Role of frequency-dependent and capacitive tissue properties in spinal cord stimulation models

Objective.Spinal cord stimulation (SCS) models simulate the electric fields (E-fields) generated in targeted tissues, which in turn govern physiological and then behavioral outcomes. Notwithstanding increasing sophistication and adoption in therapy optimization, SCS models typically calculateE-fields using quasi-static approximation (QSA). QSA, as implemented in neuromodulation models, neglects the frequency-dependent tissue conductivity (dispersion), as well as propagation, capacitive, and inductive effects on theE-field. The objective of this study is to calculate the impact of frequency-dependent tissue conductivity and permittivity in SCS models, across a broad frequency range.Approach.We solved a high-resolution RADO-SCS finite element model to simulateE-field magnitudes in spinal column tissues under voltage-controlled (VC) and current-controlled (CC) SCS. Varied combinations of epidural space and dura conductivity based on prior SCS modeling studies (under the QSA-method), as well as values from the Gabriel (1996Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies) dataset for 1 Hz, 1 kHz, 2.5 kHz, 16.66 kHz, and 1 MHz were considered. We assessed the relative contribution of epidural space and dura permittivity on peakE-field magnitude and neural activation, and compared results to the QSA-method models.Main results.Across published SCS models, the conductivities of epidural space (considered either fat or mixed tissues; 0.025-0.25 S m^-1) and dura (0.02-0.6 S m^-1) vary by over an order of magnitude, associated with differences in predicted spinal cord peakE-field magnitudes for VC-SCS (6.55-43.71 V m^-1per V) and CC-SCS (10.94-25.20 V m^-1per mA). These literature variations in conductivity and resulting peakE-field magnitude are greater than from epidural/dura tissue dispersion (1 kHz-1 MHz) based on Gabriel (1996Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies) database (VC-SCS: 7.26-8.09 V m^-1per V; CC-SCS: 21.14-21.25 V m^-1per mA). Changes inE-field magnitudes were not associated with significant changes in relative spatial profiles of theE-field or activating function. The impact of epidural space/dural permittivity (at 1 kHz) onE-field magnitudes and activating function was minimal (⩽1%) for both SCS modes.Significance.The impact of dispersion/permittivity is significantly less than existing variations in tissue conductivities used across SCS modeling studies. As relativeE-field or activating function profiles were not significantly changed by tissue conductivities, any impact of neuronal activation thresholds tracks changes inE-field magnitude. We limited our analysis to a single geometry and epidural/dural properties to isolate the impact of QSA.