Gizzi A, Loppini A, Ruiz-Baier R, Ippolito A, Camassa A, La Camera A, Emmi E, Di Perna L, Garofalo V, Cherubini C, Filippi S
Department of Engineering, University Campus Bio-Medico of Rome, Unit of Nonlinear Physics and Mathematical Modeling, Via A. del Portillo 21, 00128 Rome, Italy.
Mathematical Institute, University of Oxford, Woodstock Road, OX2 6GG Oxford, United Kingdom.
Chaos. 2017 Sep;27(9):093919. doi: 10.1063/1.4999610.
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q and Moore factors are used to describe thermo-electric feedback in a 10° range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra, and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis.
这项工作报告了在考虑热电耦合和扩散非线性的广义双变量心脏动作电位模型中，对非线性动力学和螺旋波破裂进行理论研究的结果。按照可激发介质中的惯例，常用的Q因子和摩尔因子用于描述10°范围内的热电反馈。受心脏组织多孔性质的启发，在本研究中，我们还提出了一种非线性菲克通量，它是通过将电压依赖性扩散系数泰勒展开至二次项来制定的。在匹配等效电缆模型的传导速度之前，先对扩散参数进行微调。然后，通过在一维电缆上数值模拟不同的刺激方案，研究由此产生的综合效应。从动作电位形态、恢复曲线、频谱和时空相位差等方面对模型特征进行比较。最后进行二维长期模拟，以表征在不同热状态下持续颤动期间的螺旋破裂。发现温度和非线性扩散效应会以非单调模式影响动作电位波的复极化阶段，并增加心律失常的倾向。
