[Mathematical Modeling of HIV Replicaton and the Response of the Interferon System].

Developing physiologically meaningful mathematical models that describe multilevel regulation in a complex network of immune processes, in particular, of the system of interferon-regulated virus production processes, is a fundamental scientific problem, within the framework of an interdisciplinary systems approach to research in immunology. Here, we have presented a detailed high-dimensional model describing HIV (human immunodeficiency virus) replication, the response of type I interferon (IFN) to the virus infection of the cell, and suppression of the action of IFN-induced proteins by HIV accessory proteins. As a result, this model includes interactions of all three processes for the first time. The mathematical model is a system of 37 nonlinear ordinary differential equations including 78 parameters. Importantly, the model describes not only the processes of the IFN response of the cell to virus infection, but also the mechanisms used by the virus to prevent effects of the IFN system.

[Screening of patients with cerebral aneurysms: mathematical analysis and economic justification]. / Skrining patsientov s anevrizmami golovnogo mozga: matematicheskii analiz i ekonomicheskoe obosnovanie.

Subarachnoid hemorrhages due to rupture of cerebral aneurysms have a high risk of disability and mortality. Screening of the population to detect aneurysms in patients with risk factors is currently not carried out in Russia. However, the detection of clinically silent aneurysms and their subsequent prophylactic surgical treatment are justified, according to numerous studies. BACKGROUND: Demonstrate the clinical and economic feasibility of screening the population (including first-line relatives) for cerebral aneurysms using an economic and mathematical model of the RF virtual population. MATERIAL AND METHODS: Mathematical modeling was carried out using an algorithm that implements a discrete Markov chain. The virtual population consisted of 145 million people (the population of the Russian Federation). Magnetic resonance angiography 3DTOF was chosen as a screening method. Virtual patients underwent preventive surgical treatment in case of detection of aneurysm during screening. The number of aneurysms in the population, the number of aneurysmal subarachnoid hemorrhage (aSAH), the cost and outcomes of treatment, and the risk of disability were calculated. RESULTS: In the case of screening and preventive surgical treatment of aneurysms, there is a decrease in the number of aSAH by 14.3% (37.5% in first-line relatives (RPLR), which affects the reduction in mortality due to aSAH by 14.4% (24.1% in The total number of disabled people is reduced by 1.5% (5.1% for the RPHR). A shift in the structure of disability towards greater labor and social adaptation of patients was noted. An economic analysis for the entire population showed that screening saves 7.7 billion annually rubles, including in the population consisting of RPLR - 4.9 billion rubles. CONCLUSION: The created mathematical model of the virtual population demonstrated that screening and prophylactic treatment of cerebral aneurysms makes it possible to reduce the number of aSAH and associated mortality among the entire population and in the RPLR group. The number of individuals with severe disabilities is decreasing. Thus, population screening for the detection of cerebral aneurysms may be clinically effective and cost-effective in the general population, especially in RPCR.

Bifurcation analysis of multistability and hysteresis in a model of HIV infection.

The infectious disease caused by human immunodeficiency virus type 1 (HIV-1) remains a serious threat to hu- man health. The current approach to HIV-1 treatment is based on the use of highly active antiretroviral therapy, which has side effects and is costly. For clinical practice, it is highly important to create functional cures that can enhance immune control of viral growth and infection of target cells with a subsequent reduction in viral load and restoration of the immune status. HIV-1 control efforts with reliance on immunotherapy remain at a conceptual stage due to the complexity of a set of processes that regulate the dynamics of infection and immune response. For this reason, it is extremely important to use methods of mathematical modeling of HIV-1 infection dynamics for theoretical analysis of possibilities of reducing the viral load by affecting the immune system without the usage of antiviral therapy. The aim of our study is to examine the existence of bi-, multistability and hysteresis properties with a meaningful mathematical model of HIV-1 infection. The model describes the most important blocks of the processes of interaction between viruses and the human body, namely, the spread of infection in productively and latently infected cells, the appearance of viral mutants and the develop- ment of the T cell immune response. Furthermore, our analysis aims to study the possibilities of transferring the clinical pattern of the disease from a more severe state to a milder one. We analyze numerically the conditions for the existence of steady states of the mathematical model of HIV-1 infection for the numerical values of model parameters correspond- ing to phenotypically different variants of the infectious disease course. To this end, original computational methods of bifurcation analysis of mathematical models formulated with systems of ordinary differential equations and delay differ- ential equations are used. The macrophage activation rate constant is considered as a bifurcation parameter. The regions in the model parameter space, in particular, for the rate of activation of innate immune cells (macrophages), in which the properties of bi-, multistability and hysteresis are expressed, have been identified, and the features characterizing transi- tion kinetics between stable equilibrium states have been explored. Overall, the results of bifurcation analysis of the HIV-1 infection model form a theoretical basis for the development of combination immune-based therapeutic approaches to HIV-1 treatment. In particular, the results of the study of the HIV-1 infection model for parameter sets corresponding to different phenotypes of disease dynamics (typical, long-term non-progressing and rapidly progressing courses) indicate that an effective functional treatment (cure) of HIV-1-infected patients requires the development of a personalized ap- proach that takes into account both the properties of the HIV-1 quasispecies population and the patient's immune status.

