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As an initial step to investigate stimulus-response relations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D-inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process. However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnover on growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.

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.

matical models of cardiac mechanics can potentially be used to relate abnormal cardiac deformation, as measured noninvasively by ultrasound strain rate imaging or magnetic resonance tagging (MRT), to the underlying pathology. However, with current models, the correct prediction of wall shear strain has proven to be difficult, even for the normal healthy heart. Discrepancies between simulated and measured strains have been attributed to 1) inadequate modeling of passive tissue behavior, 2) neglecting active stress development perpendicular to the myofiber direction, or 3) neglecting crossover of myofibers in between subendocardial and subepicardial layers. In this study, we used a finite-element model of left ventricular (LV) mechanics to investigate the sensitivity of midwall circumferential-radial shear strain (Ecr) to settings of parameters determining passive shear stiffness, cross-fiber active stress development, and transmural crossover of myofibers. Simulated time courses of midwall LV Ecr were compared with time courses obtained in three healthy volunteers using MRT. Ecr as measured in the volunteers during the cardiac cycle was characterized by an amplitude of ϳ0.1. In the simulations, a realistic amplitude of the Ecr signal could be obtained by tuning either of the three model components mentioned above. However, a realistic time course of Ecr, with virtually no change of Ecr during isovolumic contraction and a correct base-to-apex gradient of Ecr during ejection, could only be obtained by including transmural crossover of myofibers. Thus, accounting for this crossover seems to be essential for a realistic model of LV wall mechanics. magnetic resonance tagging; finite-element model; cardiac mechanics; myofiber angle DEFORMATION OF THE CARDIAC WALL can be assessed noninvasively using ultrasound strain rate imaging (11) or magnetic resonance tagging (MRT) (4). The deformation patterns acquired may deviate from normal in the case of cardiac pathology, e.g., aortic stenosis, ischemia, or conduction disorders (39,40,43). The analysis of abnormal deformation patterns toward the underlying pathology is not straightforward: the relation between the change in the deformation pattern and the pathology is complex, and the criteria for normal and abnormal strain patterns have not yet been defined. A mathematical model capable of predicting the forward relation between pathology and deformation could, if used in an inverse analysis, be a useful clinical tool, not only in diagnosis but also in intervention selection and planning, by simulating candidate interventions beforehand.Several models describing the deformation of cardiac walls have been proposed (5,6,14,19,20,28,35,41,42,45), but none of these models have already been used as a diagnostic tool. As a first step toward this application, one would require the models to be able to correctly predict deformation in the wall of the healthy heart. Most models are able to correctly predict circumferential, longitudinal, and radial strain (5,14,28,41,42,45). However, ...

A computational method of reduced complexity is developed for simulating vascular hemodynamics by combination of one-dimensional (1D) wave propagation models for the blood vessels with zero-dimensional (0D) lumped models for the microcirculation. Despite the reduced dimension, current algorithms used to solve the model equations and simulate pressure and flow are rather complex, thereby limiting acceptance in the medical field. This complexity mainly arises from the methods used to combine the 1D and the 0D model equations. In this paper a numerical method is presented that no longer requires additional coupling methods and enables random combinations of 1D and 0D models using pressure as only state variable. The method is applied to a vascular tree consisting of 60 major arteries in the body and the head. Simulated results are realistic. The numerical method is stable and shows good convergence.