Vinnytsia National Technical University

The object of research is the process of designing and optimizing parking areas in complex geometric configurations in conditions of dense development. The main problem is to solve the use of areas of complex geometric configuration for parking areas. In addition, there are currently no universal models and methods for the corresponding calculation and optimization. The result of the work was the receipt of a universal mathematical model with which it is possible to determine the number of parking spaces based on the geometric dimensions and area of the plot. A special feature is the possibility of calculating for complex geometric configurations (polygons). For this, the Gauss formula and the JavaScript programming language are used. The initial data are geodetic measurements, and the error in such a calculation is less than 2%. The development of JavaScript code based on the shoelace formula was practical importance. The experimental object was the residential area “Vyshenka” in Vinnytsia (Ukraine). The selected plot has an area of 1350 m2 with an initial number of parking spaces before optimization –50, after –59. In general, the efficiency of using the area increased from 70% to 88%. In addition, a 22% reduction in accidents is noted, which indicates the significant effectiveness of the model and minimal calculation error. A feature of the proposed solution is also that not only linear dimensions are taken into account, but also the relief, infrastructure facilities and the initial shape of the site. There is also the possibility of integration into web applications and CAD programs for simultaneous planning and construction, which allows for an increase in the number of parking spaces of up to 20% without expanding the territories. The results of the modeling can be used by engineers and builders to improve the landscaping of residential areas where there is no possibility for expanding the territories, programmers – by integrating the model into web applications and business.

This article focuses on the application of bioceramic materials in therapeutic dentistry, particularly in the management of acute deep caries in young patients. It presents a clinical case involving the treatment of a 10‑year‑old patient diagnosed with chronic reversible pulpitis of tooth 1.2. The bioceramic material MTA White (Angelus) was used as a therapeutic base, supporting natural healing and preserving tooth vitality. All procedures were performed under a dental microscope with field isolation using a rubber dam system. Following the treatment stages—including antiseptic preparation, pulp isolation, and restoration—radiological monitoring was conducted. At one‑ and two‑year follow‑ups, the patient reported no pain, and radiological examinations revealed no pathological changes. These findings highlight the effectiveness of bioceramic materials in the treatment of deep caries in young patients, ensuring the preservation of tooth function and aesthetics.

Tree pollen allergies are influenced by regional atmospheric pollen concentrations and flora distribution. Climate change and urban landscaping have altered airborne pollen profiles in Ukraine, potentially affecting sensitization patterns. We examined 7518 patients (57.63% children) sensitized to at least one of 26 molecular components from 19 tree species using ALEX testing (2020–2022). Atmospheric pollen data from Ukrainian aerobiology stations were integrated with clinical data. Regional sensitization was mapped using the Geographic Information System, and Bayesian network modeling determined hierarchical relationships. Sensitization to Cry j 1 (46.01%), Bet v 1 (41.67%), and Fag s 1 (34.38%) dominated across age groups. High Fagales sensitization correlated with elevated atmospheric Betula, Alnus, and Corylus pollen concentrations, confirming environmental exposure-sensitization relationships. Bayesian modeling identified Bet v 1 as the root allergen (89.43% accuracy) driving cascading sensitization to other Fagales and non-Fagales allergens. Unexpectedly high Cry j 1 sensitization despite minimal atmospheric Cryptomeria presence suggests Thuja and Ambrosia cross-reactivity. Fagales sensitization dominated 10 of 17 regions, correlating with forest geography and urban landscaping. This study validates aerobiological monitoring’s clinical relevance. Diagnostic protocols should prioritize Bet v 1 while interpreting Cry j 1 positivity as potential cross-reactivity. Climate-driven shifts in atmospheric pollen patterns require ongoing coordinated aerobiological and clinical surveillance.

Phantom limb pain (PLP) is a common condition after limb amputation which is notoriously difficult to treat. The Russian full-scale invasion of Ukraine has resulted in over 100,000 people with amputated limbs and persistent PLP. This study reports on the feasibility of implementing two novel treatment approaches, Phantom Motor Execution (PME) and Progressive Motor Training (PMT), during the Russian war on Ukraine. PME and PMT follow the principle of facilitating motor training of the phantom limb and are grounded on the Stochastic Entanglement hypothesis for the pathogenesis of PLP. PME employs myoelectric pattern recognition on residual limb muscles to control virtual and augmented reality environments (mixed reality). PMT uses mixed reality to guide patients to imagine or execute predefined movements according to their evolving motor skills, and it is suitable for patients where myoelectric signals are not viable. Nineteen participants with major limb amputation were treated with PME (N=8) and PMT (N=11). Participants who completed 9 sessions reported a reduction of PLP greater than 50%. Participants received half of the training time per session and less sessions than reported in previous studies, yet clinically meaningful pain reductions were observed. This study demonstrates the feasibility of implementing PME and PMI for the treatment of PLP during war time and constraint resources. Ukrainian clinicians found the technologies and treatment approaches efficient and effective at reducing PLP and have introduced them as part of their clinical practice.

