Lopour Beth A, Szeri Andrew J
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA.
J Comput Neurosci. 2010 Jun;28(3):375-87. doi: 10.1007/s10827-010-0215-x. Epub 2010 Feb 5.
Here we present several refinements to a model of feedback control for the suppression of epileptic seizures. We utilize a stochastic partial differential equation (SPDE) model of the human cortex. First, we verify the strong convergence of numerical solutions to this model, paying special attention to the sharp spatial changes that occur at electrode edges. This allows us to choose appropriate step sizes for our simulations; because the spatial step size must be small relative to the size of an electrode in order to resolve its electrical behavior, we are able to include a more detailed electrode profile in the simulation. Then, based on evidence that the mean soma potential is not the variable most closely related to the measurement of a cortical surface electrode, we develop a new model for this. The model is based on the currents flowing in the cortex and is used for a simulation of feedback control. The simulation utilizes a new control algorithm incorporating the total integral of the applied electrical potential. Not only does this succeed in suppressing the seizure-like oscillations, but it guarantees that the applied signal will be charge-balanced and therefore unlikely to cause cortical damage.
在此，我们展示了对用于抑制癫痫发作的反馈控制模型的若干改进。我们使用了人类皮层的随机偏微分方程（SPDE）模型。首先，我们验证了该模型数值解的强收敛性，特别关注电极边缘处发生的急剧空间变化。这使我们能够为模拟选择合适的步长；由于空间步长必须相对于电极尺寸较小，以便解析其电行为，所以我们能够在模拟中纳入更详细的电极轮廓。然后，基于平均胞体电位并非与皮质表面电极测量最密切相关的变量这一证据，我们为此开发了一个新模型。该模型基于皮质中流动的电流，并用于反馈控制模拟。模拟采用了一种结合所施加电势总积分的新控制算法。这不仅成功抑制了癫痫样振荡，而且保证了所施加的信号将是电荷平衡的，因此不太可能导致皮质损伤。
