Asymptotic Bounds for the Time-Periodic Solutions to the Singularly Perturbed Ordinary Differential Equations

The periodical in time problem for singularly perturbed second order linear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented

Cholesterolosis in routine histopathological examination after cholecystectomy: What should a surgeon behold in the reports?

AbstractIntroduction: Cholecystectomy is one of the most common surgical procedures. Postoperative investigation of cholecystectomy specimen has a great value since histopathological reports may document some entities with significant clinical consequences. The aim of this study was to evaluate the association between cholesterolosis and the reports indicating some histopathological alterations in symptomatic cholecystitis. Methods: This paper is based on a retrospective study. Histopathological reports of 432 cholecystectomy specimens between January 2011 and June 2013 were reviewed. Three reports were excluded due to perioperative diagnosis of cancer. Reports of 429 cholecystectomy specimens of the acute and symptomatic chronic cholecystitis patients were analyzed. Standardization of the reporting was questioned. Age, gender, histopathological wall thickness of gallbladder, reporting rates of acute inflammation, cholesterolosis, polypoid lesions, epithelial hyperplasia, gastric or intestinal metaplasia, dysplasia and incidental cancer were investigated and compared between patients with and without cholesterolosis. Reported rates of histopathological findings were comparable between patients under and over 60 years old and patients with and without reported cholesterolosis. Results: Reported histopathological findings were presented as acute inflammation in 46 (10.7%), cholesterolosis in 79 (18.4%), gallbladder polypoid lesions in 7 (1.6%), epithelial hyperplasia in 16 (3.7%), metaplasia of any type in 34 (7.9%) of 429 patients. Dysplasia was excluded whereas one incidental gallbladder carcinoma was reported. Epithelial hyperplasia and metaplasia were found to be related to age. Gallbladder wall thickness was decreased with cholesterolosis. However, only a correlation between cholesterolosis and gender or metaplasia was noted. Conclusion: Recent study suggests that cholesterolosis is somehow associated with metaplasia. Thus, surgeons should carefully interpret the histopathology reports based on unusual or exceptional findings corresponding to the cholecystectomy specimens. Any abnormal finding in the reports should be investigated in terms of the progress of the pathology and also its clinical consequences