1,141 research outputs found

    Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics

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    In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media. In our previous works, we have introduced contrast-independent partially explicit time discretizations. In this paper, we extend these ideas to multiscale QGD problems. Because of high contrast, explicit methods require a very small time stepping. By designing appropriate spatial splitting and temporal splitting, partially explicit methods remove this constraint. The proposed partially explicit time discretization consists of two steps. First, we split the space into contrast dependent (fast) and contrast independent (slow) components on a coarse grid that is much larger compared to spatial heterogeneities. Secondly, we design a temporal splitting algorithm in a such way that it is stable and the time step is independent of the contrast and only depends on the coarse mesh size. Using proposed method, a few degrees of freedom are treated implicitly and the approach is mostly explicit. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast

    Multicontinuum homogenization and its relation to nonlocal multicontinuum theories

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    In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing boundary effects. We discuss different choices of constraints for cell problems. We present numerical results that show how oversampling reduces boundary effects. Finally, we discuss the relation of the proposed methods to our previously developed methods, Nonlocal Multicontinuum Approaches

    An analogue of the Lyapunov inequality for an ordinary second-order differential equation with a fractional derivative and a variable coefficient

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    This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found

    Comparison of the Capabilities of Spectroscopic and Quantitative Video Analysis of Fluorescence for the Diagnosis and Photodynamic Therapy Control of Cholangiocellular Cancer

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    Cholangiocellular cancer (CCC) is a malignant neoplasm of the hepatobiliary system that is difficult to diagnose and treat. Currently, the most effective treatment of CCC is demonstrated under the control by fluorescent diagnosis. Photodynamic therapy (PDT) has also shown good results in the treatment of this disease, and fluorescence analysis of the photosensitizer is a good approach to control PDT. This article presents the results of a comparison of spectroscopic and quantitative video-fluorescent analysis of chlorin e6 photosensitizer fluorescence in vivo during cholangiocellular cancer surgery. Spectroscopic analysis provides accurate information about the concentration of the photosensitizer in the tumor, while the video-fluorescence method is convenient for visualizing tumor margins. A direct correlation is shown between these two methods when comparing the fluorescence signals before and after PDT. The applied paired Student’s t-test shows a significant difference between fluorescence signal before and after PDT in both diagnostic methods. In this regard, video-fluorescence navigation is not inferior in accuracy, sensitivity, or efficiency to spectroscopic methods

    Фотодинамическая терапия предраковых заболеваний и рака шейки матки (обзор литературы)

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    The paper presents the results of literature data analysis on the main directions of precancerous diseases of the cervix uteri and cervical cancer treatment. Side effects following surgery or radiation treatment can lead to structural deformities, scarring, hyperpigmentation, systemic side effects, and destruction of normal tissue. In addition, the use of traditional methods of treatment can cause multidrug resistance, which will lead to ineffective treatment and the development of a relapse of the disease. To avoid toxicity and reduce side effects, alternative treatment strategies have been proposed. Photodynamic therapy (PDT) is a promising organ-preserving highly selective method for treating cervical neoplasia, which includes two stages: the introduction of a photosensitizer and local exposure to directed light radiation. A number of studies have demonstrated the high clinical efficacy of this method in the treatment of patients with cervical neoplasia and carriage of human papillomavirus infection without adverse consequences for fertility. The use of PDT contributes to the successful outcome of the treatment of pathological foci on the mucous membrane of the cervix, the effectiveness and safety of the method is ensured by the selective effect on tissues. In the course of treatment, normal surrounding tissues are not damaged, there is no gross scarring and stenosis of the cervical canal, thereby PDT allows maintaining the normal anatomical and functional characteristics of the cervix.Представлены результаты анализа данных литературы об основных направлениях лечения предраковых заболеваний шейки матки и рака шейки матки. Побочные эффекты после хирургического или лучевого лечения могут привести к структурным деформациям, рубцам, гиперпигментации, системным побочным эффектам и разрушению нормальных тканей. Использование традиционных методов лечения может вызвать множественную лекарственную устойчивость, что приведет к неэффективности лечения и развитию рецидива заболевания. Чтобы избежать токсичности и уменьшить побочные эффекты были предложены альтернативные стратегии лечения. Перспективным органосохраняющим высокоселективным методом лечения неоплазии шейки матки является фотодинамическая терапия (ФДТ), которая включает два этапа: введение фотосенсибилизатора и локальное воздействие направленного светового излучения. В ряде исследований продемонстрирована высокая клиническая эффективность этого метода в лечении пациенток с цервикальной неоплазией и носительством инфекции вируса папилломы человека без неблагоприятных последствий для фертильности. Использование ФДТ способствует успешному результату лечения патологических очагов на слизистой оболочке шейки матки, эффективность и безопасность метода обеспечивается избирательностью воздействия на ткани. В процессе лечения не повреждаются нормальные окружающие ткани, не происходит грубого рубцевания и стеноза цервикального канала, тем самым ФДТ позволяет сохранить нормальные анатомо-функциональные характеристики шейки матки

    Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics

    No full text
    In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media. In our previous works, we have introduced contrast-independent partially explicit time discretizations. In this paper, we extend these ideas to multiscale QGD problems. Because of high contrast, explicit methods require a very small time stepping. By designing appropriate spatial splitting and temporal splitting, partially explicit methods remove this constraint. The proposed partially explicit time discretization consists of two steps. First, we split the space into contrast dependent (fast) and contrast independent (slow) components on a coarse grid that is much larger compared to spatial heterogeneities. Secondly, we design a temporal splitting algorithm in a such way that it is stable and the time step is independent of the contrast and only depends on the coarse mesh size. Using proposed method, a few degrees of freedom are treated implicitly and the approach is mostly explicit. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast

    A Pilot Study of Fluorescence-Guided Resection of Pituitary Adenomas with Chlorin e6 Photosensitizer

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    Fluorescence diagnostics is one of the promising methods for intraoperative detection of brain tumor boundaries and helps in maximizing the extent of resection. This paper presents the results of a pilot study on the first use of the chlorin e6 photosensitizer and a two-channel video system for fluorescence-guided resection of pituitary adenomas. The study’s clinical part involved two patients diagnosed with hormonally inactive pituitary macroadenomas and one patient with a hormonally active one. All neoplasms had different sizes and growth patterns. The data showed accumulation of chlorin e6 in tumor tissues in high concentrations: Patient 1: 2 mg/kg, Patient 2: 5 mg/kg, and Patient 3: 4 mg/kg. For Patient 1, the residual part of the tumor was not resected since it was intimately attached to the anterior genu of the internal carotid artery. For Patients 2 and 3, no regions of increased Ce6 accumulation were detected in the tumor foci after resection. Therefore, the use of the Ce6 and a two-channel video system helped to achieve a high degree of tumor resection in each case

    Phototheranostics of Cervical Neoplasms with Chlorin e6 Photosensitizer

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    (1) Purpose: Improving the treatment effectiveness of intraepithelial neoplasia of the cervix associated with human papillomavirus infection, based on the application of the method of photodynamic therapy with simultaneous laser excitation of fluorescence to clarify the boundaries of cervical neoplasms. (2) Methods: Examination and treatment of 52 patients aged 22 to 53 years with morphologically and cytologically confirmed mild to severe intraepithelial cervix neoplasia, preinvasive, micro-invasive, and squamous cell cervix carcinoma. All patients were carriers of human papillomavirus infection. The patients underwent photodynamic therapy with simultaneous laser excitation of fluorescence. The combined use of video and spectral fluorescence diagnostics for cervical neoplasms made it possible to control the photodynamic therapy process at all stages of the procedure. Evaluation of the photodynamic therapy of intraepithelial cervical neoplasms was carried out with colposcopic examination, cytological conclusion, and morphological verification of the biopsy material after the photodynamic therapy course. The success of human papillomavirus therapy was assessed based on the results of the polymerase chain reaction. (3) Results. The possibility of simultaneous spectral fluorescence diagnostics and photodynamic therapy using a laser source with a wavelength of 660 nm has been established, making it possible to assess the fluorescence index in real-time and control the photobleaching of photosensitizers in the irradiated area. The treatment of all 52 patients was successful after the first photodynamic therapy procedure. According to the PCR test of the discharge from the cervical canal, the previously identified HPV types were not observed in 48 patients. Previously identified HPV types were absent after repeated PDT in four patients (CIN III (n = 2), CIS (n = 2)). In 80.8% of patients, regression of the lesion was noted. (4) Conclusions. The high efficiency of photodynamic therapy with intravenous photosensitizer administration of chlorin e6 has been demonstrated both in relation to eradication therapy of human papillomavirus and in relation to the treatment of intraepithelial lesions of the cervix
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