Abstract
Cardiovascular modeling of the blood pressure regulation system requires mathematical description of the viscoelastic mechanical properties of the arterial wall. These mathematical models involve using springs (elastic elements) and dashpots (viscous elements) in various series/parallel configurations, and can be described using linear ODEs in terms of the strain and stress of the system. An essential step in analyzing such a model is to determine whether the model is structurally identifiable, which means that the unknown parameters of the model can be quantified given perfect (noise-free) data. In such a model, the total stress and strain are known, but the individual spring and dashpot constants represent unknown parameters. We will find simple algebraic conditions to determine whether or not a given model is identifiable, and also give a constructive result on how to obtain an identifiable model when forming a spring-dashpot network. In particular, we will show that determining whether or not a model is identifiable amounts to solving a certain polynomial factorization problem.
This is joint work with Adam Mahdi and Seth Sullivant.