T. Fritz, E. Kovacheva, G. Seemann, O. Dössel, and A. Loewe. The inverse problem of cardiac mechanics - estimation of cardiac active stress from endocardial motion tracking. In Computational & Mathematical Biomedical Engineering Proceedings, vol. 1, pp. 91-95, 2019
The heart acts as the pump of the cardiovascular system due to the active stress developed in individ- ual cardiac muscle cells. The spatio-temporal distribution of this active stress could contain relevant diagnostic information but can currently not be measured in vivo. We introduce a method to esti- mate dynamic cardiac active stress fields from endocardial surface motion tracking derived from e.g. magnetic resonance imaging data. This ill-posed non-linear problem is solved using Tikhonov regu- larization in space and time in conjunction with a continuum mechanics forward model. We present a proof-of-concept using data from a biophysically detailed multiscale model of cardiac electrome- chanics (7649 tetrahedral elements) in which we could accurately reproduce cardiac motion (surface error <0.4 mm) and identify non-contracting regions due to myocardial infarction scars (active stress error <10 kPa). This inverse method could eventually be used to non-invasively derive personalized diagnostic information in terms of dynamic active stress fields which are not accessible today.