Khadka Niranjan, Wang Boshuo, Bikson Marom
Department of Biomedical Engineering, The City College of New York, CUNY, New York, NY.
Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC.
bioRxiv. 2024 Nov 25:2024.11.22.624883. doi: 10.1101/2024.11.22.624883.
Models of spinal cord stimulation (SCS) simulate the electric fields (E-fields) generated in targeted tissues, which in turn can predict physiological and then behavioral outcomes. Notwithstanding increasing sophistication and use in optimizing therapy, SCS models typically calculate E-fields using the quasi-static approximation (QSA). QSA, as implemented in neuromodulation models, neglects the frequency dispersion of tissue conductivity, as well as propagation, capacitive, and inductive effects on the E-field. The reliability of QSA specifically for SCS has not been considered in detail, especially for higher-frequency SCS.
We implemented a frequency-dependent finite element method (FEM) and solved a high-resolution RADO-SCS model with voltage-controlled (VC) and current-controlled (CC) stimulation to assess the impact of frequency-dependent conductivity (dispersion) and permittivity of spinal tissues on E-fields generated at three different spinal column locations (epidural space, spinal cord, and root) for frequencies spanning from 1 Hz to 10 MHz. Results were compared with predictions of QSA method, with varied conductivity values of purely resistive tissues. We further assessed the impact of frequency-dependent and capacitive tissue properties on spinal heating and distortion of the E-field waveform.
Tissue-specific electric properties around the energized leads and mode of stimulation-control impacted the magnitude of E-fields. In the spinal cord, the VC-SCS E-field generated with the frequency-dependent and capacitive properties was comparable to the QSA with 2X epidural fat conductivity, whereas the CC-SCS generated E-field was minimally impacted by frequency-dependent and capacitive properties up to 10 kHz. Spinal cord heating predicted by frequency-dependent and capacitive tissue properties was comparable to the QSA conditions with VC-SCS, whereas with CC-SCS, there was no impact of the frequency-dependent and capacitive tissue properties in spinal cord heating. E-field waveform distortion in the spinal cord, with CC-SCS at 1 kHz-specific electrical properties, was significant when fat capacitance (permittivity) was increased by 10X, whereas with VC-SCS, there was no effect of tissue capacitance.
Regardless of the mode of SCS, QSA was still valid in predicting SCS-induced E-field and heating at the spinal tissues- across and dispersion region of spinal tissue's dielectric spectrum for VC-SCS and up to 10 kHz for CC-SCS.
脊髓刺激（SCS）模型模拟目标组织中产生的电场（E场），进而可以预测生理以及行为结果。尽管SCS模型在优化治疗方面越来越复杂且应用广泛，但通常使用准静态近似（QSA）来计算E场。神经调节模型中实施的QSA忽略了组织电导率的频率色散，以及对E场的传播、电容和电感效应。尚未详细考虑QSA对SCS的可靠性，特别是对于高频SCS。
我们实施了频率相关的有限元方法（FEM），并求解了具有电压控制（VC）和电流控制（CC）刺激的高分辨率RADO-SCS模型，以评估脊髓组织的频率相关电导率（色散）和介电常数对在三个不同脊柱位置（硬膜外间隙、脊髓和神经根）产生的E场的影响，频率范围为1Hz至10MHz。将结果与QSA方法的预测进行比较，采用纯电阻性组织的不同电导率值。我们进一步评估了频率相关和电容性组织特性对脊髓加热和E场波形失真的影响。
通电导线周围的组织特异性电学特性和刺激控制模式影响了E场的大小。在脊髓中，具有频率相关和电容性特性产生的VC-SCS E场与具有2倍硬膜外脂肪电导率的QSA相当，而CC-SCS产生的E场在高达10kHz时受频率相关和电容性特性的影响最小。频率相关和电容性组织特性预测的脊髓加热与VC-SCS的QSA条件相当，而对于CC-SCS，频率相关和电容性组织特性对脊髓加热没有影响。当脂肪电容（介电常数）增加10倍时，在1kHz特定电学特性下CC-SCS导致的脊髓E场波形失真很显著，而对于VC-SCS，组织电容没有影响。
无论SCS模式如何，对于VC-SCS，在整个脊髓组织介电谱的频率范围和色散区域，以及对于CC-SCS高达10kHz的情况下，QSA在预测SCS诱导的脊髓组织E场和加热方面仍然有效。
