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Abstract A method for calculating the 1/d expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive form. A possible type of such substitutions is proposed for the case of vacuum integrals. Its applicability is shown for several families of massless (with one massive line) vacuum integrals up to the 7-loop level.

The article describes the method for determining the optimal angular velocity and the number of turns of the generator winding on permanent magnets powered by a wind turbine operating in specific operating conditions according to the wind speed regime. The optimization criterion is the maximum potential of energy that can be used to charge the battery. The permissible power of the generator and wind turbine, current and battery charging voltage are accepted as limiting factors. The restriction is provided by connecting a ballast resistor to the generator output. The power developed by the turbine is determined taking into account the wind energy utilization factor, which depends on the angular velocity of its shaft and wind speed. Two variants of power limitation are compared: by limiting the angular velocity by aerodynamic means and by stopping the wind turbine. The return of energy to charging in both cases is determined taking into account the distribution of wind speeds, obeying the Weibull probability distribution law. As an example, the calculation of the possible annual power generation for charging a battery with a capacity of 200 A∙h with a voltage of 24 volts from a synchron generator with a number of poles of 48 driven by a wind turbine with a radius of 2 meters, operating in an area with an average wind speed of 5 m/s. The calculation shows that for the parameters and operating conditions of the electrical installation used in the example, the maximum annual energy output (3.3 × 103 kWh) is observed at optimal 11 turns of the winding at each of the poles of the generator. The deviation of the number of turns from the optimal one in both directions by 2 times leads, with the same dimensions of the wind turbine, to a decrease in annual energy output by 3...5 times, which is a clear proof of the need to carry out such a calculation for each specific wind turbine.

Objective. To analyze the literature data and to present recommendations on the use of the minimum clinically important difference (MCID) in the practice of spinal surgeon-researcher. Material and Methods. The article is a non-systematic review of the literature. A search was performed for sources, which describe the calculation and analysis of the MCID parameter on a cohort of patients with degenerative spinal diseases in the PubMed, Scopus and Web of Science databases. Further, the analysis of the literature was carried out on the application of MCID to assess the effectiveness of surgical treatment. Results. The MCID parameter is illustrated for the most common clinical scales used to assess the effectiveness of treatment in spinal surgery, with their detailed description and discussion of their benefits and drawbacks. The specific MCID values for cervical and lumbar pathologies, first of all degenerative ones, and follow-up periods, which can be used in assessing the results of the treatment, as well as in planning prospective comparative studies are presented. Conclusion. The MCID parameter is required for sample size calculation and for the analysis of treatment outcomes. The MCID reflects not just the change in the baseline indicator, but also the clinical significance for the patient.

Introduction A cascade of degenerative spine changes affects the structures including vertebral endplates and bodies of adjacent vertebrae that can be visualized on MRI imaging as Modic changes. The aim of the study was to assess the role of changes in the endplates and adjacent vertebral bodies in radiological results of monosegmental posterior lumbar interbody fusion (PLIF) in patients with degenerative lesions of the spine. Material and methods The design of the study was a monocenter retrospective comparative cohort study. The radiological results of PLIF performed in combination with transpedicular screw fixation for 122 patients with Modic changes in adjacent endplates and adjacent vertebral bodies were evaluated for interbody fusion, subsidence of interbody implants, segmental angle, interbody space height. The followup period was 1-2 years. Results Complete interbody fusion was seen in 94.4 % of Modic type 0 and in 77.3 % of Modic type II changes. Interbody cage subsidence occurred in 38.9 % Modic type I, 22.7 % in Modic type II, 9.1 % in Modic type III and in 11.3 % Modic type 0 changes. A significant decrease in the segmental angle was found in all types of Modic changes (p < 0.05) at 1-2 years with the greatest decrease noted in Modic type I (p = 0.000438). A significant decrease in the interbody space height was noted in all groups (p < 0.05) with the greatest decrease seen in Modic type I changes (p = 0.000438) and the minimum decrease noted in Modic type III changes (p = 0.000438). Discussion The role of the endplates and adjacent vertebral bodies in the results of surgical treatment was evident, and more research is needed to explore the sort of this relationship. Conclusions Modic changes in the endplates and adjacent red bone marrow showed a significant relationship with the radiological outcomes of monosegmental PLIF. The interbody fusion Tan grade I and Tan grade II was more common for Modic type 0 and less common for Modic type II changes. Subsidence of interbody implants was more common for Modic type I and less common for Modic type III changes (9.1%). Postoperative loss of interbody space height and segmental correction was common for Modic type I.

