Inverse parameter identification for a branching 1D arterial network

Abstract

In this paper we investigate the invertability of a branching 1D arterial blood flow network. We limit our investigation to a single bifurcating vessel, where the material properties, unloaded areas and variables characterizing the input and output boundary conditions are included as free parameters. The synthetic time data used for the optimization problem, as well as the blood flow analysis is performed using a 1D finite volume vascular network model. We pose and investigate four different problem formulations based on synthetic data which could hypothetically be measured experimentally. We will demonstrate the invertibality of the problem based on synthetic time data at a single location within the bifurcation as well as demonstrate the influance of the number of data points included within these time signals. Lastly, we will show how the addition of increasing levels of noise to the synthetic data influences the ability of obtaining the correct system parameters. For purposes of the inverse optimization we make use of a bounded BFGS algorithm where the gradients are approximated using the complex step method.