Mechanical and Aerospace Engineering, University of Texas at Arlington (UTA), Arlington, TX, 76019, USA.
Department of Neural and Behavioral Sciences, College of Medicine, Penn State University (PSU), Hershey, PA, USA.
J Comput Neurosci. 2020 Aug;48(3):253-263. doi: 10.1007/s10827-020-00750-9.
Focal axon swelling refers to localized swelling in axons that may occur because of trauma (e.g., traumatic brain injury) or neurodegenerative diseases (e.g., Alzheimer's disease). Since the swelling region can be many times larger than its original axon size, many researchers hypothesize that the swelling can alter the action potential (AP) signal. This article discusses the results of a series of newly developed computational studies to elucidate the possible intervention or blockage of AP signals due to swelling in the brain. We argue that the spherical geometry of the swelling site with its enlarged conducting interior causes the entering electric currents to spread evenly over the entire swelled membrane. As such, when the swelled surface becomes larger than the threshold size, the electric current will spread too thin to trigger the AP to spike. In this study, we have used a hybrid membrane model to simulate AP propagation across axons of different radii and swelling radii. We used an integrated model where a cylindrical symmetric 2D model is used to examine the electric current inside a spherical swelling site. In addition, two 1D models are used to capture the current flows along the upstream and downstream stretch before and after the swelling site. The parameters for this model are obtained from literature dedicated to modeling the experimental outcomes of mammal neurons. We observed two factors, which simultaneously affect AP transmission across a swelled axon: a) the axon radius and b) the ratio of the swelled and unswelled axon radii. In general, a thicker axon needs a smaller swelling size and axon ratio to block AP transmission. On the other hand, a thinner axon will reach the threshold at a larger swelling size and axon ratio. When only swelling size is considered, then thinner axons will block AP transmission at a smaller swelling radius. The AP transmission delay inside the swelled region determines whether the AP transmits forward or not. Notably, the blockage is worse if the AP fires at a high frequency. An increase in the charging and reset time due to swelling appears to be the main reason for the variation in axonal response.
轴突局限性肿胀是指轴突发生局部肿胀，这种肿胀可能由创伤（例如，脑外伤）或神经退行性疾病（例如，阿尔茨海默病）引起。由于肿胀区域可能比原始轴突大很多倍，许多研究人员假设肿胀会改变动作电位（AP）信号。本文讨论了一系列新开发的计算研究的结果，这些研究旨在阐明由于大脑肿胀而对 AP 信号进行干预或阻断的可能性。我们认为，肿胀部位的球形几何形状及其扩大的内部传导使进入的电流均匀地扩散到整个肿胀的膜上。因此，当肿胀表面大于阈值尺寸时，电流将扩散得太细而无法触发 AP 产生尖峰。在这项研究中，我们使用混合膜模型来模拟不同半径和肿胀半径的轴突中的 AP 传播。我们使用了一种集成模型，其中使用圆柱形对称 2D 模型来检查球形肿胀部位内部的电流。此外，使用两个 1D 模型来捕获肿胀部位前后沿上游和下游延伸的电流流动。该模型的参数是从专门用于模拟哺乳动物神经元实验结果的文献中获得的。我们观察到两个因素同时影响肿胀轴突中的 AP 传输：a）轴突半径和 b）肿胀和未肿胀轴突半径的比值。一般来说，较厚的轴突需要较小的肿胀尺寸和轴突比值才能阻断 AP 传输。另一方面，较薄的轴突将在较大的肿胀尺寸和轴突比值下达到阈值。仅考虑肿胀尺寸时，较细的轴突将在较小的肿胀半径处阻断 AP 传输。肿胀区域内的 AP 传输延迟决定了 AP 是否向前传输。值得注意的是，如果 AP 以高频发射，阻塞会更严重。肿胀导致的充电和重置时间的增加似乎是轴突响应变化的主要原因。
