A difference scheme for the numerical solution of an advection equation with aftereffect

We propose a family of grid methods for the numerical solution of an advection equation with a time delay in a general form. The methods are based on the idea of separating the current state and the prehistory function. We prove the convergence of the second-order method coordinatewise and do that of the first-order with respect to time. The proof is based on techniques applied for proving analogous theorems for functional differential equations and on the general theory of difference schemes. We illustrate the obtained results with a test example. © 2013 Allerton Press, Inc

A Parallel Algorithm for Solving the Advection Equation with a Retarded Argument

We describe a parallel implementation of a difference scheme for the advection equation with time delay on a hybrid architecture computation system. The difference scheme has the second order in space and the first order in time and is unconditionally stable. Performance of a sequential algorithm and several parallel implementations with the MPI technology in the C++ language has been studied

A difference scheme for multidimensional transfer equations with time delay

This paper continues research initiated in Solodushkin et al. (2015). We develop a finite difference scheme for a first order multidimensional partial differential equation including a time delay. This class of equations is used to model different time lapse phenomena, e.g. birds migration, proliferation of viruses or bacteria and transfer of nuclear particles. For the constructed difference schemes the order of approximation, stability and convergence order are substantiated. To conclude we support the obtained results with some test examples. © 2016 Elsevier B.V

Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator

The problem to be considered is a numerical solving of nonlinear partial differential equations with heredity effect. Nonlinearity is contained in the operator of differentiation as well as in the inhomogeneity function. We propose a nonlinear implicit difference scheme, which implies the use of iterative methods to find the solution on each time layer. To take into account the heredity effect the interpolation and extrapolation of grid solution were used. Stability and convergence of the proposed difference scheme were proved. Numerical experiments were carried out and results coincides with the theoretical ones. © 2018 Gorbova T.V., Pimyenov V.G., Solodushkin S.I

Evaluation of the long-term effectiveness of cardiac resynchronization therapy

Aim. To determine quantitative criteria for assessing the therapeutic benefits and the most informative time frames after cardiac resynchronization therapy (CRT) to assess its long-term effectiveness (1, 2, 3 years of follow-up) based on retrospective analysis. To assess the CRT effectiveness, parameters of left ventricular (LV) reverse remodeling and signs characterizing the clinical CRT response were considered.Material and methods. This single-center, retrospective, non-randomized study included data from 278 patients with implanted CRT devices. Quantitative criteria for assessing CRT effectiveness were determined using a two-step cluster analysis of patients 1, 2, and 3 years after CRT by LV reverse remodeling parameters.Results. In the dataset with satisfactory division accuracy, after the first year, two clusters were identified, which are conventionally named as “non-responders” and “responders”. Two and three years after therapy, patients were classified into three clusters: “non-responders”, “responders” and “super-responders”. For the obtained clusters, we found cutoff values for LV reverse remodeling parameters, which can be used as criteria for response to therapy.The study identified the most informative time frames for assessing the postoperative CRT effectiveness 1, 2, 3 years after the surgery. At the same time, the clinical response to therapy is manifested earlier in comparison with the reverse LV remodeling.Despite the high divisibility of patients into responders and non-responders, predictive models of CRT effectiveness created using the available data from standard diagnostic protocols for heart failure patients have insufficient accuracy to be used for making decisions on therapy appropriateness. This circumstance indicates the need to receive additional data to improve the forecasting quality.Conclusion. The study revealed a period for assessing the clinical response and changes in LV reverse remodeling after CRT surgery, which is important for the optimal choice of postoperative therapy. It has been shown that in most cases, one year after surgery is sufficient to assess the clinical response, and the process of LV reverse remodeling can last up to two years on average.When assessing the CRT effectiveness by reverse remodeling, along with a change in LV end-systolic volume (ESV), it is necessary to take into account LV end-diastolic volume (EDV) changes. The change in LV ejection fraction showed a significantly lower value among the analyzed parameters in assessing the CRT effectiveness. Based on the cluster classification of patients, a dividing rule was established for responders and non-responders in the first and second years after surgery with an accuracy of 97%: a decrease in LV ESV and EDV by 9% or more compared to preoperative values

