Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure

In this paper, we deal with approximate solutions in vector-optimization problems with respect to a variable order structure. In the case of exact solutions of a vector optimization problem, especially in the variable order case, authors use a cone or a pointed convex cone-valued map in order to describe the solution concepts but in this paper, we use a set-valued map and this map is not a (pointed convex) cone-valued map necessarily. We characterize these solution concepts by a general scalarization method by means of nonlinear functionals. In the last section, an extension of Ekeland’s variational principle for a vector optimization problem with a variable order structure is given.     

Sodium Phytate-Incorporated Gelatin-Silicate Nanoplatelet Composites for Enhanced Cohesion and Hemostatic Function of Shear-Thinning Biomaterials

Shear-thinning biomaterials (STBs) based on gelatin-silicate nanoplatelets (SNs) are emerging as an alternative to conventional coiling and clipping techniques in the treatment of vascular anomalies. Improvements in the cohesion of STB hydrogels pave the way toward their translational application in minimally invasive therapies such as endovascular embolization repair. In the present study, sodium phytate (Phyt) additives are used to tune the electrostatic network of SNs-gelatin STBs, thereby promoting their mechanical integrity and facilitating injectability through standard catheters. We show that an optimized amount of Phyt enhances storage modulus by approximately one order of magnitude and reduces injection force by ≈58% without compromising biocompatibility and hydrogel wet stability. The Phyt additives are found to decrease the immune responses induced by SNs. In vitro embolization experiments suggest a significantly lower rate of failure in Phyt-incorporated STBs than in control groups. Furthermore, the addition of Phyt leads to accelerated blood coagulation (reduces clotting time by ≈45% compared to controls) due to the contributions of negatively charged phosphate groups, which aid in the prolonged durability of STB in coagulopathic patients. Therefore, the proposed approach is an effective method for the design of robust and injectable STBs for minimally invasive treatment of vascular malformations.