the method of high-energy milling of single crystals is an effective method of obtaining single-phase nanospinels. Selenium nanopinels present a homogeneous phase without impurities. Reducing the size of single crystals to nanosize resulted in (1) a shift in the ferromagnetic long- and short-range interactions toward lower temperatures by about 200 K, (2) a change in the nature of


In this work, we formulate the following question: How the distribution of aminoacyl-tRNA synthetases (aaRSs) went from an ancestral bidirectional gene (mirror symmetry) to the symmetrical distribution of aaRSs in a six-dimensional hypercube of the Standard Genetic Code (SGC)? We assume a primeval RNY code, two Extended Genetic RNA codes type 1 and 2, and the SGC. We outline the types of symmetries of the distribution of aaRSs in each code. The symmetry groups of aaRSs in each code are described, until the symmetries of the SGC display a mirror symmetry. Considering both Extended RNA codes the 20 aaRSs were already present before the Last Universal Ancestor. These findings reveal intricacies in the diversification of aaRSs accompanied by the evolution of the genetic code. The understanding of the genetic code, its origin and evolution, remains as a fundamental problem in biology. Several informational molecules participate in the implementation of the genetic code, such as DNA, DNA polymerase, RNA polymerase, mRNA, tRNA, rRNA, amino acids, and aminoacyl-tRNA synthetases (aaRSs). There are specific interactions between these molecules, which involve transcription that results in mRNA and translation that produce proteins. There are several mathematical models aimed to model the genetic code and most of them focus on the mapping of 61 codons or triplets to 20 canonical amino acids. The genetic code includes three triplets that are stop signals. To our knowledge, theoretical mathematical works on the distribution of aaRSs in the genetic code are nonexistent. For example, there are mathematical models on the symmetries (Hornos and Hornos Aminoacyl-tRNA synthetases (aaRSs) are essential enzymes that catalyze the esterification of a tRNA to its cognate L-amino acid   model divides the table of the genetic code into two classes of aminoacyl-tRNA synthetases (Classes I and II) with recognition from the minor or major groove sides of the tRNA acceptor stem  motivated a phylogenetic analysis that indicated that these proteins were originally coded for by opposite strands of the same gene  were built and whole genomes of bacteria and archaea were used to test hypotheses about the evolution of the SGC  to the symmetrical distribution of aaRSs in the 6D representation of the SGC? We assume a primeval RNY code, two Extended Genetic RNA codes type 1 and 2  based on similarity in sequences and structures  are the member classes of the factor group over the binary subgroup that contains the null element. Further mathematical properties of the Four-Klein Group useful for the representation of the genetic code can be found elsewhere  group in which every element, different of the neutral, has order 2. Every element is its own inverse, and the sums of complementary RNA/DNA bases, the so-called Watson–Crick base pairs, are constant. All the Klein four-groups are pairwise isomorphic. The Four-Klein Group is the smallest finite group that is not cyclic, but it arises from the direct product of 2 binary cyclic groups. Indeed, the direct product All hypercubes shown in Figs. The distribution of both Classes of aaRSs assuming a RNY code is shown in the 4-dimensional hypercube in Fig. These 3 patterns altogether are here defined as the codons of the Extended RNA code type 2. This extended code includes 48 triplets which specify 18 amino acids, including AUG, the start codon, but not the 3 stop codons. The remaining 16 codons, the YNR triplets, can only be obtained by double transversions in the RNY triplets, occurring simultaneously, in the first and the third nucleotide base. The first set corresponds to the so-called primaeval RNA code (RNY pattern); the second (YNY pattern) and the third (RNR pattern) sets correspond to triplets obtained by transversion in the first nucleotide or in the third nucleotide, respectively. The fourth set (YNR pattern) corresponds to triplets obtained by transversions, occurring simultaneously in the first and in the third nucleotide. Each of these 4 sets can be partitioned into 2 subsets by replacing the N by Y or R. Hence, the set of RNY triplets is the union of the set of RYY triplets with the set of RRY. Analogously, the set of YNY triplets is the