Introduction. Gonarthrosis is one of the most pressing medical and social issues in modern society. Aim. To characterize morphometric differences in the distal femur in knee osteoarthritis, depending on the morphotype determined using a proprietary clustering system. Materials and methods. One hundred knee joint X-rays from 70 patients with medial compartment osteoarthritis were analyzed (26 (37.14%) men and 44 (62.86%) women). The mean age was 63.56±8.10 years. Morphotype I was identified in 21 patients (21.00%), morphotype II in 38 (38.00%), morphotype III in 29 (29.00%), and morphotype IV in 12 (12.00%). Morphometric parameters of the distal femur were measured relative to the axis drawn from the center of the intercondylar notch to the femoral condyles: lateral femoral condyle angle (LFCA), lateral mid-condylar femoral angle (LFMA), medial mid-condylar femoral angle (MFMA), and medial femoral condyle angle (MFCA). These angles were also assessed relative to the tangent axis to the femoral condyles: LFCA2, LFMA2, MFMA2, and MFCA2. Statistical analysis was performed using Statistica 13, with significance set at p ≤0.05. Results. The mean LFCA in patients with morphotype I was 94.71±3.94°, II – 89.17±4.78°, III – 91.48±4.79°, and IV – 90.25±4.05° (p=0.001). LFMA values were 82.26±5.11° in morphotype I, 81.08±2.65° in II, 84.12±3.41° in III, and 86.50±5.33° in IV (p=0.0004). The mean MFMA was 74.67±4.63° (morphotype I), 75.43±6.14° (morphotype II), 72.84±3.17° (morphotype III), and 70.92±3.00° (morphotype IV) (p=0.01). MFCA values in patients with morphotype I were 87.90±4.50°, II – 86.01±5.26°, III – 87.69±3.52° and IV – 89.96±4.15° (p=0.04). LFCA2 was 107.62±4.39° in morphotype I, 102.17±6.21° in II, 105.36±6.54° in III, and 103.92±5.12° in IV (p=0.006). LFMA2 values in patients with morphotype I were 95.55±4.05°, II – 95.08±2.45°, III – 96.84±2.68° and IV – 97.79±3.01° (p=0.03). MFMA2 values were 85.36±4.70° (morphotype I), 85.71±4.57° (morphotype II), 83.19±2.67° (morphotype III), and 82.08±2.87° (morphotype IV) (p=0.007). The mean MFCA2 in individuals with morphotype I was 99.52±4.64°, II – 97.00±5.20°, III – 98.74±4.39° and IV – 101.88±4.16° (p=0.02). Conclusions. Significant differences in the morphometric parameters of the distal femur depending on the knee joint morphotype were demonstrated.

The article is devoted to the current issues of increasing the efficiency of laser polarimetric systems for mapping Jones matrix elements of optically thin biological layers in the diagnosis of pathologies. An improved method of mapping amplitudes and phase angles of 2-D Jones-matrix elements of biological layers in the system, supplemented by information analysis and classification by the decision tree method, was presented. Informative signs for the diagnosis of normal and sepsis of the tissues of the large and small intestine was established. The accuracy of classification of the large and small intestines in the system based on the analysis of the amplitudes of the 2-D "orientation" element of the Jones matrix was achieved at the level of 91% and 93%, respectively, and based on the analysis of phases at the level of 90% and 92%.

The paper analyzes the main areas of application of mathematical methods in medical diagnostics, formulates the principles of diagnostics based on fuzzy logic. The basic structure of the MIS medical information system for assessing the degree of engraftment of effectiveness of odontogenic phlegmons treatment of the maxillofacial region was developed and the main recommendations for its design were put forward, namely: the selection and purpose of the system; selection of the structural scheme of the system; formation and analysis of the list of nosological forms, collection of statistically reliable information about the severity of symptoms; choosing a method of processing biomedical information; construction of an algorithm for solving the problems of evaluating biomedical information and forming diagnostic and prognostic conclusions. The practical value of the work lies in the possibility of using an automated medical expert system to solve the problems of medical diagnosis based on fuzzy logic when assessing the degree of engraftment of effectiveness of odontogenic phlegmons treatment of the maxillofacial region.

The paper presents the results of establishing time intervals and accuracy of determining the age of damage to human internal organs by digital histological methods of polarisation reconstruction (tomography) of the degree of crystallisation of samples and optical activity of histological sections of the brain and liver. The maps of linear and circular birefringence were calculated using polarisation reconstruction algorithms. The values of a set of statistical moments of the 1st - 4th orders, characterising the distributions of the polarisation-reconstructed index of the degree of crystallisation and optical activity of the substance of the experimental tissues, were determined. Within the control and experimental groups of biological tissues of internal organs with different duration of damage, the mean value and error of each of the statistical moments of the 1st-4th orders were determined. The age of the injury and its accuracy were algorithmically calculated by polarisation tomographic histological examination. For the practical implementation of the developed methodology, the article considers the issues of life and safety at work, which constitute a fundamental right and sustainable development goals of decent work and economic growth, promoting inclusive and sustainable economic growth by creating jobs for the actively working population.