Donders Institute for Brain, Cognition and Behaviour, Centre for Neuroscience, Radboud University Nijmegen, Nijmegen, The Netherlands.
PLoS Comput Biol. 2010 Jan 29;6(1):e1000653. doi: 10.1371/journal.pcbi.1000653.
By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.
通过对大神经元群体的平均活动进行建模，连续均值场模型（MFMs）已成为理解皮质组织涌现活动的一种越来越重要的理论工具。为了便于计算，MFMs 中的长程活动传播通常用偏微分方程（PDEs）来近似。然而，目前使用的 PDE 近似对应于与实验测量不一致的潜在轴突速度分布。为了纠正这一缺陷，我们在这里引入了新的传播 PDE，这些 PDE 产生了平滑的单峰轴突传导速度分布。我们还认为，分别从切片中的纤维直径和潜伏期测量中估计的速度与这种分布的关系非常不同，这对任何现象学描述都是一个重要的观点。然后，我们将这些 PDE 成功地拟合到来自人类胼胝体和大鼠皮质下白质的纤维直径数据。这使得首次能够使用现实、方便的 PDE 模拟哺乳动物大脑中的长程传导。此外，所得结果表明，大鼠和人类的活动传播除了简单的缩放之外，差异非常显著。我们新公式的动力学后果在一个著名的神经场模型的背景下进行了研究。基于图灵不稳定性分析，我们得出结论，使用我们更现实的传播器更容易引发模式形成。通过增加特征传导速度，可以从自维持的体振荡平滑过渡到各种波长的行波，这可能会影响发育过程中的轴突生长。我们的解析结果也使用大空间网格上的模拟得到了数值验证。因此，我们在这里提供了 MFMs 中受经验约束的活动传播的综合分析，这将允许未来对哺乳动物大脑活动进行更现实的研究。