union of the YYY with the YRY triplets, while the set of RNR triplets is the union of the RYR with the RRR triplets. Finally, the set of YNR triplets is the union of the YYR with the YRR triplets. These 8 sets conform a partition of the set of 64 triplets, having each of them 8 elements. In fact, each one of these 8 sets is a 3-dimensional coordinated affine subspace , that is, a cube, contained in the 6-dimensional hypercube. This is so since the Hamming distance  between triplets on the same edge is 1.A primaeval RNA world was proposed which comprises the codons with an RNY pattern. These 16 codons code for eight amino acids, having every amino acid two triplets that specify it. Allowing transversions in the first or in the third nucleotide base the YNR and RNR patterns emerge. The 16 YNY triplets can be obtained from the triplets of the primaeval RNA code, by transversion in the first nucleotide Fig. . Note thThe 16 RNR triplets can be obtained from the triplets of the primaeval RNA code, by transversion in the third nucleotide. Again, a 4D-hypercube is obtained, which means a symmetric transformation. The set of triplets of the form RNR is a disjoint set with the set of the RNY. The 16 triplets of the form RNR specify 9 amino acids, 6 of which were already found amongst those coded by the NNY triplets. Then, the triplets of the form RNR give rise to only 3 new amino acids. The set of codons of the form RNR is the union of the cubes RYR and RRR. Note that in the cube RYR Fig. , or a 4-, there are also 3 stop codons, located in 2 connected edges of the cube. It means that the set of codons of the form RNR conforms a 4-dimensional hypercube, which is a coordinated affine subspace, or a 4-dimensional hyperface of the 6-dimensional hypercube of the 64 triplets. Now we observe that the union of the sets RNR and YNR, that is the set of the NNR triplets, those that end in purines, is a 5-dimensional affine subspace, or a 5-dimensional hypercube, whose associated vector subspace is that of the NNY triplets. The hypercube of the NNR triplets specify only 5 new amino acids, not specified by the NNY triplets. They are the amino acids whose canonical triplets end in purines, A or G.The 16 YNR triplets can be obtained from the triplets of the primaeval RNA code, by simultaneous transversions in the first and the third nucleotides. The set of triplets of the form YNR is also a disjoint set with the set of the RNY. The 16 triplets of the form YNR specify 6 amino acids, 4 of which were already found amongst those coded by the NNY triplets. Then, the triplets of the form YNR give rise to only 2 new amino acids. In Fig. 4A note of caution: all the hypercubes presented in Figs. The distribution of both Classes of aaRSs assuming the Extended RNA code type 1 and type 2 will each form a 5-dimensional hypercube (not shown). New synthetases appear in this Extended RNA code type 1, to wit, LeuRS, CystRS, ArgRS, and MetRS that belong to Class1a, GlnRS is of Class 1b, TrpRS and TyrRS are members of Class 1c, and HisRS pertains to Class 2a. In the Extended RNA code type 2, new aaRSs appear: GluRS is of Class 1b, ProRS is of Class 2a, PheRS pertains to Class 2c, and LysRS can be Class 1b or Class 2b. Stop codons  appear only in the Extended RNA code type 1 and are included for determining the symmetry groups. Stop codons are also used in mitochondria and chloroplasts.The distribution of both Classes of aaRSs assuming the SGC is shown in Fig. In this work, we have determined and analyzed the distribution of aaRSs for different genetic codes: RNY, Extended RNA code type 1 and type 2, and the SGC. We represented each code by their corresponding polytopes (hypercubes), and we have outlined the type of symmetries for both Classes of aaRSs. All synthetases of Class II can be found in the first two 4D-hypercubes (RNY and YNY). Also note that Class I and II of aaRSs existed for all 20 amino acids in the Extended RNA codes 1 and 2, before the completion of the SGC. The 20 amino acids plus the stop codons were already present when both Extended codes are considered. This agrees with the proteomes before LUCA , which does not recognize the anticodon of tRNANote from the distribution of aaRSs in both Extended RNA code type I and II, and the SGC, are symmetrical, which is consistent with the notion that the evolution of the two aaRS classes evolved in parallel  groups, which correspond to the I and II classes of aaRSs, as can be seen in the hypercube in Fig. The main difference between the amino acids recognized by the two aaRS Classes is their average size (Carter et al.