Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.

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Over the last decades, computational models have been applied in in-silico simulations of the heart biomechanics. These models depend on input parameters. In particular, four parameters are needed for the constitutive law of Guccione 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 relationship. 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=7.1and bft=12A. In general, this approach allows to identify optimized parameters for a constitutive law, for a patient-specific heart geometry. 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.

The human heart is an organ of high complexity and hence, very challenging to simulate. To calculate the force developed by the human heart and therefore the tension of the muscle fibers, accurate models are necessary. The force generated by the cardiac muscle has physiologically imposed limits and depends on various characteristics such as the length, strain and the contraction velocity of the cardiomyocytes. Another characteristic is the activation time of each cardiomyocyte, which is a wave and not a static value for all cardiomyocytes. To simulate a physiologically correct excitation, the functionality of the cardiac simulation framework CardioMechanics was extended to incorporate inhomogeneous activation times. The functionality was then used to evaluate the effects of local activation times with two different tension models. The active stress generated by the cardiomyocytes was calculated by (i) an explicit function and (ii) an ode-based model. The results of the simulations showed that the maximum pressure in the left ventricle dropped by 2.3% for the DoubleHill model and by 5.3% for the Lumens model. In the right ventricle the simulations showed similar results. The maximum pressure in both the left and the right atrium increased using both models. Given that the simulation of the inhomogeneously activated cardiomyocytes increases the simulation time when used with the more precise Lumens model, the small drop in maximum pressure seems to be negligible in favor of a simpler simulation model

The contraction of the heart is a complex process involving the interaction of the passive properties of the tissue and the active tension development, which is elicited by the electrical activation of the cells. In this study, the electro-mechanical delay (EMD) was investigated as well as its dependence on the length of the sarcomeres, which are the contractile units within the cell. EMD was defined as the time offset between the electrical activation of the cell and the time of maximal tension. On a simple bar geometry with unidirectional fibre orientation and a linear local activation time distribution, the EMD proved to be inhomogeneous. The contraction of the early activated regions caused an elongation of the sarcomere (stretch) in the neighbouring regions, which ware electrically activated at a later time. The tension in the stretched region reached twice the value of the cells in the not-stretched, early activated region. Furthermore, the EMD in the early electrically activated region was more than 0.2 s, which was about twice the EMD of the stretched regions. In conclusion, the stretched region developed higher tension within a shorter time interval compared to the early activated region. Future studies will investigate how the inhomogeneous EMD affects cardiac output.