Frequency-dependent and capacitive tissue electrical properties in spinal cord stimulation models

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 α and β dispersion region of spinal tissue's dielectric spectrum for VC-SCS and up to 10 kHz for CC-SCS.