A posteriori error estimates in the finite element method for elliptic BVP with degeneration

We consider a class of elliptic boundary value problems with degenerating coefficients for which we construct FEM schemes with optimal convergence on the basis of multiplicative extraction of the singularity. For a scale of weighted Sobolev norms including the energy norm of the differential operator, we prove a posteriori estimates for the error of the discrete solutions. © 2014 Pleiades Publishing, Ltd

High-Order Accuracy Approximation for a Two-Point Boundary Value Problem of Fourth Order with Degenerate Coefficients

© 2018, Pleiades Publishing, Ltd. High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved

Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator

The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality. © 2008 MAIK Nauka

A Hardy inequality with a point-singular weight inside a domain

Sobolev spaces with weights taking infinite values at some interior points of a two-dimensional domain are considered. For functions from these spaces, a Hardy inequality is obtained. Embedding theorems for weighted Lebesgue spaces and equivalent renorming theorems are proved. © 2013 Pleiades Publishing, Ltd

Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients

In this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides. © Allerton Press, Inc., 2011

Sharp estimates for the polynomial approximation in weighted Sobolev spaces

© 2015, Pleiades Publishing, Ltd. We obtain sharp estimates for the accuracy of the best approximation of functions by algebraic polynomials on an interval, the half-line, and the entire line in weighted Sobolev spaces with Jacobi, Laguerre, and Hermite weights, respectively. We show that the orthogonal polynomials associated with these weights form orthogonal bases in the respective weighted Sobolev spaces. We obtain sharp estimates of Markov–Bernstein type

Characterization of the binding sites of the anticancer ruthenium(III) complexes KP1019 and KP1339 on human serum albumin via competition studies

Indazolium trans-[tetrachloridobis(1H-indazole)ruthenate(III)] (KP1019) and its Na+ analogue (KP1339) are two of the most prominent non-platinum antitumor metal complexes currently undergoing clinical trials. After intravenous administration, they are known to bind to human serum albumin (HSA) in a noncovalent manner. To elucidate their HSA binding sites, displacement reactions with the established site markers warfarin and dansylglycine as well as bilirubin were monitored by spectrofluorimetry, ultrafiltration-UV-vis spectrophotometry, and/or capillary zone electrophoresis. Conditional stability constants for the binding of KP1019 and KP1339 to sites I and II of HSA were determined, indicating that both Ru(III) compounds bind to both sites with moderately strong affinity (log K (1)' = 5.3-5.8). No preference for either binding site was found, and similar results were obtained for both metal complexes, demonstrating low influence of the counter ion on the binding event

Inhospital changes of left ventricular diastolic function in patients undergoing coronary bypass surgery

Aim. To evaluate changes of left ventricular (LV) diastolic function in patients with multivessel coronary artery disease before coronary artery bypass grafting (CABG) and in the early postoperative period (7-10 days), as well as to assess the relation- ship between diastolic LV dysfunction and postoperative atrial fibrillation (POAF).Material and methods. This original prospective study of included 50 patients undergoing CABG at the Cardiac Surgery Unit № 1 of the N. V. Sklifosovsky Research Institute for Emergency Medicine from December 2020 to December 2021. All patients underwent standard echocardiography before and after surgery. Diastolic function was assessed using the following parameters: septal mitral annulus velocity (e’septal), lateral mitral annulus velocity (e’lateral), the ratio of the peak early transmitral velocity to peak early diastolic velocity of the mitral annulus movement (E/e’), left atrial volume index (ml/m2), peak tricuspid regurgitation velocity (m/s), the ratio of the peak early to late filling velocity (E/A).Results. After CABG, 35 patients maintained sinus rhythm in the early postoperative period (group 1), while 15 patients had POAF (group 2). According to echocardiography, type 1 diastolic dysfunction prevailed in both groups; types 2 and 3 LV diastolic dysfunction were not identified. Among the parameters characterizing myocardial relaxation, in group 1 after CABG, a significant increase in the peak E (p=0,001) was noted, and due to this, the normalization of the E/A ratio was recorded (p<0,0001). An increase in e’lateral (p=0,05) was also revealed, in connection with which an increase in the E/e’ (p=0,02) was noted. In the group of patients with POAF, such changes were not detected. Left atrial volume index (ml/ m2) was significantly higher in the POAF group (p=0,02).Conclusion. Surgical myocardial revascularization has a positive effect on LV diastolic function. Improvement in LV diastolic function after CABG may be a sign of the restoration of hibernating myocardium function, while the absence of LV diastolic function improvement, together with left atrial dilatation, may be predictors of early POAF

Хирургическая реконструкция левого желудочка у пациентов с постинфарктной дилатацией и сердечной недостаточностью