Evaluation of the Long-term Effectiveness of Cardiac Resynchronization Therapy

Aim. To determine quantitative criteria for assessing the therapeutic benefits and the most informative time frames after cardiac resynchronization therapy (CRT) to assess its long-term effectiveness (1, 2, 3 years of follow-up) based on retrospective analysis. To assess the CRT effectiveness, parameters of left ventricular (LV) reverse remodeling and signs characterizing the clinical CRT response were considered. Material and methods. This single-center, retrospective, non-randomized study included data from 278 patients with implanted CRT devices. Quantitative criteria for assessing CRT effectiveness were determined using a two-step cluster analysis of patients 1, 2, and 3 years after CRT by LV reverse remodeling parameters. Results. In the dataset with satisfactory division accuracy, after the first year, two clusters were identified, which are conventionally named as “non-responders” and “responders”. Two and three years after therapy, patients were classified into three clusters: “non-responders”, “responders” and “super-responders”. For the obtained clusters, we found cutoff values for LV reverse remodeling parameters, which can be used as criteria for response to therapy. The study identified the most informative time frames for assessing the postoperative CRT effectiveness 1, 2, 3 years after the surgery. At the same time, the clinical response to therapy is manifested earlier in comparison with the reverse LV remodeling. Despite the high divisibility of patients into responders and non-responders, predictive models of CRT effectiveness created using the available data from standard diagnostic protocols for heart failure patients have insufficient accuracy to be used for making decisions on therapy appropriateness. This circumstance indicates the need to receive additional data to improve the forecasting quality. Conclusion. The study revealed a period for assessing the clinical response and changes in LV reverse remodeling after CRT surgery, which is important for the optimal choice of postoperative therapy. It has been shown that in most cases, one year after surgery is sufficient to assess the clinical response, and the process of LV reverse remodeling can last up to two years on average. When assessing the CRT effectiveness by reverse remodeling, along with a change in LV end-systolic volume (ESV), it is necessary to take into account LV end-diastolic volume (EDV) changes. The change in LV ejection fraction showed a significantly lower value among the analyzed parameters in assessing the CRT effectiveness. Based on the cluster classification of patients, a dividing rule was established for responders and non-responders in the first and second years after surgery with an accuracy of 97%: a decrease in LV ESV and EDV by 9% or more compared to preoperative values. © 2021, Silicea-Poligraf. All rights reserved.Relationships and Activities. This work was supported by a Russian Science Foundation grant № 19-14-00134

ПРОГНОЗИРОВАНИЕ ПОСЛЕОПЕРАЦИОННОГО ИНФАРКТА МИОКАРДА У ПАЦИЕНТОВ ПОЖИЛОГО И СТАРЧЕСКОГО ВОЗРАСТА ПОСЛЕ ЭНДОПРОТЕЗИРОВАНИЯ ТАЗОБЕДРЕННОГО СУСТАВА

The retrospective study was conducted aimed at the detection of risk factors of myocardial infection in elderly and senile patients after hip arthroplasty. Materials and methods. 303 elderly and senile patients (older than 65 years old) with subcapital fracture and consequent hip arthroplasty were enrolled into the study. Logistic regression equations were used for assessment of prognostic value of signs of myocardial infraction development. Results. In the early post-operative period myocardial infraction developed in 12 cases (3.9%). The following controlable and uncontrolable risk factors were detected in elderly and senile patients, most significant are presented first: cardial risk as per K.A. Eagle score – 2 scores and more, acute post-operative anemia with hemoglobin level below 95 g/l and type of anesthesia. The indicator integrating these three rates had the highest prognostic value. Проведено ретроспективное исследование, направленное на выявление факторов риска развития инфаркта миокарда (ИМ) у пациентов пожилого и старческого возраста после тотального эндопротезирования тазобедренного сустава. Материал и методы. В исследование включено 303 пациента пожилого и старческого возраста (старше 65 лет) с переломами шейки бедренной кости, которым выполнено тотальное эндопротезирование тазобедренного сустава. Оценку прогностической значимости признаков развития инфаркта миокарда проводили с помощью уравнений логистической регрессии. Результаты. ИМ развился в раннем послеоперационном периоде в 12 (3,9%) случаях. У пациентов пожилого и старческого возраста выявлены управляемые и неуправляемые факторы риска в порядке убывания их значимости: кардиальный риск по индексу K. A. Eagle, равный 2 баллам и более, острая послеоперационная анемия с уровнем гемоглобина меньше 95 г/л и вид анестезии. Наибольшую прогностическую ценность имеет показатель, интегрирующий эти три фактора.

INFLUENCE EXERTED BY SOMATIC PATHOLOGY ON RISKS OF OCCUPATIONAL LUNG FIBROSIS IN WORKERS EMPLOYED AT REFRACTORY PRODUCTION