of BMD in Hounsfield units (HU) according to CT data is a more accurate method versus to the "gold" standard – densitometry. Purpose To determine BMD of key anatomical areas of the lumbar vertebrae in HU and correlate with densitometry data. Methods A retrospective cohort of patients was studied prior to decompression and stabilization intervention at the lumbar level. The BMD of each lumbar vertebra in its different anatomical regions in HU was assessed according to CT of the lumbar spine and was compared with densitometry data. Results In the roots of the L2-S1 arch of the vertebrae, BMD was significantly higher than in the bodies of the same vertebrae (p < 0.01); in the L1 and S1 vertebrae, the difference in BMD between the body and the roots of the arch was not significant. An increase in the density of bone tissue in the vertebral bodies to the underlying levels was determined; BMD in the roots of the arch also increases, but only up to the L5 vertebra. BMD in the roots of the arch of the S1 vertebra is significantly lower than in the overlying L5 vertebra (p = 0.032). Discussion The obtained findings supplement the reported data in the current literature. The HU value is a more accurate and significant parameter of BMD, which should be considered in the practice by a spinal surgeon. Conclusions According to CT data of the lumbar spine, the BMD of L2-L5 in the arch roots is significantly higher than in the vertebral bodies. The BMD of the S1 vertebra in the arch roots is significantly lower than in the L5 vertebra. It may be the reason of high failure rate of caudal fixation at this level. Particular attention should be paid to the planning and surgical techniques in patients not only with osteoporosis but also with osteopenia. BMD findings obtained by densitometry in these conditions do not have a significant difference.

Objective. To determine the values of Hounsfield units (HU) of the lumbar vertebrae predicting unsatisfactory radiological results of circumferential interbody fusion at the lumbar level. Material and Methods. The data of patients who underwent a single-level decompression and stabilization intervention at the L4–L5 or L5–S1 level for degenerative diseases of the spine were analyzed. The CT images of the lumbar spine were assessed before surgery with the measurement of HU values of the vertebral bodies at the intervention level, as well as CT images one year after surgery to evaluate the degree of interbody block formation and subsidence of the cage. Three groups of patients were distinguished: patients with a formed interbody bone block and without cage subsidence (control group), patients with failed fusion and patients with cage subsidence. Results. The study presents CT data of 257 patients. The incidence of non-union was 32.3 % (83/257), and of cage subsidence – 43.6 % (112/257). The proportion of patients with reduced bone mineral density (BMD) was 26.1 % (67/257). Patients with non-union and subsidence had higher ODI scores (p = 0.045 and p = 0.050, respectively) compared to controls. The presence of fusion failure and subsidence is associated with reduced BMD (p < 0.05), HU values of vertebrae (p < 0.05), and higher ODI score (p < 0.05). According to the ROC analysis, threshold HU values were determined equal to 127 HU, 136 HU and 142 HU for the L4, L5, S1 vertebral bodies, respectively. Upon reaching these values, the risk of a combination of fusion failure and subsidence increases significantly (p = 0.022). Conclusions. Patients with non-union and cage subsidence have less satisfactory clinical outcomes. The HU values of the vertebral bodies equal to 127 HU, 136 HU and 142 HU for the L4, L5, and S1, respectively, are advisable to use in practice to predict non-union and subsidence after a single-level decompression and stabilization intervention at the lower lumbar levels.

Abstract We derive explicit expressions for the elements of the {β}-expansion for the nonsinglet Adler D A -function and Bjorken polarized sum rules S Bjp in the N4LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the {β}-expansion for D A and S Bjp at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.

