Consequences of Using an Orthotropic Stress Tensor for Left Ventricular Systole

Tobias Gerach1, Steffen Schuler2, Ekaterina Kovacheva3, Olaf Doessel4, Axel Loewe1
1Karlsruhe Institute of Technology (KIT), 2Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 3KIT, IBT, 4Institute of Biomedical Engineering, Karlsruhe Institute of Technology


A variety of biophysical and phenomenological active tension models has been proposed during the last decade that show physiological behaviour on a cellular level. However, applying these models in a whole heart finite element simulation framework yields either unphysiological values of stress and strain or an insufficient deformation pattern compared to magnetic resonance imaging data.

In this study, we evaluate how introducing an orthotropic stress tensor affects the deformation pattern by conducting a sensitivity analysis regarding the active tension at resting length Tref and three orthotropic activation parameters (Kss, Ksn and Knn). Deformation of left ventricular contraction is evaluated on a truncated ellipsoid using four features: wall thickening (WT), longitudinal shortening (LS), torsion (Theta) and ejection fraction (EF).

We show that EF, WT and LS are positively correlated with the parameters Tref and Kss while Knn reduces all of the four observed features. Introducing shear stress to the model has little to no effect on EF, WT and LS, although it reduces torsion by up to 5 degrees.

We find that added stress in the sheet direction can support healthy deformation patterns. However, the twisting motion, which has been shown to be important for cardiac function, reduces by up to 10 degrees.