No abstract

Magnetic resonance imaging-guided LITT is a well-tolerated procedure and may be effective in treating tumor recurrence/radiation necrosis.

In this paper we study a class of Petrov-Galerkin solutions that have global optimal convergence rates for linear Volterra integro-differential equations. These solutions also possess certain local and global superconvergence. Asymptotic expansions of the errors in these solutions are established which can be used to form higher order approximations by Richardson extrapolation and defect corrections. Several postprocessing techniques are introduced to enhance these solutions. As by-products, these higher order numerical approximations can be used to generate a posteriori error estimators. Representative numerical results are also provided.

A series of β-carboline-benzimidazole conjugates bearing a substituted benzimidazole and an aryl ring at C3 and C1 respectively were designed and synthesized. The key step of their preparation was determined to involve condensation of substituted o-phenylenediamines with 1-(substituted phenyl)-9H-pyrido[3,4-b]indole-3-carbaldehyde using La(NO3)3·6H2O as a catalyst and their cytotoxic potential was evaluated. Conjugates 5a, 5d, 5h and 5r showed enhanced cytotoxic activity (GI50 values range from 0.3 to 7.1 μM in most of the human cancer cell lines) in comparison to some of the previously reported β-carboline derivatives. To substantiate the cytotoxic activity and to understand the nature of interaction of these conjugates with DNA, spectroscopy, DNA photocleavage and DNA topoisomerase I inhibition (topo-I) studies were performed. These conjugates (5a, 5d and 5r) effectively cleave pBR322 plasmid DNA in the presence of UV light. In addition, the effect of these conjugates on DNA Topo I inhibition was studied. The mode of binding of these new conjugates with DNA was also examined by using both biophysical as well as molecular docking studies, which supported their multiple modes of interaction with DNA. Moreover, an in silico study of these β-carboline-benzimidazole conjugates reveals that they possess drug-like properties.