Modeling of a Simplified 2D Cardiac Valve by Means of System Identification

Abstract

The function of a heart valve is to maintain the correct circulation of blood from the heart to the entire Cardiovascular System (CVS). The CVS has become a main target in the health science and engineering, due to the importance of the detection anomalies or pathologies. Some techniques that deal with these problems, like Magnetic Resonance Imaging (MRI), Ultrasound and Electrocardiography (ECG) among them, require important investments to acquire measurement instruments. Numerical simulations have arisen as an alternative, by means of Fluid-Structure Interaction (FSI) analysis. The combination of computational methods, such as Finite Element Method (FEM) and Incompressible Computational Fluid Dynamics (ICFD), have allowed the development of FSI software, which leads to design versatility and economic advantages. However, computational time is high even for simplified designs. Lumped models appear as another solution. They consist in simplified zero-dimensional models that allow to mimic the Cardiovascular System (CVS) with low computational cost and good approximations. Nevertheless, they require a parameter identification and the calculation process for each scenario, which becomes increasingly complicated when the number of parameters is high. Therefore, an alternative approach is proposed in the present manuscript. Taking the volumetric flow rate and the Pressure Difference (PD) as the input and output parameters, respectively, of the flow across a heart valve of simple geometry, a System Identification (SI) is performed. The proposed methodology requires low computational cost and provides a good approximation. Results obtained guarantee a 99.76% of goodness of fit.