Abstract:

As direct activators of the contractile apparatus of cardiac myocytes, calcium ions have a strong impact on the tension development of the heart. Therefore, the standard procedure for modelling the electromechanical coupling is based on the transfer of the calcium transient from the cell model to the force model. As a consequence, the coupling of various models can lead to significantly different trajectories of active tension due to diverging implementations of calcium dynamics. As this phenomenon is not to be expected in a healthy human heart, the aim of this thesis was to generate standardized tension development in coupled force- and cell models for atria and ventricles. The ventricular cell models according to O’Hara et al. [1], Tomek et al. [2] and Ten Tusscher and Panfilov [3] as well as the atrial models following Courtemanche et al. [4], Koivumäki et al. [5] and Maleckar et al. [6] were considered. The calcium sensitivity of the parameters of the force models according to Land et al. [7, 8] were evaluated by means of a sensitivity analysis and categorized by their influence on the active tension. Based on the findings obtained, a parameter optimization of the Land models was developed. The results obtained showed that standardized tension developments could only be achieved when coupling selected models. For the cell model according to Courtemanche et al. and all considered cell models of the ventricle the optimization using constant stretches in the interval λ = [0.85, 1.2] gave convincing results with an error ≤ 50 %. The error refers to the average relative error of each considered characteristic of the active tension. With the use of time-variable stretches, the optimization did not yield satisfactory results so far, because only Courtemanche et al. was found to be robust to changes in stretch with an error of 40.4 %. It could also be concluded that calcium transients with unusual behavior hamper the parameter optimization. The limitations of the optimization were confirmed by tissue simulations. With the simu- lations an alternative method for the re-parameterization of the force models was also investigated. However, the considered scaling of the parameter Tref showed a second contrac- tion in the atrium and a maximum force of ≈ 320 kPa in the ventricle. Thus, the optimization based on single cells was still the better method for generating physiologically justified tension development. Furthermore, the implementations of the cell models according to Courtemanche et al. and O’Hara et al. were adapted to take into account the sarcomere length dependent calcium binding to Troponin C (TnC) described in Land et al. To re-determine the calciumsensitive parameters, parameter estimation methods were developed based on the previously designed optimization. It was shown that the simulated intracellular calcium concentration of the rescaled feedback systems, regarding varying sarcomere lengths, partly behave in reverse to experimental findings. This might be explained by the insufficiently detailed implementation of the cell models with respect to the calcium handling.