The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using the squid giant axon. However, the experimental determination of conductances of neurons is difficult, in particular under the presence of spatial and temporal heterogeneities, and it is also reasonable to expect variations between species or even between different types of neurons of the same species.We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution in the simpler setting of a passive cable equation, both in a single or branched neurons. To do so, we consider the minimal error iteration, a computational technique used to solve inverse problems. We provide several numerical results showing that the method is able to provide reasonable approximations for the conductances, given enough information on the voltages, even for noisy data.

中文翻译：

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神经元电导测定逆问题的计算方法。

艾伦霍奇金和安德鲁赫胥黎对他们著名的神经元电导模型的推导依赖于使用鱿鱼巨轴突收集的实验数据。然而，神经元电导的实验确定是困难的，特别是在存在空间和时间异质性的情况下，预计物种之间甚至同一物种的不同类型神经元之间的差异也是合理的。 我们解决了逆问题在给定电压数据的情况下，在单个或分支神经元中的无源电缆方程的更简单设置中确定具有非均匀分布的电导。为此，我们考虑了最小误差迭代，这是一种用于解决逆问题的计算技术。