Occupational lungs and bronchial pathology occurs not only under exposure to dusts, their aerosol structure and aggression, but also depends on individual properties of a body. The latter can determine either increased body resistance or susceptibility to occupational pathology occurrence. Our research goal was to determine influence exerted by somatic pathology on occupational lung fibrosis occurrence as well as to estimate prevalence of risk factors for cardiovascular and metabolic pathology occurrence in workers employed at refractory production. At the first stage 449 workers employed at refractory production were examined at a periodical medical examination (PME). Patients' average age was 41.59 ± 0.45 and average work experience was 14.47 ± 0.39 years. At the second stage 172 workers were examined at an occupational pathology center; 75 out of them were workers who had silicosis and were included into the test group and the remaining 97 workers didn't have any occupational pathology and were included into the reference group. Both groups were comparable as per sex (p = 0.0052) and work experience under exposure to dusts (p = 0.862). Workers examined at a PME most frequently had overweight and obesity (68 %). Arterial hypertension (AH) prevalence amounted to 19.5%; carbohydrate metabolism disorders, 19.8 %; 48.1 % workers had hypercholesterolemia. Patients with silicosis had certain disorders significantly more frequently than workers with long work experience but without any occupational pathologies; those disorders were AH, cardiac muscle hypertrophy in the left ventricle, ischemic heart disease, heart rate disorders, as well as mixed (obstructive and restrictive) breath mechanics disorders. We determined some factors that authentically produced certain effects on occupational lung fibrosis occurrence in workers employed at refractory production. Median time of silicosis occurrence was significantly shorter (by 11.5 years) among workers with severe AH, arrhythmia (by 13 years), lower hemoglobin in blood (by 11.5 years). Besides, silicosis occurred significantly earlier (by 10.8) among women than among men. © 2020 Obukhova T.Yu., Budkar' L.N., Gurvich V.B., Solodushkin S.I., Shmonina O.G., Karpova E.A.,. All Rights Reserved

Mathematical Modeling of the Development of Chronic Fluorine Intoxication in Aluminium Industry Workers

Introduction. Chronic fluorine intoxication prevails among the newly discovered occupational diseases in aluminum industry workers. Mathematical modeling is one of the helpful tools in ensuring better risk management with respect to the development of occupational fluorosis. Objective. Developing a logistic regression model predicting a probability of occupational fluorosis development in an occupational staff of aluminum plants in order to suggest adequate prophylactic strategies. Material and methods. A logistic regression model predicting a probability of the development of occupational fluorosis in aluminum industry workers of the Sverdlovsk region was constructed. The model embraced the results of a univariate analysis conducted with respect to major occupational exposures and health characteristics of 201 workers. Results. Six major factors were identified as being predictive of occupational fluorosis development in aluminum industry workers: age (fluorosis risk increases with age); type 2 diabetes mellitus; atrophic gastritis; kidney cysts; X-ray examination data (fluorosis risk increases with the stage as determined by X-ray); the hydro fluoride concentration increases by more than 2 occupational exposure limits. The developed model was verified by clinical cases and showed a high predictive ability (86.2 %). Both sensitivity (true positive rate) and specificity (true negative rate) of the model amounted to 86.2 %. Conclusion. By multivariate analysis the significant, mutually independent factors were identified, their combination being associated with chronic fluorine intoxication in an occupational staff of aluminum plants. The developed mathematical model has a high predictive ability and can be recommended as a sure tool to forecast the course of occupational fluorosis development in the workers at the aluminum industry. © 2020 Izdatel'stvo Meditsina. All rights reserved.The work of Solodushkin was supported by Act 211 Government of the Russian Federation, contract No 02.A03.21.0006

Cardiovascular and Metabolic Disorders Associated with Occupational Lung Fibrosis in Employees Exposed to the Dust at the Workplace

Introduction. The attribution of certain medical conditions in industrial workers to hazardous exposures at the workplace remains a challenging issue of occupational health. Material and methods. In order to identify cardiovascular conditions associated with occupational lung diseases in workers exposed to fibrogenic dust, we conducted a medical check-up examination of individuals employed in refractory production and asbestos industry. The main group consisted of the patients with a confirmed diagnosis of lung fibrosis (asbestosis, silicosis); the reference group was age- and tenure-matched workers without occupational fibrosis. Results. We e stablished a significantly h igher prevalence of arterial hypertension, left ventricular hypertrophy, s inus tachycardia, obesity, hypertriglyceridemia and impaired fasting glycemia in workers with silicosis and asbestosis if compared to those without work-related diseases. Based on the relative risk and attributable fraction estimates, we assume there is moderate occupational causation for arterial hypertension and a strong one for left ventricular hypertrophy, sinus tachycardia, and obesity. Very strong causation was found between occupational exposure to fibrogenic dust and carbohydrate metabolism disorders. High-stage hypertension, dyslipidemia and left ventricular hypertrophy were found to have a statistically significant impact on the timing of silicosis. Whereas high-stage hypertension, coronary artery disease, left ventricular hypertrophy and obesity were found to impact the timing of asbestosis. Conclusion. Cardiovascular and metabolic disorders are statistically more occurrent in workers with silicosis or asbestosis. Therefore, the disease can be regarded as work-related. We established cardiovascular and metabolic disorders to have a statistically significant impact on the timing of silicosis and asbestosis. Therefore, a timely CVD prophylaxis could reduce the risk of occupational lung fibrosis in workers exposed to fibrogenic dust. © 2020 Izdatel'stvo Meditsina. All rights reserved.The work of Solodushkin was supported by Act 211 Government of the Russian Federation, contract No 02.A03.21.0006