Background & Aim: The purpose of this presentation to present our data in evaluating whether venous indocyanine green (ICG) videoangiography has any potential for predicting the presence of a safe collateral circulation for veins that are at risk for intentional or unintentional damage during surgery.Methods & Materials/Patients: We performed venous ICG videoangiography during 153 consecutive neurosurgical procedures. On those occasions in which a venous sacrifice occurred during surgery, whether that sacrifice was preplanned (intended) or unintended, venous ICG videoangiography was repeated so as to allow us to study the effect of venous Sacrifice. A specific test (clipping test) to predict the presence of venous collateral circulation was also applied in 21 of these cases.Results: Venous ICG videoangiography allowed for an intraoperative real-time flow assessment of the exposed veins with excellent image quality and resolution in all cases. The veins observed in this study were found to be extremely different with RESPECT to flow dynamics and could be divided in 3 groups: 1) arterialized veins; 2) fast-draining veins with uniform filling and clear flow direction; and 3) slow-draining veins with nonuniform filling. Temporary clipping was found to be a simple and reversible way to test for the presence of potential anastomotic circulation.Conclusion: Venous ICG videoangiography is able to reveal substantial variability in the venous flow dynamics. "Slow veins, " when they are tributaries of bridging veins, might hide a potential for anastomotic circulation that deserve further investigation.

Since the theory of filters plays an important role in the theory of lattices, in this paper, we will make an intensive study of the notions of semisimple lattices and the socle of lattices based on their filters. The bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the rings. It is shown that, if $L$ is a semisimple distributive lattice, then $L$ is finite. Also, an application of the results of this paper is given. It is shown that if $R$ is a right distributive ring, then the lattice of right ideals of $R$ is semisimple iff  $R$ is a semisimple ring.

Let M be a right module over a ring R,  M a pre-radical on  [M], and N 2  [M]. In this note we show that if N1; N2 2  [M] are two  M-lifting modules such that Ni is Nj-projective (i; j = 1; 2), then N = N1  N2 is  M-lifting. We investigate when homomorphic image of a  M-lifting module is  M-lifting.

Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $SO(G)=\sum\limits_{uv\in E(G)}\sqrt{d_{u}^{2}+d_{v}^{2}}$, where $d_{u}$ denotes the degree of vertex $u$. In this paper, we first determine the maximum Sombor index among cacti with $n$ vertices and $t$ cycles, then determine the maximum Sombor index among cacti with perfect matchings. We also characterize corresponding maximum cacti.

In this paper, we study the concept of exponential convex functions with RESPECT to $s$ and prove Hermite-Hadamard type inequalities for the newly introduced this class of functions. In addition, we get some refinements of    the Hermite-Hadamard (H-H) inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, RESPECTively at least one, is exponential convex with RESPECT to $s$. Our results coincide with the results obtained previously in special cases.