title: A mathematical model of aortic aneurysm formation.
abstract: Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient's aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient's abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material.
authors.affiliation: Department of Mathematics, Pennsylvania State University, State College, PA, United States of America.
authors.forename: Wenrui
authors.initials: W
authors.lastname: Hao
authors.affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing, China.
authors.forename: Shihua
authors.initials: S
authors.lastname: Gong
authors.affiliation: Department of Mathematics, Pennsylvania State University, State College, PA, United States of America.
authors.forename: Shuonan
authors.initials: S
authors.lastname: Wu
authors.affiliation: Department of Mathematics, Pennsylvania State University, State College, PA, United States of America.
authors.forename: Jinchao
authors.initials: J
authors.lastname: Xu
authors.affiliation: Division of Vascular Diseases & Surgery, The Ohio State University Wexner Medical Center, Columbus, OH, United States of America.
authors.forename: Michael R
authors.initials: MR
authors.lastname: Go
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, OH, United States of America.
authors.forename: Avner
authors.initials: A
authors.lastname: Friedman
authors.affiliation: Yunnan Cocreative Scientific Computing and Datamining Center, Kunming, China.
authors.forename: Dai
authors.initials: D
authors.lastname: Zhu
mesh_terms: D017542:Aneurysm, Ruptured / Q000378:metabolism / Q000473:pathology; D017544:Aortic Aneurysm, Abdominal / Q000378:metabolism / Q000473:pathology*; D005786:Gene Expression Regulation; D015850:Interleukin-6 / Q000378:metabolism; D008954:Models, Biological; D012306:Risk
chemical_list: D015850:Interleukin-6