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In this work, the authors use computer modeling to theoretically investigate the mechanisms involved in figure-of-eight reentry during acute regional myocardial ischemia, a pattern of excitation which may lead to ventricular fibrillation and sudden cardiac death. For this purpose, a modified version of the Luo–Rudy dynamic model for the action potential and ionic currents has been used, together with a two-dimensional model of the regionally ischemic ventricle. The virtual tissue comprises several realistically dimensioned and located transitional border zones for hyperkalemia, hypoxia and acidosis, simulating the substrate heterogeneity created by acute ischemia. Different types of patterns of excitation following the delivery of a premature stimulus were obtained, including figure-of-eight reentry. Action potentials and selected ionic currents which explain the reentry process are analyzed. The effect of the degree of ATP-sensitive current activation in the vulnerability to reentry is also studied. The results are in accordance with experimental observations, and demonstrate the ability of second-generation mathematical models to analyze and explain the mechanisms involved in ischemic reentry.

Computational electrophysiology is a very active field with tremendous potential in medical applications, albeit it leads to highly intensive simulations. We here propose a surface-based electrophysiology formulation, motivated by the modeling of thin structures such as cardiac atria, which greatly reduces the size of the computational models. Moreover, our model is specifically devised to retain the key features associated with the anisotropy in the diffusion effects induced by the fiber architecture, with rapid variations across the thickness that cannot be adequately represented by naive averaging strategies. Our proposed model relies on a detailed asymptotic analysis in which we identify a limit model and establish strong convergence results. We also provide detailed numerical assessments that confirm an excellent accuracy of the surface-based model – compared with the reference 3D model – including in the representation of a complex phenomenon, namely, spiral waves.

A two-dimensional modified Luo-Rudy model was created to represent a 40 mm by 40 mm slab of myocardial tissue. An inhomogeneity was introduced to simulate acute myocardial ischemia, with components of hyperkalemia, acidosis and anoxia. Simulations were carried out for various degrees of ischemia, to study both the interaction of the propagation front with the inhomogeneity, and the reconstructed signals. The simulations utilized a modified LR model, with a realistic anisotropy of myocardial tissue. Each cluster (.4 mm ×.4 mm) was given bulk electric properties, R_x and R_y (25Ω and 250Ω, respectively). The slab was stimulated and the 2D depolarization pattern was computed by numerical integration. To study ischemia, a circular inhomogeneity with concentric regions (r_o=12.8 mm{border zone, BZ}, r_i=11.2 mm{extreme zone, EZ}) regions was introduced in the model. From the 2D simulations and the regional action potentials (AP), unipolar and bipolar lead potentials were reconstructed. Time-frequency decomposition was performed on the lead signals by wavelet analysis. Isochrone and (dV/dt)_max maps were obtained to study depolarization. Our results indicate that spatial inhomogeneities yield dramatic spatial dispersion of the wavefront and are the origin of mid-frequency intra-QRS components in cardiac signals. Severe APD shortening and spatial distortion of the isochrone and upstroke maps are also observed.

Mathematical modeling of cardiovascular system provides an ability to study hemodynamics and to predict the results of treatment based on individual anatomical and physiological data of patients. However, the presently developed models of cardiovascular system have a limitation on use in clinical practice due to their physical and computational complexities. The aim of this study is to derive a lumped parameter model of cardiovascular system with pulsating heart in which all parameters have a physically based quantitative value and can be identified using clinical methods. For development of a cardiovascular system model the chamber analog was used which describes whole cardiovascular system as a set of elastic chambers. The proposed model consists of systemic and pulmonary circulation, four-chamber heart and four valves. The description of heart is based on a four-element representation of a cardiac muscle. The reverse blood flow via valves is considered. The accuracy of the derived model was evaluated by comparing the data of numerical simulation with experimental data. The limitations of the model were discussed as well as possible applications of the model were suggested. The proposed lumped parameter model can be used to support clinicians in their decisions in treating cardiovascular disorders.