An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of nonevanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full-brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the commonly agreed paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation because of the cortex wave modes in the highly folded areas will exhibit no apparent correlation with the fiber directions. Nonlinear coupling of those linear weakly evanescent wave modes then provides a universal mechanism for the emergence of synchronized brain wave field activity. The resonant and nonresonant terms of nonlinear coupling between multiple modes produce both synchronous spiking-like high-frequency wave activity as well as low-frequency wave rhythms. Numerical simulation of forced multiple-mode dynamics shows that, as forcing increases, there is a transition from damped to oscillatory regime that can then transition quickly to a nonoscillatory state when a critical excitation threshold is reached. The resonant nonlinear coupling results in the emergence of low-frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these weakly evanescent cortical wave modes have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and magnetoencephalography, and for the understanding of brain activity in general, including mechanisms of memory.

提出了大脑皮层的非均匀各向异性物理模型，该模型预测了在与平均神经纤维方向和皮层空间梯度横向的薄皮层层中传播的非消逝（弱阻尼）波状模式的出现。尽管这些模式的幅度低于通常观察到的轴突尖峰电位，但这些模式的寿命可能显着超过尖峰电位逆衰减常数。基于从扩散和结构 MRI 中提取的参数的全脑数值模拟证实了这些波模式的存在和延长的持续时间。与普遍认同的范式相反，即神经纤维决定了大脑中信号传播的途径，由于高度折叠区域中的皮层波模式，信号传播与纤维方向没有明显的相关性。这些线性弱渐逝波模式的非线性耦合然后为同步脑波场活动的出现提供了通用机制。多模之间非线性耦合的共振和非共振项产生同步尖峰状高频波活动以及低频波节律。强制多模动力学的数值模拟表明，随着强迫的增加，存在从阻尼到振荡状态的转变，然后在达到临界激发阈值时可以快速转变为非振荡状态。谐振非线性耦合导致低频节律的出现，其频率比参与耦合的模式的线性频率低几个数量级。这些弱渐逝皮层波模式的定位和持久性具有重要意义，特别是对于检测电磁生理活动的神经成像方法，如 EEG 和脑磁图，以及对大脑活动的一般理解，包括记忆机制。