Ventricular wall deformation is widely assumed to have an impact on the morphology of the T-wave that can be measured on the body surface. This study aims at quantifying these effects based on an in silico approach. To this end, we used a hybrid, static-dynamic approach: action potential propagation and repolarization were simulated on an electrophysiologically detailed but static 3-D heart model while the forward calculation accounted for ventricular deformation and the associated movement of the electrical sources (thus, it was dynamic). The displacement vectors that describe the ventricular motion were extracted from cinematographic and tagged MRI data using an elastic registration procedure. To probe to what extent the T-wave changes depend on the synchrony/asynchrony of mechanical relaxation and electrical repolarization, we created three electrophysiological configurations, each with a unique QT time: a setup with physiological QT time, a setup with pathologically short QT time (SQT), and pathologically long QT time (LQT), respectively. For all three electrophysiological configurations, a reduction of the T-wave amplitude was observed when the dynamic model was used for the forward calculations. The largest amplitude changes and the lowest correlation coefficients between the static and dynamic model were observed for the SQT setup, followed by the physiological QT and LQT setups.
Conference Contributions (8)
O. Jarrousse, T. Fritz, and O. Dössel. Modeling breast tissue mechanics from Prone to supine positions with a modified mass-spring system. In Proceedings BMT 2010, 44. DGBMT Jahrestagung, 3-Länder-Tagung D-A-CH, Rostock, vol. 55(S1) , pp. 87-90, 2010
A volumetric mass-spring system, originally developed for myocardial mechanics modeling , is used to simulate the elasto-mechanical deformation of several breast datasets from prone to supine positions. Segmented MRI datasets of pa- tients in prone position, available from the online repository provided by Susan C. Hagness at the University of Wisconsin- Madison  were used in the biomechanical simulations. These models were considered to be consisting of two materi- als, fat and fibroconnective/glandular tissues. Each tissue is represented as a nearly incompressible Neo-Hookean elastic isotropic material. Each simulation was conducted in two steps: in the first step, the unloaded model is generated by apply- ing gravity forces to the original model pointing toward the body. The unloaded model is then used in the second step, by applying gravity forces. Eventually, the breast model in supine position is obtained.
O. Jarrousse, T. Fritz, and O. Dössel. Implicit time integration in a volumetric mass-spring system for modeling myocardial elastomechanics. In IFMBE Proceedings World Congress on Medical Physics and Biomedical Engineering, vol. 25/4, pp. 876-879, 2009
A modified mass-spring system for simulating the passive and active elastomechanical properties of the myocardial tissue was presented in a previous publication. The previously presented results are combined with the method also published earlier to use continuum mechanics calculate passive forces in a mass-spring system directly starting from the energy density function of the stress-strain relation. An efficient method for volume preservation is presented and the implementation of an implicit time integration method for solving the systems equations of motion is described. The computational complexity of the system is analyzed and shown to be of O(n). At the end several simulations are conducted to demonstrate the method.
O. Jarrousse, T. Fritz, and O. Dössel. A volumetric mass-spring system for modeling myocardial elastomechanics. In The Cardiac Physiome: Multi-scale and Multi-physics Mathematical Modelling Applied to the Heart, 2009
A volumetric mass-spring system for simulating the passive and active elastomechanical properties of the myocardial tissue is presented. A 3D computer model containing information about the ﬁber, sheet, and sheet-normal directions and about the modeled objects physiological properties, is used to initialize the systems structure.Using an electrophysiology model and a force development model, contracting forces are introduced to the systems elements at each time step of the simulation loop.Using the methods of continuum mechanics, suitable springs functions were derived analytically from the energy density function of describing the hyperelastic properties of heart. That eliminated the need of springs parametrization. An efficient method for volume preservation is used to ensure the conservation of the model's volume under deformation.Implicit time integration is implemented to solve the equations of motion, that improves the stability of the simulation and allows larger simulation time steps. An iterative solver that take advantage of the sparsity of the system's matrices is used and the systems complexity is shown to be of O(n) where n is the the count of the models elements.
O. Jarrousse, T. Fritz, and O. Dössel. A modifed mass-spring system for myocardial mechanics modeling. In Proceedings of the 4th European Congress for Medical and Biomedical Engineering 2008. 23-27 November 2008, Antwerp, Belgium, vol. 22, pp. 1943-1946, 2008
T. Fritz, O. Jarrousse, D. Keller, G. Seemann, and O. Dössel. In silico analysis of the impact of transmural myocardial infarction on cardiac mechanical dynamics for the 17 AHA segments. In Proceedings of the 6th International Conference on Functional Imaging and Modeling of the Heart, vol. LNCS, 6666, pp. 241-249, 2011
The impact of transmural infarctions of the left ventricle on the cardiac mechanical dynamics is evaluated for all 17 AHA segments in a computer model. The simulation framework consists of two parts: an electrophysiological model and an elastomechanical model of the ventricles. The electrophysiological model is used to simulate the electrophysiological processes on cellular level, excitation propagation and the tension development. It is linked to the elastomechanical model, which is based on nonlinear finite element analysis for continuum mechanics. Altogether, 18 simulations of the contraction of the ventricles were performed, 17 with an infarction in the respective AHA segment and one simulation for the control case. For each simulation, the mechanical dynamics as well as the wall thickening of the infarct region were analyzed and compared to the corresponding region of the control case. The simulation revealed details of the impact of the myocardial infarction on wall thickening as well as on the velocity of the infarct region for most of the AHA segments
T. Fritz, O. Jarrousse, G. Seemann, and O. Dössel. Analyzing the transmural electromechanical heterogeneity of the left ventricle in a computer model. In Biomedizinische Technik / Biomedical Engineering (Proceedings BMT2010), vol. 55(Suppl 1) , 2010
There is a large number of published studies analyzing the inhomogeneously distributed electrophysiological properties of the ventricles in a computer model. However only few of them deal with the impact on the hearts mechanics. In 2003 Cordeiro and colleagues  analyzed the influence of the transmural left ventricular electrophysiological heterogeneity on the myocardial mechanics. Therefore, they examined the unloaded cell shortening of sub-epicardial cells, sub-endocardial cells, and cells from the middle of the wall, isolated from canine left ventricle.In this work a heterogenous electromechanical model was used to reconstruct these experiments of Cordeiro et al. in the computer. A simulation framework, which is consisting of an electrophysiological cell model, a tension development model and an elastomechanical model was used to simulate the cell shortening. Two experiments with different heterogeneities had been conducted. The first experiment examined, how the heterogeneity of the membrane channels influences the cell shortening. In the second experiment the additional impact of the heterogeneity of the intracellular calcium handling was analyzed. The results of the simulations were compared qualitatively to the findings of Cordeiro et al.
T. Fritz, O. Jarrousse, and O. Dössel. Adapting a mass-spring system to energy density function describing myocardial mechanics. In Proceedings of the 4th European Congress for Medical and Biomedical Engineering 2008. 23-27 November 2008, Antwerp, Belgium, vol. 22, pp. 2003-2006, 2008
O. Jarrousse. Modified mass-spring system for physically based deformation modeling. KIT Scientific Publishing. Dissertation. 2012
Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented.