IEEE Trans Biomed Eng. 2024 Jan;71(1):307-317. doi: 10.1109/TBME.2023.3299734. Epub 2023 Dec 25.
Biophysical models of neural stimulation are a valuable approach to explaining the mechanisms of neuronal recruitment via applied extracellular electric fields. Typically, the applied electric field is estimated via a macroscopic finite element method solution and then applied to cable models as an extracellular voltage source. However, the field resolution is limited by the finite element size (typically 10's-100's of times greater than average neuronal cross-section). As a result, induced charges deposited onto anatomically realistic curved membrane interfaces are not taken into consideration. However, these details may alter estimates of the applied electric field and predictions of neural tissue activation.
To estimate microscopic variations of the electric field, data for intra-axonal space segmented from 3D scanning electron microscopy of the mouse brain genu of corpus callosum were used. The boundary element fast multipole method was applied to accurately compute the extracellular solution. Neuronal recruitment was then estimated via an activating function.
Taking the physical structure of the arbor into account generally predicts higher values of the activating function. The relative integral 2-norm difference is 90% on average when the entire axonal arbor is present. A large fraction of this difference might be due to the axonal body itself. When an isolated physical axon is considered with all other axons removed, the relative integral 2-norm difference between the single-axon solution and the complete solution is 25% on average.
Our result may provide an explanation as to why Deep Brain Stimulation experiments typically predict lower activation thresholds than commonly used FEM/Cable model approaches to predicting neuronal responses to extracellular electrical stimulation.
These results may change methods for bi-domain neural modeling and neural excitation.
神经刺激的生物物理模型是一种通过施加细胞外电场来解释神经元募集机制的有价值的方法。通常，通过宏观有限元方法求解来估计施加的电场，然后将其作为细胞外电压源应用于电缆模型。然而，场的分辨率受到有限元尺寸的限制（通常比平均神经元横截面积大 10 到 100 倍）。因此，没有考虑到沉积在解剖上逼真的弯曲膜界面上的感应电荷。然而，这些细节可能会改变施加电场的估计和神经组织激活的预测。
为了估计电场的微观变化，使用了从 3D 扫描电子显微镜对小鼠大脑胼胝体脑回的轴内空间进行分段的数据。边界元快速多极方法被应用于精确计算细胞外溶液。然后通过激活函数来估计神经元的募集。
考虑到树突的物理结构，通常会预测激活函数的更高值。当整个轴突树突存在时，相对积分 2-范数的差异平均为 90%。这种差异的很大一部分可能是由于轴突体本身造成的。当考虑到去除所有其他轴突的单个物理轴突时，单轴突解与完整解之间的相对积分 2-范数差异平均为 25%。
我们的结果可能解释了为什么深部脑刺激实验通常预测比常用的 FEM/Cable 模型方法更低的激活阈值，来预测细胞外电刺激对神经元的反应。
这些结果可能会改变双域神经建模和神经兴奋的方法。