Objective. To analyze clinical and radiological results of corrective fusion in the lumbar spine in the treatment of patients with sagittal imbalance after previous surgical interventions. Material and Methods. A retrospective monocentric study, clinical case series. The data of 18 patients operated on using a combination of surgical methods with obligatory anterior corrective fusion at the L4–L5 and/or L5–S1 levels to achieve optimal parameters of the sagittal balance disturbed or developed after previous interventions were analyzed. Clinical and radiological parameters were assessed during hospital stay and at least 10 months later. Results. The study presents data from 3 (16.7 %) men and 15 (83.3 %) women with an average age of 57.5 ± 9.1 years. Average length of hospital stay was 26.9 ± 10.1 days. In 7 (38.9 %) cases, the deformity occurred at the previously operated level and in 11 (61.1 %) – at the adjacent one. The duration of surgery was 481.4 ± 101.7 minutes, and blood loss was 1028.9 ± 594.9 ml. Back and leg pain VAS scores decreased in 10–19 months after surgery from 6.4 ± 0.9 and 4.8 ± 1.3 to 3.2 ± 1.2 and 0.9 ± 0.8, respectively (p < 0.001). The ODI score decreased from 59.6 ± 5.9 to 39.9 ± 7.7 (p < 0.001). The ideal Roussouly type was restored in 11 (61.1 %) cases, below ideal – in 3 (16.7 %), and overcorrection – in 4 (22.2 %). LL increased from 48.1 ± 13.6 ° to 56.9 ± 11.6 ° (p < 0.001), and LDI – from 40.1 ± 16.9 to 58.8 ± 10.3 (p

Introduction. Artificial materials used in regenerative medicine induce a balanced inflammatory response after implantation, which is an important step for effective regeneration of damaged bone tissue. The contact of the implant with tissues and biological fluids is accompanied by the deposition of blood proteins on its surface, which contributes to the activation of the complement system and initiates blood clotting, leading to the formation of a fibrin clot. On the surface of the implant, fibrin ensures the adhesion of stem cells and their maturation into fibroblasts that produce collagen and its derivatives. The formed extracellular matrix is the basis for the formation of a tissue structure (callus). To prevent the development of postoperative pathological conditions caused by hypercoagulatory syndrome, therapeutic strategies with anticoagulants such as heparin are used. However, their use limits the formation of a fibrin clot in vivo, which may slow down the migration of mesenchymal stromal cells (MSCs) and the subsequent formation of callus.Aim. To investigate of the effect of heparin at pharmacological concentrations on stemness and the ability of MSCs from human adipose tissue to undergo osteogenic differentiation under conditions of in vitro cultivation.Materials and methods. To assess the morphofunctional state of cells cultured in the presence of heparin, 2 experimental groups were formed: 1) MSCs in the presence of heparin at a therapeutic concentration (1.3 IU/ml); 2) MSCs in the presence of heparin at a toxic concentration (13 IU/ml).Results and discussion. Flow cytometry results showed that the addition of heparin at both concentrations used in the study to MSC culture leads to an increase in the number of cells expressing the surface markers CD73 and CD90, indicating the maintenance of their stem state. On the other hand, a stimulatory effect of heparin at both concentrations used on the transcription of mRNA of osteogenic genes (BMP2, BMP6, ALPL, RUNX2, BGLAP and SMURF1) in MSCs was also observed, which may indicate the osteogenic potential of heparin for the cell culture studied.Conclusion. The results of the study are useful for regenerative medicine related to the use of MSCs in clinical practice; they may serve as a prerequisite for the development of new therapeutic strategies for orthopedic and traumatologic patients at high risk of postoperative thrombosis after endoprosthetics surgery and osteosynthesis.

Relevance. Pepper is a common crop both for fresh consumption and for the preparation of spices. Recently, along with the increasing popularity of C. annuum L. pepper, there is increasing interest in other species of this genus, which have a number of breeding and important properties. The most important method of enriching the gene pool of cultivated plants is distant hybridization, through which valuable traits are transferred from wild species to cultivated ones. The development of a new variety is a lengthy process, stretching over several years. In this regard, breeders have faced the challenge of obtaining pure lines to create a pepper hybrid with desired properties by applying modern biotechnological methods that will accelerate this process. One of them is the method of microspore culture, which allows mass production of haploid plants, reducing the time for creating constant parental lines.Material and methods. The aim of the work was to create an interspecific hybrid of hot pepper (C. annuum L. x C. frutescens L.) with high ornamental properties, a complex of economically valuable traits, with good taste qualities. The research was carried out in the film greenhouse of FSBSI FSVC in the Moscow region. The research material was a variety population of hot pepper Capsicum frutescens Cz-544-14, used as a paternal line, which was heterogeneous, and a pure line of C. annuum L. (Pb-551) created by classical breeding.Results. The pepper hybrid F1 Christmas bouquet was created as a result of hybridization of species parental forms obtained by different methods (biotechnological and classical). To accelerate the production of an aligned paternal form of C. frutescens L., the technology of doubled haploids through microspore culture was used. As a result, doubled haploid plants meeting the planned model (compact low habit, purple fruit colouring in technical ripeness and red in biological ripeness) were obtained. The resulting hybrid combined all the necessary economic features: high ornamentality, compactness, bouquet arrangement of fruits, high taste and aroma. Thus, the use of remote interspecific hybridization in the breeding process in combination with biotechnological approaches can accelerate the production of new forms of hot peppers that meet the demands of the market.

