Data-Driven Modeling of Pressure Differentials over Vascular Junctions*

Cardiovascular flow simulations provide valuable insight for surgical planning, but the high computational cost of traditional finite element modeling limits their use in clinical settings. Reduced-order models make simplifying assumptions that decrease computational cost, but also reduce their accuracy. We consider a zero-dimensional (0D) model in which a vasculature is modeled as an electric circuit, and pressure and flow are modeled as voltage and current respectively. The 0D model usually assumes constant pressure (static or dynamic) over vascular junctions, but this does not capture the complex, geometry-dependent flow effects in a junction, and is often a significant source of error. We propose a data-driven approach to predict the pressure drop over a vascular junction so that it can be accounted for in a 0D model. In particular, we represent the junction dynamics in the context of the electric circuit using a linear resistor, quadratic resistor, and inductor. The resistance/inductance of these elements is determined using data-fitting techniques trained on data from three-dimensional finite element simulations of flows in a cohort of synthetic junction geometries. We study the accuracy of our formulation using different regression techniques and compare it against the Unified0D+ model previously proposed by Mynard et al.