Huang Xuelin, Wang Jiang, Yi Guosheng
School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072 China.
Cogn Neurodyn. 2024 Jun;18(3):1245-1264. doi: 10.1007/s11571-023-09980-w. Epub 2023 May 20.
Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except ) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.
经颅交流电刺激（tACS）以频率特异性方式广泛应用于脑功能研究和神经精神疾病治疗。然而，tACS如何作用于神经元活动仍知之甚少。在本文中，我们使用线性系统分析来研究弱交变电场（EFs）在频域中如何影响神经元的膜极化。我们开发了两个基于生物物理现实电导的皮质锥体神经元双室模型，以模拟弱交变EFs作用下的阈下膜极化。我们在稳定平衡点处对原始非线性模型进行线性化，并进一步将其简化为二维或三维线性系统。因此，我们计算低维线性模型的传递函数以模拟神经元极化模式。基于传递函数，我们计算幅度和相频特性以描述弱EFs与膜极化之间的关系。我们还计算了传递函数的参数（增益、零点和极点）和结构（零点和极点的数量），以揭示神经元内在特性如何影响传递函数的参数和结构，进而影响交变EFs作用下的频率依赖性膜极化。我们发现膜极化的幅度和相位都强烈依赖于EF频率，并且这些频率响应受到神经元内在特性的调制。隔室几何形状、内部耦合电导和离子电流（除 外）主要通过改变传递函数的增益和极点来影响频率依赖性极化。较大的增益有助于产生较大的幅度频率特性。极点离虚轴越近，相位频率特性越低。然而， 通过引入一对新的零极点改变了树突中传递函数的结构，这降低了低频时的幅度并因此导致明显的共振。这些结果突出了被动特性和主动离子电流在频域中对交变EFs作用下阈下膜极化的影响，这为神经元内在特性如何通过弱EF刺激调节神经元输入输出功能提供了一个可解释的联系。
