Admissible singular solutions to gas dynamics systems with non-positive pressure

Karakteristika hiperboličnih sistema zakona odrržanja je da čak i u slučaju glatkog po-četnog uslova rešenja uglavnom razvijaju prekide u konačnom vremena. Zbog toga se posmatraju slaba rešenja koja dati sistem zadovoljavaju u distributivnom smislu i mogu biti čak i neograničena što se ispoljava kroz pojavu Dirakove delta funkcije u rešenju. U ovoj disertaciji se akcenat stavlja na analizu protoka stišljivog neviskoznog fluida koji ne menja pravac prilikom kretanja. Protok je opisan Ojlerovim sistemom iz gasne dinamike koji se sastoji iz zakona održanja mase, količine kretanja i energije, dok su karakteristike fluida određene konstitutivnim relacijama. U slučaju izentropskog ili izotermnog protoka sistem se svodi na zakone održanja mase i količine kretanja. Glatka rešenja takvog sistema automatski zadovoljavaju zakon održanja energije, dok prelaskom na slabu formulaciju dolazi do gubitka energije. Za predstavnike sistema gasne dinamike sa nepozitivnim pritiskom su uzeti sistem gasne dinamike bez pritiska i model za  Čapliginov gas i njegova uopštenja. Data su rešenja Rimanovih problema za te sisteme koja se mogu predstaviti kao kombinacija klasičnih elementarnih talasa i senka talasa koji aproksimiraju rešenja u obliku delta udarnih talasa i koji omogućavaju rešavanje početnog problema koji u početnom uslovu sadrži delta funkciju. Na primeru modela za uopšten Čapliginov gas dokazano je da uslov prekompresivnosti nije jači od entropijskog uslova, što je prvi takav rezultat u literaturi. Dalje su korišćena rešenja Rimanovih problema, kao i problema singularne interakcije i dat je algoritam za konstrukciju globalnog dopustivog približnog rešenja početnog problema za sistem gasne dinamike bez pritiska. Algoritam je univerzalan i ideja se može proširiti na veliki broj sistema zakona održanja i veliki broj početnih uslova. Diskutovane su promene energije u približnom rešenju i posle interakcija. Dobijeno približno rešenje slabo konvergira u prostoru Radonovih mera sa predznakom.  A solutions to hyperbolic conservation laws systems starting out as smooth often develop singularities in a finite time. As a consequence, we are forced to look for weak solutions that satisfy the system in distributional sense. Those solutions are often unbounded, which is expressed through the appearance of Dirac delta function. In this theses we study a one-dimensional, compressible and inviscid flow of a fluid. The process is described by compressible Euler gas dynamics system which consists of conservation laws of mass, linear momentum and energy, while the characteristics of the fluid are described using constitutive relations. In the case of isentropic or isothermal flow the system reduces to conservation laws of mass and linear momentum. The energy is conserved for smooth solutions to such systems, but while passing to the weak formulation the energy is being dissipated. As representatives, we  consider pressureless gas dynamics system, as well as Chaplygin gas model and its generalizations. We give the solutions to Riemann problems which can be represented as a combinations of classical elementary waves and shadow waves that approximate the solutions in the form of delta shock and allow as to solve the problems with initial data containing delta function. We use generalized Chaplygin gas model as demonstration of the fact that overcompressibility condition is not stronger that entropy condition, which is the first result of that kind in the literature. Further, we use solutions  to the Riemann problems, as well as singular interaction problems to give the algorithm for construction of global admissible approximate solution to the pressureless gas dynamics initial value problem. The algorithm is universal and idea can be applied to large number of conservation laws systems and large number of initial data. We discuss  energy changes in approximate solution and after the interactions. The constructed approximate solution converges in the space of signed Radon measures

The Effects of a Meldonium Pre-Treatment on the Course of the Faecal-Induced Sepsis in Rats

