Toward Quantification and Visualization of Active Stress Waves for Myocardial Biomechanical Function Assessment

Estimating and visualizing myocardial active stress wave patterns is crucial to understanding the mechanical activity of the heart and provides a potential non-invasive method to assess myocardial function. These patterns can be reconstructed by analyzing 2D and/or 3D tissue displacement data acquired using medical imaging. Here we describe an application that utilizes a 3D finite element formulation to reconstruct active stress from displacement data. As a proof of concept, a simple cubic mesh was used to represent a myocardial tissue "sample" consisting of a 10 x 10 x 10 lattice of nodes featuring different fiber directions that rotate with depth, mimicking cardiac transverse isotropy. In the forward model, tissue deformation was generated using a test wave with active stresses that mimic the myocardial contractile forces. The generated deformation field was used as input to an inverse model designed to reconstruct the original active stress distribution. We numerically simulated malfunctioning tissue regions (experiencing limited contractility and hence active stress) within the healthy tissue. We also assessed model sensitivity by adding noise to the deformation field generated using the forward model. The difference image between the original and reconstructed active stress distribution suggests that the model accurately estimates active stress from tissue deformation data with a high signal-to-noise ratio.