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 active 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 (Θ) and ejection fraction (EF). We show that EF, WT and LS are positively correlated with the parameters Tref and Knn while Kss 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 3◦. We find that added stress in the normal direction can support healthy deformation patterns. However, the twisting motion, which has been shown to be important for cardiac function, reduces by up to 20◦.
In silico studies are often used to analyze mechanisms of cardiac arrhythmias. The electrophysiological cell models that are used to simulate the membrane potential in these studies range from highly detailed physiological models to simplistic phenomenological models. To effectively cover the middle ground between those cell models, we utilize the manifold boundary approxi- mation method (MBAM) to systematically reduce the widely used O’Hara-Rudy ventricular cell model (ORd) and investigate the influence of parametrization of the model as well as different strategies of choosing input quantities, further called quantities of interest (QoI). As a result of the reduction process, we present three re- duced model variants of the ORd model that only contain a fraction of the original model’s ionic currents resulting in a twofold speedup in computation times compared to the original model. We find that the reduced models show similar action potential duration restitution and repolarization rates. Additionally, we are able to initialize and observe stable spiral wave dynamics on a 3D tissue patch for 2 out of the 3 reduced models.
Individualized computer models of the geometry of the human heart are often based on mag- netic resonance images (MRI) or computed tomography (CT) scans. The stress distribution in the imaged state cannot be measured but needs to be estimated from the segmented geometry, e.g. by an iterative algorithm. As the convergence of this algorithm depends on different geometrical conditions, we system- atically studied their influence. Beside various shape alterations, we investigated the chamber volume, as well as the effect of material parameters. We found a marked influence of passive material parameters: increasing the model stiffness by a factor of ten halved the residual norm in the first iteration. Flat and concave areas led to a reduced robustness and convergence rate of the unloading algorithm. With this study, the geometric effects and modeling aspects governing the unloading algorithm’s convergence are identified and can be used as a basis for further improvement.
Over the last decades, computational models have been applied in in-silico simulations of the heart biomechan- ics. These models depend on input parameters. In particular, four parameters are needed for the constitutive law of Guc- cione et al., a model describing the stress-strain relation of the heart tissue. In the literature, we could find a wide range of values for these parameters. In this work, we propose an optimization framework which identifies the parameters of a constitutive law. This framework is based on experimental measurements conducted by Klotz et al.. They provide an end-diastolic pressure-volume relation- ship. We applied the proposed framework on one heart model and identified the following elastic parameters to optimally match the Klotz curve: 𝐶 = 313 Pa, 𝑏𝑓 = 17.8, 𝑏𝑡 = 7.1 and 𝑏𝑓𝑡 = 12.4. In general, this approach allows to identify optimized param- eters for a constitutive law, for a patient-specific heart geome- try. The use of optimized parameters will lead to physiological simulation results of the heart biomechanics and is therefore an important step towards applying computational models in clinical practice.