Sepsis is a life-threatening condition caused by the dysregulated and overwhelming response to infection, accompanied by an exaggerated pro-inflammatory state and lipid metabolism disturbance leading to sequential organ failure. Meldonium is an anti-ischemic and anti-inflammatory agent which negatively interferes with lipid metabolism by shifting energy production from fatty acid oxidation to glycolysis, as a less oxygen-demanding pathway. Thus, we investigated the effects of a four-week meldonium pre-treatment on faecal-induced sepsis in Sprague-Dawley male rats. Surprisingly, under septic conditions, meldonium increased animal mortality rate compared with the meldonium non-treated group. However, analysis of the tissue oxidative status did not provide support for the detrimental effects of meldonium, nor did the analysis of the tissue inflammatory status showing anti-inflammatory, anti-apoptotic, and anti-necrotic effects of meldonium. After performing tissue lipidomic analysis, we concluded that the potential cause of the meldonium harmful effect is to be found in the overall decreased lipid metabolism. The present study underlines the importance of uninterrupted energy production in sepsis, closely drawing attention to the possible harmful effects of lipid-mobilization impairment caused by certain therapeutics. This could lead to the much-needed revision of the existing guidelines in the clinical treatment of sepsis while paving the way for discovering new therapeutic approaches

The Effects of a Meldonium Pre-Treatment on the Course of the LPS-Induced Sepsis in Rats

A dysregulated and overwhelming response to an infection accompanied by the exaggerated pro-inflammatory state and metabolism disturbance leads to the fatal outcome in sepsis. Previously we showed that meldonium, an anti-ischemic drug clinically used to treat myocardial and cerebral ischemia, strongly increases mortality in faecal-induced peritonitis (FIP) in rats. We postulated that the same mechanism that is responsible for the otherwise strong anti-inflammatory effects of meldonium could be the culprit of the increased mortality. In the present study, we applied the LPS-induced model of sepsis to explore the presence of any differences from and/or similarities to the FIP model. When it comes to energy production, despite some shared similarities, it is evident that LPS and FIP models of sepsis differ greatly. A different profile of sympathoadrenal activation may account for this observation, as it was lacking in the FIP model, whereas in the LPS model it was strong enough to overcome the effects of meldonium. Therefore, choosing the appropriate model of sepsis induction is of great importance, especially if energy homeostasis is the main focus of the study. Even when differences in the experimental design of the two models are acknowledged, the role of different patterns of energy production cannot be excluded. On that account, our results draw attention to the importance of uninterrupted energy production in sepsis but also call for much-needed revisions of the current recommendations for its treatment. © 2022 by the authors. Licensee MDPI, Basel, Switzerland

Mandibular Caffey's disease: case report

The case of a six-month-old boy with mandibular Caffey's disease is described. Emphasis is placed on the role of bone scintigraphy, as a diagnostic method which would be, because of the clinical picture and the beginning of the disease (suspected osteomyelitis), one of the first methods performed. Highly characteristic scintigraphic image, when the mandible is involved, can play the most important role in further treatment, and its recognition can also spare many unnecessary procedures

The effects of a meldonium pre-treatment on the course of the faecal-induced sepsis in rats

Sepsis is a life-threatening condition caused by the dysregulated and overwhelming response to infection, accompanied by an exaggerated pro-inflammatory state and lipid metabolism disturbance leading to sequential organ failure. Meldonium is an anti-ischemic and anti-inflammatory agent which negatively interferes with lipid metabolism by shifting energy production from fatty acid oxidation to glycolysis, as a less oxygen-demanding pathway. Thus, we investigated the effects of a four-week meldonium pre-treatment on faecal-induced sepsis in Sprague-Dawley male rats. Surprisingly, under septic conditions, meldonium increased animal mortality rate compared with the meldonium non-treated group. However, analysis of the tissue oxidative status did not provide support for the detrimental effects of meldonium, nor did the analysis of the tissue inflammatory status showing anti-inflammatory, anti-apoptotic, and anti-necrotic effects of meldonium. After performing tissue lipidomic analysis, we concluded that the potential cause of the meldonium harmful effect is to be found in the overall decreased lipid metabolism. The present study underlines the importance of uninterrupted energy production in sepsis, closely drawing attention to the possible harmful effects of lipid-mobilization impairment caused by certain therapeutics. This could lead to the much-needed revision of the existing guidelines in the clinical treatment of sepsis while paving the way for discovering new therapeutic approaches