Surrogate models provide new insights on metrics based on blood flow for the assessment of left ventricular function

Recent developments on the grading of cardiac pathologies suggest flow-related metrics for a deeper evaluation of cardiac function. Blood flow evaluation employs space-time resolved cardiovascular imaging tools, possibly integrated with direct numerical simulation (DNS) of intraventricular fluid dynamics in individual patients. If a patient-specific analysis is a promising method to reproduce flow details or to assist virtual therapeutic solutions, it becomes impracticable in nearly-real-time during a routine clinical activity. At the same time, the need to determine the existence of relationships between advanced flow-related quantities of interest (QoIs) and the diagnostic metrics used in the standard clinical practice requires the adoption of techniques able to generalize evidences emerging from a finite number of single cases. In this study, we focus on the left ventricular function and use a class of reduced-order models, relying on the Polynomial Chaos Expansion (PCE) technique to learn the dynamics of selected QoIs based on a set of synthetic cases analyzed with a high-fidelity model (DNS). The selected QoIs describe the left ventricle blood transit and the kinetic energy and vorticity at the peak of diastolic filling. The PCE-based surrogate models provide straightforward approximations of these QoIs in the space of widely used diagnostic metrics embedding relevant information on left ventricle geometry and function. These surrogates are directly employable in the clinical analysis as we demonstrate by assessing their robustness against independent patient-specific cases ranging from healthy to diseased conditions. The surrogate models are used to perform global sensitivity analysis at a negligible computational cost and provide insights on the impact of each diagnostic metric on the QoIs. Results also suggest how common flow transit parameters are principally dictated by ejection fraction.