Bédard Claude, Kröger Helmut, Destexhe Alain
Département de Physique, Université Laval, Québec, Québec G1K 7P4, Canada.
Biophys J. 2004 Mar;86(3):1829-42. doi: 10.1016/S0006-3495(04)74250-2.
Extracellular local field potentials are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of extracellular local field potentials, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is nonhomogeneous, there is induction of nonhomogeneous charge densities that may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na(+)-mediated action potentials) attenuate very steeply with distance, whereas slower (K(+)-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.
细胞外局部场电位通常被建模为由嵌入均匀细胞外介质中的一组电流源产生。尽管这种形式主义能够成功地模拟细胞外局部场电位的若干特性，但它并未考虑其随距离的频率依赖性衰减，而这一特性对于正确模拟细胞外尖峰至关重要。在此，我们推导了包含这种频率依赖性衰减的细胞外电位表达式。我们首先表明，如果细胞外电导率是非均匀的，就会诱导出非均匀电荷密度，这可能导致一个低通滤波器。接下来，我们推导了一个简化模型，该模型由一个点（或球形）电流源以及围绕该源的具有球对称电导率/电容率梯度的区域组成。我们分析了电导率和电容率的不同径向分布对该模型频率滤波行为的影响。我们表明，这个简单模型通常呈现低通滤波行为，其中快速电事件（如钠介导的动作电位）随距离急剧衰减，而较慢的（钾介导的）事件在细胞外空间中传播更远的距离，这与实验观察结果在定性上是一致的。这个简单模型可用于获得频率依赖性细胞外场电位，而无需明确考虑细胞外空间的复杂折叠情况。