INTRODUCTION The cause of heart failure in patients with coronary artery disease after anterior myocardial infarction may be dilatation of the cavity of the left ventricle (LV) with subsequent unfavorable course of the disease. In the case of early reperfusion, which prevents transmural myocardial necrosis, the damaged segment more often becomes akinetic than dyskinetic. Surgical remodeling of the left ventricle (SRLV) is aimed at reducing the volume and restoring its elliptical shape by eliminating scars in the akinetic and/or dyskinetic segments.AIM OF STUDY To evaluate the survival of patients with chronic heart failure (CHF) who had anterior wall myocardial infarction in the early and late periods after surgical remodeling of the left ventricle, in combination with coronary bypass grafting and/or interventions on the mitral valve.MATERIAL AND METHODS The study included 99 patients with coronary artery disease (CAD) who had myocardial infarction of the anterior LV wall and with severe heart failure, who underwent surgical LV remodeling in the period from 2002 to 2020. The analysis of early and long-term results was carried out. The risk factors influencing lethality were determined.The mean age of the patients was 56.0±10.2 years (from 23 to 81 years). The vast majority of patients (90%) were men. LV ventriculoplasty was combined with coronary bypass grafting in 97 (98%) patients, with mitral valve repair in 2 (2%) patients, with mitral valve replacement in 2 (2%) patients.RESULTS In the early postoperative period, all patients showed an improvement in global LV systolic function. The ejection fraction (EF) of the left ventricle increased from the average preoperative average value of 34.2±3.7% to 43±4.2% in the postoperative period (р<0,001). Left ventricular end systolic volume index (LVESV) decreased from 71.4±15.3 ml/m2 to 43.8±9.6 ml/m2, respectively (р<0,001). In the early postoperative period, 5 (5%) patients used the following means of mechanical hemodynamic support: intra-aortic balloon pump (IABP), non-implantable device for temporary support of the left ventricle (LVAD) and extracorporeal membrane oxygenation (ECMO). The 30-day mortality rate after LVESV was 6%. Prior to surgery, all patients had NYHA functional class (FC) III or IV. In the postoperative period, all patients experienced regression of heart failure symptoms and improved exercise tolerance. NYHA functional class improved to I and II in 100% of cases. Using univariate analysis, it was possible to determine that EF ≤30%, LVESV ≥80 ml/m2 and pulmonary artery pressure (PAP) >60 mm Hg. were risk factors for hospital mortality. The overall fifteen-year survival rate was 59.8±0.13%. The absence of readmission to the hospital due to recurrent angina pectoris, mitral valve dysfunction and progression of heart failure (HF) was 72% among surviving patients.CONCLUSION Surgical remodeling reduces the volume of the dilated left ventricle and restores its elliptical shape in patients with CAD after anterior myocardial infarction. The results of our study demonstrate an improvement in LV systolic function in all patients in the early postoperative period and low mortality, an acceptable fifteen-year survival rate, and a low readmission rate due to the progression of chronic heart failure (CHF).ВВЕДЕНИЕ Причиной сердечной недостаточности (СН) у пациентов с ишемической болезнью сердца (ИБС) после перенесенного переднего инфаркта миокарда может быть дилатация полости левого желудочка (ЛЖ) с последующим неблагоприятным течением заболевания. В случае ранней реперфузии, которая предотвращает трансмуральный некроз миокарда, поврежденный сегмент чаще становится акинетическим, чем дискинетическим. Хирургическая реконструкция ЛЖ (ХР ЛЖ) направлена на уменьшение объема и восстановление его эллиптической формы за счет исключения рубцов в акинетических и (или) дискинетических сегментах.ЦЕЛЬ ИССЛЕДОВАНИЯ Оценить выживаемость пациентов с хронической СН, перенесших инфаркт миокарда передней стенки в раннем и отдаленном периодах после ХР ЛЖ, в сочетании с коронарным шунтированием (КШ) и (или) вмешательствами на митральном клапане (МК).МАТЕРИАЛ И МЕТОДЫ В исследование включены 99 пациентов с ИБС, перенесших инфаркт миокарда передней стенки ЛЖ и с выраженной СН, которым выполняли хирургическую реконструкцию ЛЖ в период с 2002 по 2020 год. Проведен анализ ранних и отдаленных результатов. Определены факторы риска, влияющие на летальность.Средний возраст пациентов составил 56,0±10,2 года (от 23 лет до 81 года). Подавляющее большинство пациентов (90%) были мужчинами. Вентрикулопластика ЛЖ сочеталась с КШ у 97 пациентов (98%), с пластикой МК — у 2 пациентов (2%), с протезированием МК — у 2 пациентов (2%).РЕЗУЛЬТАТЫ В раннем послеоперационном периоде у всех пациентов отмечено улучшение глобальной систолической функции ЛЖ. Фракция выброса (ФВ) ЛЖ в послеоперационном периоде статистически значимо возросла со среднего дооперационного среднестатистического значения — с 34,2±3,7 до 43±4,2% (р<0,001). Индекс конечного систолического объема (ИКСО) ЛЖ статистически значимо снизился соответственно с 71,4±15,3 до 43,8±9,6 мл/м2 (р<0,001). В раннем послеоперационном периоде у 5 пациентов (5%) использовали следующие средства механической поддержки гемодинамики: внутриаортальную баллонную контрпульсацию, не имплантируемый аппарат для временной поддержки ЛЖ (LVAD) и экстракорпоральную мембранную оксигенацию. 30-дневная летальность после ХР ЛЖ составила 6%. До операции у всех пациентов был III или IV функциональный класс (ФК) сердечной недостаточности по NYHA. В послеоперационном периоде у всех пациентов наблюдали регрессирование явлений СН и улучшение переносимости физической нагрузки. ФК по NYHA улучшился до I и II во всех случаях. С помощью одномерного анализа удалось определить, что ФВ не более 30%, ИКСО не менее 80 мл/м2 и давление в легочной артерии не менее 60 мм рт.ст. являлись факторами риска госпитальной летальности. Общая 15-летняя выживаемость составила 59,8±0,13%. Отсут­ствие повторной госпитализации в стационар в связи с рецидивом стенокардии, дисфункцией МК и прогрессированием СН составило 72% среди выживших пациентов.ВЫВОДЫ Хирургическая реконструкция уменьшает объем дилатированного левого желудочка и восстанавливает его эллиптическую форму у пациентов с ишемической болезнью сердца, перенесших передний инфаркт миокарда. Результаты нашего исследования демонстрируют улучшение систолической функции левого желудочка у всех пациентов в раннем послеоперационном периоде и низкую летальность, приемлемую пятнадцатилетнюю выживаемость и низкую частоту повторных госпитализаций в связи с прогрессированием хронической сердечной недостаточности