A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations

We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.Comment: 10 pages, no figur

Vascular resection for intrahepatic cholangiocarcinoma: Current considerations

Intrahepatic cholangiocarcinoma (iCCA) accounts for approximately 10% of all primary liver cancers. Surgery is the only potentially curative treatment, even in cases of macrovascular invasion. Since resection offers the only curative chance, even extended liver resection combined with complex vascular or biliary reconstruction of the surrounding organs seems justified to achieve complete tumour removal. In selected cases, the major vascular resection is the only change to try getting the cure. The best results are achieved by the referral centre with a wide experience in complex liver surgery, such as ALPPS procedure, IVC resection, and ante-situ and ex-situ resections. However, despite aggressive surgery, tumour recurrence occurs frequently and long-term oncological results are very poor. This suggests that significant progress in prognosis cannot be expected by surgery alone. Instead, multimodal treatment including neoadjuvant chemotherapy, radiotherapy, and subsequent adjuvant treatment for iCCA seem to be necessary to improve results. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Boundary value problems for the diffusion equation of the variable order in differential and difference settings

Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori estimates for these problems exactly as in the classical case. The credibility of the obtained results is verified by performing numerical calculations for a test problem.Comment: 19 pages. Presented at the 4-th IFAC Workshop on Fractional Differentiation and Its Applications, Badajoz, Spain, October 18-20, 201

Vascular resection in perihilar cholangiocarcinoma

Among the cholangiocarcinomas, the most common type is perihilar (phCC), accounting for approximately 60% of cases, after which are the distal and then intrahepatic forms. There is no staging system that allows for a comparison of all series and extraction of conclusions that increase the long-term survival rate of this dismal disease. The extension of the resection, which theoretically depends on the type of phCC, is not a closed subject. As surgery is the only known way to achieve a cure, many aggressive approaches have been adopted. Despite extended liver resections and even vascular resections, margins are positive in around one third of patients. In the past two decades, with advances in diagnostic and surgical techniques, surgical outcomes and survival rates have gradually improved, although variability is the rule, with morbidity and mortality rates ranging from 14% to 76% and from 0% to 19%, respectively. Extended hepatectomies and portal vein resection, or even right hepatic artery reconstruction for the left side tumors are frequently needed. Salvage procedures when arterial reconstruction is not feasible, as well as hepatopancreatoduodenectomy, are still under evaluation too. In this article, we discuss the aggressive surgical approach to phCC focused on vascular resection. Disparate results on the surgical treatment of phCC made it impossible to reach clear-cut conclusions. © 2021 by the authors. Licensee MDPI, Basel, Switzerland