Introduction: Endoscopic biliary stenting is a widely utilized procedure in the realm of interventional gastroenterology, primarily employing plastic stents for short-term biliary drainage. This case series endeavours to investigate the occurrence and ensuing clinical ramifications of forgotten or retained biliary stents. Methods: Carried out over an 8-month duration at King George Hospital in Visakhapatnam, this case series encompasses 12 patients diagnosed with forgotten biliary stents. Diagnostic confirmation was established through a combination of X-ray, abdominal ultrasound, and magnetic resonance cholangiopancreatography (MRCP). Four patients experienced complications such as fractured distal pigtails and obstructed stents, thwarting retrieval efforts via endoscopic retrograde cholangiopancreatography (ERCP) and cholangioscopy. Results: This case series featured 12 patients with a median age of 48 years (range: 18-76), comprising 7 females (58.3%) and 5 males (41.7%). The primary indication for initial stent placement was choledocholithiasis in 10 instances (83.3%), while benign biliary strictures accounted for 3 cases (25%). On average, patients presented 31.3 months post-initial stenting, primarily manifesting cholangitis symptoms (83.3%). ERCP succeeded in stent removal in 8 cases (66.6%), while the remaining cases necessitated advanced procedures such as cholangioscopy, with two patients being referred for surgical intervention. It is noteworthy that there were no instances of mortality. Conclusion: This case series, conducted against the backdrop of the COVID-19 pandemic, highlights an increased prevalence of neglected plastic biliary stents. The principal complication encountered was cholangitis, often coexisting with common bile duct (CBD) stones. Standard ERCP techniques demonstrated reduced efficacy in instances characterized by fractured, obstructed, or displaced stents, necessitating the exploration of alternative strategies like cholangioscopy or surgical intervention. This compilation of cases underscores the pressing imperative for prompt stent retrieval and the enhancement of management protocols to proactively mitigate the potential for complications.

This paper initiates the study of the mathematical aspects of the ad-hoc Lanzhou index. If G is a graph with the vertex set {x1,⋯,xn}, then the ad-hoc Lanzhou index of G is defined by Lz¯(G)=∑i=1ndi(n−1−di)2, where di represents the degree of the vertex xi. Several identities for the ad-hoc Lanzhou index, involving some existing topological indices are established. The problems of finding graphs with the extremum values of the ad-hoc Lanzhou index from the following sets of graphs are also attacked: (i) set of all connected ξ-cyclic graphs of a fixed order, (ii) set of all connected molecular ξ-cyclic graphs of a fixed order, (iii) set of all graphs of a fixed order, (iv) set of all connected molecular graphs of a fixed order.