Engelbrecht Jüri, Tamm Kert, Peets Tanel
Centre for Nonlinear Studies (CENS), Institute of Cybernetics at Tallinn University of Technology, Akadeemia 21, 12618 , Tallinn, Estonia.
Biomech Model Mechanobiol. 2015 Jan;14(1):159-67. doi: 10.1007/s10237-014-0596-2. Epub 2014 May 22.
The propagation of action potentials in nerve fibres is usually described by models based on the ionic hypotheses. However, this hypothesis does not provide explanation of other experimentally verified phenomena like the swelling of fibres and heat production during the nerve pulse propagation. Heimburg and Jackson (Proc Natl Acad Sci USA 102(28):9790-9795, 2005, Biophys Rev Lett 2:57-78, 2007) have proposed a model describing the swelling of fibres like a mechanical wave related to changes of longitudinal compressibility of the cylindrical membrane. In this paper, the possible dispersive effects in such microstructured cylinders are analysed from the viewpoint of solid mechanics, particularly using the information from the analysis of the well-known rod models. A more general governing equation is proposed which satisfies the conditions imposed by the physics of wave processes. The numerical simulations demonstrate the influence of nonlinearities, the role of various dispersion terms and the formation and propagation of solitary waves along the wall together with the corresponding transverse displacement. It is conjectured that due to the coupling effects between longitudinal and transverse displacements of a cylinder, the transverse displacement (i.e. swelling) is related to the derivative of the longitudinal displacement. In this way, the correspondence between theoretical and experimental (Tasaki in Physiol Chem Phys Med NMR 20:251-268, 1988) results can be described.
神经纤维中动作电位的传播通常由基于离子假说的模型来描述。然而，该假说并未对其他经实验验证的现象作出解释，比如神经脉冲传播过程中纤维的肿胀和产热。海姆堡和杰克逊（《美国国家科学院院刊》102(28):9790 - 9795, 2005；《生物物理评论快报》2:57 - 78, 2007）提出了一个模型，将纤维的肿胀描述为一种与圆柱形膜纵向压缩性变化相关的机械波。在本文中，从固体力学的角度分析了这种微结构圆柱体中可能存在的色散效应，特别是利用了对著名杆模型分析所得到的信息。提出了一个更通用的控制方程，该方程满足波动过程物理学所施加的条件。数值模拟展示了非线性的影响、各种色散项的作用以及孤立波沿壁面的形成和传播，以及相应的横向位移。据推测，由于圆柱体纵向和横向位移之间的耦合效应，横向位移（即肿胀）与纵向位移的导数有关。通过这种方式，可以描述理论结果与实验结果（田崎，《生理化学物理与医学核磁共振》20:251 - 268, 1988）之间的对应关系。
