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Recently, structured inverse variational inequality (SIVI) problems have attracted much attention. In this paper, we propose new splitting methods to solve SIVI problems by employing the idea of the classical Douglas-Rachford splitting method (DRSM). In particular, the proposed methods can be regarded as a novel application of the DRSM to SIVI problems by decoupling the linear equality constraint, leading to smaller and easier subproblems. The main computational tasks per iteration are the evaluations of certain resolvent operators, which are much cheaper than those methods without taking advantage of the problem structures. To make the methods more implementable in the general cases where the resolvent operator is evaluated in an iterative scheme, we further propose to solve the subproblems in an approximate manner. Under quite mild conditions, global convergence, sublinear rate of convergence, and linear rate of convergence results are established for both the exact and the inexact methods. Finally, we present preliminary numerical results to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Objective: To analyze the anatomical characteristics of the adrenal veins through adrenal venography to improve the success rate of adrenal venography (AVS). Methods: This study was a cross-sectional study. Patients who were diagnosed with primary aldosteronism and underwent AVS from January 2019 to October 2023 at the First Affiliated Hospital of Dalian Medical University were included. Adrenal vein imaging was collected from the enrolled patients. We performed statistical analysis on the adrenal vein orifice position, inflow angle, and adrenal venography morphology. The adrenal venous orifice was defined as the location where the catheter was placed at the end of the calm inhalation. Spearman correlation analysis was used to explore the relationship between the positions of bilateral adrenal vein orifices and body mass index (BMI). Results: A total of 282 patients with successful bilateral AVS and complete bilateral adrenal vein imaging were enrolled, of whom 57.1% (161/282) were male and the age was (53.3±10.7) years old. The orifice of the left adrenal vein was located between the middle segment of the 11 th thoracic vertebra and the upper segment of the 2 nd lumbar vertebra. The inflow angle relative to the position of the orifice was all leftward and upward. The orifice of the right adrenal vein was located between the upper segment of the 11 th thoracic vertebra and the lower segment of the 1 st lumbar vertebra, and 91.1% (257/282) had a rightward and downward angle of inflow relative to the position of the orifice. The position of the adrenal vein orifices on both the left ( r= 0.211, P< 0.001) and right ( r =0.196, P= 0.001) showed positive correlation with BMI. The position of the right adrenal vein orifice also increased with the position of the left adrenal orifice ( r =0.530, P< 0.001). The most common adrenal venography morphology on the right side was triangular (36.5%, 103/282), while the most common venography morphology on the left side was glandular (66.3%, 187/282). Conclusions: The anatomical morphology of adrenal veins are diverse. Being familiar with the morphological characteristics of the adrenal vein and identifying the adrenal vein accurately during surgery has important clinical value in improving the success rate of AVS.