Axonal velocity distributions in neural field equations.
Axonal velocity distributions in neural field equations.
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DOI：
10.1371/journal.pcbi.1000653
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发表时间：
2010-01-29
影响因子：
4.3
通讯作者：
Liley DT
中科院分区：
文献类型：
--
作者：
Bojak I;Liley DT
通过对大型神经元种群的平均活性进行建模，持续的平均场模型（MFM）已成为理解皮质组织的新兴活动的越来越重要的理论工具。但是，具有部分微分方程（PDE）。为了纠正这种缺陷，我们在这里引入了新型的繁殖PDE，这会导致轴突传导速度的平滑单峰分布。这样的分布，对于任何现象学描述的重要一点。人类的call体和大鼠皮层白质。在众所周知的神经场上，研究了我们新公式的动态后果。模式形成更容易使用我们的更逼真的传播器来增加特征传导速度，从而平稳地从自我维持的散装振荡到各种波长的行进波，这可能会影响我们的分析结果。在大型空间网格上使用模拟。 MFM的背景，这将允许对哺乳动物大脑活动的更现实研究。
由于神经元的数量及其相互作用的复杂性，大脑活动的建模特别具有挑战性。 ，是为了建模神经元的平均活性，而不是单个神经元的行为。方法是，他们尤其是遥远种群之间的相互作用的生物保真度。通过具有广泛速度的轴突纤维连接。平均田间理论中的连通性，并证明了如何使用它们的新型繁殖器来拟合人类和大鼠的成功实验数据，因此可以在经验基础上研究活动在健康和脱离的哺乳动物大脑中的作用。
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. Due to the sheer number of neurons and the complexity of their interactions, the modelling of brain activity is particularly challenging. How can computationally tractable models of brain function be developed that are nevertheless biologically plausible? The “mean field” approach, borrowed from statistical physics, is to model the average activity of populations of neurons rather than the behaviour of individual neurons. While a large number of promising theories have been developed with this approach, they fall short of biological fidelity in the way interactions between distant populations have been modelled. In particular, it is often assumed that all neurons interact via connections of very similar conduction velocity, when in fact experiment suggests quite the opposite: populations of neurons are connected by axonal fibres with a broad range of velocities. We develop here activity propagators that provide for the first time the ability to realistically and efficiently simulate connectivity in mean field theories, and demonstrate how to use them to fit successfully experimental data from both human and rat. With our novel propagators, one can thus study on an empirical basis the role of activity propagation in both healthy and diseased mammalian brains.
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影响因子：
2.4
作者：
Bojak, I;Liley, DTJ
通讯作者：
Liley, DTJ
影响因子：
7.8
作者：
Hutt, Axel;Atay, Fatihcan M.
通讯作者：
Atay, Fatihcan M.
影响因子：
2.5
作者：
LAMANTIA, AS;RAKIC, P
通讯作者：
RAKIC, P
影响因子：
2.4
作者：
Hutt, A;Atay, FM
通讯作者：
Atay, FM
DOI：
10.1098/rstb.2005.1625
发表时间：
2005-04-29
影响因子：
6.3
作者：
Kötter, R;Wanke, E
通讯作者：
Wanke, E