Sahin Mesut, Ur-Rahman Syed S
New Jersey Institute of Technology, Newark, NJ 07102, USA.
IEEE Trans Neural Syst Rehabil Eng. 2007 Jun;15(2):227-34. doi: 10.1109/TNSRE.2007.897027.
Analytical solutions for voltage fields in a volume conductor are available only for ideal electrodes with radially symmetric contacts and infinitely extending substrates. Practical electrodes for neural stimulation may have asymmetric contacts and finite substrate dimensions and hence deviate from the ideal geometries. For instance, it needs to be determined if the analytical solutions are adequate for simulations of narrow shank electrodes where the substrate width is comparable to the size of the contacts. As an extension to this problem, a "floating" stimulator can be envisioned where the substrate would be finite in all directions. The question then becomes how small this floating stimulator can be made before its stimulation strength is compromised by the decrease in the medium impedance between the contacts as the contacts are approaching each other. We used finite element modeling to solve the voltage and current profiles generated by these radially asymmetric electrode geometries in a volume conductor. The simulation results suggest that both the substrate size and the bipolar contact separation influence the voltage field when these parameters are as small as a few times the contact size. Both of these effects are larger for increasing elevations from the contact surface, and even stronger for floating electrodes (finite substrate in all directions) than the shank-type electrodes. Location of the contacts on the floating electrode also plays a role in determining the voltage field. The voltage field for any device size and current, and any specific resistance of the volume conductor can be predicted from these results so long as the aspect ratios are preserved.
仅对于具有径向对称接触和无限延伸基底的理想电极，才存在体积导体中电压场的解析解。用于神经刺激的实际电极可能具有不对称接触和有限的基底尺寸，因此偏离了理想几何形状。例如，需要确定解析解是否适用于模拟窄柄电极，其中基底宽度与接触尺寸相当。作为这个问题的扩展，可以设想一种“浮动”刺激器，其基底在所有方向上都是有限的。那么问题就变成了，在这种浮动刺激器的接触彼此靠近时，由于接触之间介质阻抗的降低而导致其刺激强度受到影响之前，它能做得多小。我们使用有限元建模来求解这些径向不对称电极几何形状在体积导体中产生的电压和电流分布。模拟结果表明，当这些参数小至接触尺寸的几倍时，基底尺寸和双极接触间距都会影响电压场。对于从接触表面起增加的高度，这两种效应都更大，并且对于浮动电极（在所有方向上基底有限）比柄型电极更强。接触在浮动电极上的位置在确定电压场时也起作用。只要纵横比保持不变，就可以根据这些结果预测任何器件尺寸、电流以及体积导体的任何特定电阻下的电压场。
