Kootsey J M, Johnson E A, Lieberman M
Biophys J. 1977 Feb;17(2):145-54. doi: 10.1016/S0006-3495(77)85632-4.
The passive electrical properties of a cable can be measured by injecting a step of current at a point and fitting the resulting potentials at several positions along the cable with analytic solutions of the cable equation. An error analysis is presented for this method (which is based on constant membrane resistance) when the membrane resistance is not constant, but increases linearly with time. The increase of rm produces a "creep" in the membrane potential at long times, as observed in cardiac, skeletal, and smooth muscle. The partial differential equation describing the time-varying cable was solved numberically for a step of current and these "data" were fit by standard constant-resistance methods. Comparing the resulting parameter values with the known true values, we suggest that a correction of the standard methods is not satisfactory for resistance changes of the kind observed; instead, the cable equation must be solved again for the particular form of rm(t). The practical implementation of a method by Adrian and Peachey for measuring the membrane capacitance and an approximate method for estimating the rate-of-change of membrane resistance are discussed in appendices.
电缆的被动电学特性可通过在某一点注入一个电流阶跃，并将沿电缆几个位置处产生的电位与电缆方程的解析解进行拟合来测量。当膜电阻不是常数而是随时间线性增加时，针对这种方法（基于恒定膜电阻）给出了误差分析。如在心肌、骨骼肌和平滑肌中所观察到的，rm的增加在长时间会导致膜电位出现“蠕变”。对于电流阶跃，通过数值方法求解描述时变电缆的偏微分方程，并用标准的恒定电阻方法对这些“数据”进行拟合。将所得参数值与已知真实值进行比较，我们认为对于所观察到的那种电阻变化，标准方法的校正并不令人满意；相反，对于rm(t)的特定形式，必须再次求解电缆方程。附录中讨论了Adrian和Peachey测量膜电容的方法的实际应用以及估计膜电阻变化率的一种近似方法。
