In this paper, we investigate the electric discharge of electrocytes by extending our previous work on the generation of electric potential. We first give a complete formulation of a single cell unit consisting of an electrocyte and a resistor, based on a Poisson-Nernst-Planck (PNP) system with various membrane currents as interfacial conditions for the electrocyte and a Maxwell's model for the resistor. Our previous work can be treated as a special case with an infinite resistor (or open circuit). Using asymptotic analysis, we simplify our PNP system and reduce it to an ordinary differential equation (ODE) based model. Unlike the case of an infinite resistor, our numerical simulations of the new model reveal several distinct features. A finite current is generated, which leads to non-constant electric potentials in the bulk of intracellular and extracellular regions. Furthermore, the current induces an additional action potential (AP) at the non-innervated membrane, contrary to the case of an open circuit where an AP is generated only at the innervated membrane. The voltage drop inside the electrocyte is caused by an internal resistance due to mobile ions. We show that our single cell model can be used as the basis for a system with stacked electrocytes and the total current during the discharge of an electric eel can be estimated by using our model.

中文翻译：

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电池的放电：建模，分析和模拟。

在本文中，我们通过扩展我们先前在电势产生方面的工作来研究细胞的放电。首先，我们基于Poisson-Nernst-Planck（PNP）系统，给出了由电解质和电阻组成的单电池单元的完整配方，该系统具有各种膜电流作为电解质的界面条件，并采用了麦克斯韦模型作为电阻。我们以前的工作可以看作是带有无限电阻（或开路）的特殊情况。使用渐近分析，我们简化了PNP系统，并将其简化为基于常微分方程（ODE）的模型。与无限电阻的情况不同，我们对新模型的数值模拟揭示了几个明显的特征。产生有限的电流 这会在大部分细胞内和细胞外区域产生非恒定电位。此外，与其中仅在神经支配的膜上产生AP的开路的情况相反，电流在非神经支配的膜上引起附加的动作电位（AP）。电解质内部的电压降是由于移动离子引起的内阻引起的。我们表明，我们的单细胞模型可以用作带有堆叠式电池的系统的基础，并且可以通过使用我们的模型来估计电鳗放电期间的总电流。电解质内部的电压降是由于移动离子引起的内阻引起的。我们表明，我们的单细胞模型可以用作带有堆叠式电池的系统的基础，并且可以通过使用我们的模型来估计电鳗放电期间的总电流。电解质内部的电压降是由于移动离子引起的内阻引起的。我们表明，我们的单细胞模型可以用作带有堆叠式电池的系统的基础，并且可以通过使用我们的模型来估计电鳗放电期间的总电流。