Impact of uncertainties in cardiac mechanics simulations

Abstract

Modeling the mechanics of the heart have led to considerable insights, but it still representes a complex and demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as a hyperelastic, near-incompressible and orthotropic material, which are properties very challenging for the numerical solution of the model. In particular, near-incompressibility is known to cause numerical issues. In this work, some improvements were done in a cardiac mechanics simulator in order to be more efficient in the treatment of these numerical issues. With the improved solver for cardiac mechanics, it was possible to run problems with higher computational cost, such as sensitivity and uncertainty quantification analyses. This type of analysis has been a topic of scientific interest to assess the possibility of translating patient-specific simulations to clinical applications. However, personalized simulations are still challenging problems, because of the wide biological variability among patients, the uncertainties in experimental measurements and in the geometric representation of the heart. Due to these uncertainties in model inputs, it is difficult to define a reliable model that can be translated to clinical applications. Recent studies have focused on quantifying uncertainties for cardiac models in order to investigate how they can influence simulation results and, consequently, how we can make the models more reliable. Then, the present work also quantifies how uncertainties in the geometry can impact in quantities of interest from cardiac mechanics. The polynomial chaos approach was used to quantify uncertainties in geometries of the left ventricle during cardiac mechanics simulations. Initially, we performed some studies using simplified geometries during ventricular filling phase simulations and, after, we quantify uncertainties in more realistic geometries during the full cardiac cycle.