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.
Fatigue life of components or test specimens often exhibit a significant scatter. Furthermore, size effects have a non-negligible influence on fatigue life of parts with different geometries. We present a new probabilistic model for low-cycle fatigue (LCF) in the context of polycrystalline metal. The model takes size effects and inhomogeneous strain fields into account by means of the Poisson point process (PPP). This approach is based on the assumption of independently occurring LCF cracks and the Coffin-Manson-Basquin (CMB) equation. Within the probabilistic model, we give a new and more physical interpretation of the CMB parameters which are in the original approach no material parameters in a strict sense, as they depend on the specimen geometry. Calibration and validation of the proposed model is performed using results of strain controlled LCF tests of specimens with different surface areas. The test specimens are made of the nickel base superalloy RENE 80.
AimsLeft-ventricular (LV) conduction disturbances are common in heart-failure patients and a left bundle-branch block (LBBB) electrocardiogram (ECG) type is often seen. The precise cause of this pattern is uncertain and is probably variable between patients, ranging from proximal interruption of the left bundle branch to diffuse distal conduction disease in the working myocardium. Using realistic numerical simulation methods and patient-tailored model anatomies, we investigated different hypotheses to explain the observed activation order on the LV endocardium, electrogram morphologies, and ECG features in two patients with heart failure and LBBB ECG.Methods and resultsVentricular electrical activity was simulated using reaction–diffusion models with patient-specific anatomies. From the simulated action potentials, ECGs and cardiac electrograms were computed by solving the bidomain equation. Model parameters such as earliest activation sites, tissue conductivity, and densities of ionic currents were tuned to reproduce the measured signals. Electrocardiogram morphology and activation order could be matched simultaneously. Local electrograms matched well at some sites, but overall the measured waveforms had deeper S-waves than the simulated waveforms.ConclusionTuning a reaction–diffusion model of the human heart to reproduce measured ECGs and electrograms is feasible and may provide insights in individual disease characteristics that cannot be obtained by other means.
The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser levels are examined: reducing the degrees of freedom, reducing the order of the spatial discretization, and reducing the accuracy when solving linear systems arising in implicit temporal integration. Several numerical examples demonstrate the effect of multi-level coarsening on the convergence and cost of SDC integration. In particular, MLSDC can provide significant savings in compute time compared to SDC for a three-dimensional problem
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