[Mathematical Modeling of the Intracellular Regulation of Immune Processes].

The modern era of research in immunology is characterized by an unprecedented level of detail about structural characteristics of the immune system and the regulation of activities of its numerous components, which function together as a whole distributed-parameter system. Mathematical modeling provides an analytical tool to describe, analyze, and predict the dynamics of immune responses by applying a reductionist approach. In modern systems immunology and mathematical immunology as a new interdisciplinary field, a great challenge is to formulate the mathematical models of the human immune system that reflect the level achieved in understanding its structure and describe the processes that sustain its function. To this end, a systematic development of multiscale mathematical models has to be advanced. An appropriate methodology should consider (1) the intracellular processes of immune cell fate regulation, (2) the population dynamics of immune cells in various organs, and (3) systemic immunophysiological processes in the whole host organism. Main studies aimed at modeling the intracellular regulatory networks are reviewed in the context of multiscale mathematical modelling. The processes considered determine the regulation of the immune cell fate, including activation, division, differentiation, apoptosis, and migration. Because of the complexity and high dimensionality of the regulatory networks, identifying the parsimonious descriptions of signaling pathways and regulatory loops is a pressing problem of modern mathematical immunology.

[The treatment of an acute paraproctitis].

The results of surgical treatment of an acute paraproctitis in 708 patients, in 9 (1.27%) of whom gangrenous -- putrificated form of paraproctitis was diagnosed, are adduced. In 187 (42.6%) patients the abscess disclosure with intraintestinal purulent fistula, going into intestinal lumen, excision was performed, together with cryptectomy -- in 182 (41.4%), the ligature method was applied in 18 (4.1%) with subsequent fistula excision and its internal orifice plasty using mucosal-submucosal flap. For extrasphincteric or transsphincteric purulent tunnel the abscess was opened and drained, its internal orifice sutured, using 'distant" removable suture. It internal orifice was not revealed there was accomplished procedure of disclosure and draining of purulent cavity, the wound sanation with insufflation of ozone-oxygen mixture. In anaerobic paraproctitis the procedure consisted of disclosure and draining of purulent cavities with necrectomy was performed. To all the patients antibacterial therapy was conducted. In 20 (4.5%) patients an acute paraproctitis recurrence had occurred, in 9 (2%) -- pararectal fistula, and in 5 (1.1%) -- the anal sphincter stage I insufficiency.

[Strategies of treatment of acute obturative colonic ileus]. / Taktika lecheniia ostroi obturatsionnoi neprokhodimosti tolstoi kishki.

Results of surgical treatment of 326 patients with an acute obturation colonic ileus (AOCI) were analyzed. Tumor was localized in left half of colon and retrosygmoid part in 76.8% of observations. There were admitted to the hospital 49.1% of patients with AOCI in subcompensation and decompensation stages. Radical operation was done in 65.4% and palliative one--in 34.6% of patients. Decompression of upper and lower parts of the gut, using oxygenated solutions, was done in complex of preoperative preparation and during operation performance. The method of colonic intraoperative decompression was depicted. In 26.3% of patients for AOCI postoperative complications occurred. Mortality have constituted 11.7%: after operation for AOCI in compensation stage--2.4%, while in subcompensation and decompensation--21.3%.