Galinsky Vitaly L, Frank Lawrence R
Center for Scientific Computation in Imaging, University of California at San Diego, La Jolla, CA 92037-0854, USA.
Center for Functional MRI, University of California at San Diego, La Jolla, CA 92037-0677, USA.
Front Phys (Beijing). 2023 Aug;18(4). doi: 10.1007/s11467-023-1273-7. Epub 2023 Mar 22.
Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics [ 2, 023061 (2020); 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.
从一般非线性波动哈密顿形式推导出来的脑电波谱标度的解析表达式，与实验“神经元雪崩”数据显示出极佳的一致性。弱衰减非线性脑波动力学理论[2, 023061 (2020); 32, 2178 (2020)]揭示了隐藏在神经元雪崩现象学统计描述背后的潜在集体过程，并将整个脑活动状态范围联系在一起，从振荡波状模式到神经元雪崩，再到非相干尖峰，表明神经元雪崩只是皮质组织中丰富的波动过程不同非线性方面的表现。从更广泛的角度来看，这些结果表明，一个由一般波动哈密顿量描述的通过三阶非线性项的所有可能组合相互作用的波动模式系统，必然会产生具有遵循无标度幂律的时间和空间标度特性的非谐波波动模式。据我们所知，这在物理文献中从未有过报道，并且可能适用于许多涉及波动过程的物理系统，而不仅仅是神经元雪崩。