Amaranth (Amaranthus spp.) is an important food crop source of nutrients and bioactive compounds. Different species of amaranth showed considerable phenotypic variations and could possess diverse nutritional properties. The presented study strove to determine the diversity of amaranth collection for morphological and biochemical traits and their antioxidant potential for developing new cultivars adapted to the environmental conditions of Central Russia. The selected 16 amaranth accessions had high variability in morphological and biochemical traits. With red-colored leaves, amaranthine content ranged from 0.319a to 2.031f mg/g fresh weight (FW). The water-soluble antioxidant content ranged from 0.425a to 1.439h mg of gallic acid equivalent (GAE)/g FW. In amaranth accessions, the phenolic compound content in leaves varied from 2.700a to 4.825g mg GAE/g FW. In the amaranth collection, the total chlorophyll content ranged from 0.9946a to 3.5467j mg/g, and carotenoids from 0.2196a to 0.8289i mg/g. A strong positive correlation (P ≤ 0.05) was evident between total chlorophyll and carotenoid contents (r≈0.90), plant height and inflorescence length (r≈0.79), and inflorescence length and seed weight harvested per plant (r≈0.76). In summary, when evaluating the antioxidant levels in various samples, the Valentina cultivar, characterized by red leaves, appeared to have the highest amaranthine concentration. Both Valentina and Fakel cultivars exhibited the maximum overall antioxidant capacity. Additionally, the Valentina and Duimovochka cultivars emerged as the top accumulators of polyphenols. These findings highlight the significant antioxidant potential present in these specific cultivars. [ABSTRACT FROM AUTHOR]

Objective. To analyze the nearest clinical and radiological results of simultaneous and staged surgical treatment of patients with degenerative sagittal imbalance. Material and Methods. Retrospective monocentric cohort study included analysis of data from 54 patients who underwent simultaneous combination of surgical methods with obligatory corrective anterior fusion at the L4–L5 or at L4–L5 and L5–S1 levels (Group I, n = 27) or similar surgical intervention though divided into stages with an interval of 5 days or more (Group II, n = 27). A comparison of clinical, radiological, and operational data during inpatient treatment was carried out. Results. The duration of surgery was 410.93 ± 76.34 minutes in Group I and 594.63 ± 102.61 minutes in Group II (p = 0.000001); the blood loss was 926.67 ± 378.63 ml versus 1345.19 ± 522.97 ml, respectively (p = 0.001575). Postoperative clinical and radiological parameters did not differ between groups: VAS back (p = 0.248647), VAS leg (p = 0.196140), PT (p = 0.115965), SVA (p = 0.208449), LL (p = 0.023654), LDI (p = 0.931646), PI-LL (p = 0.693045), GAP (p = 0.823504), and restoration of the ideal Russoly type (p = 0.111476). The incidence of perioperative complications in groups was comparable: 17 (62.96 %) in Group I and 15 (55.56 %) in Group II (p = 0.583171). Patients with a high Charlson comorbidity index had a significantly higher incidence of complications (p = 0.023471). The index of surgical invasiveness in Group I had a significant correlation with the total number of complications (= 0.421332). Conclusion. Clinical and radiological results and the incidence of complications are comparable between single- and multistage approaches to correct sagittal balance disorders. In staged treatment, the total duration of surgery and the volume of blood loss are significantly higher. With a high Charlson comorbidity index and Mirza surgical invasiveness index, a multistage approach to the treatment of patients with sagittal imbalance is preferred.

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