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

Khadka N, Wang B, Bikson M. Role of frequency-dependent and capacitive tissue properties in spinal cord stimulation models. J Neural Eng. 2025 May 27;22(3). doi: 10.1088/1741-2552/add76e. PDF

Abstract

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 calculate E-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 the E-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 simulate E-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 (1996 Compilation 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 peak E-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 peak E-field magnitudes for VC-SCS (6.55–43.71 V m−1 per V) and CC-SCS (10.94–25.20 V m−1 per mA). These literature variations in conductivity and resulting peak E-field magnitude are greater than from epidural/dura tissue dispersion (1 kHz–1 MHz) based on Gabriel (1996 Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies) database (VC-SCS: 7.26–8.09 V m−1 per V; CC-SCS: 21.14–21.25 V m−1 per mA). Changes in E-field magnitudes were not associated with significant changes in relative spatial profiles of the E-field or activating function. The impact of epidural space/dural permittivity (at 1 kHz) on E-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 relative E-field or activating function profiles were not significantly changed by tissue conductivities, any impact of neuronal activation thresholds tracks changes in E-field magnitude. We limited our analysis to a single geometry and epidural/dural properties to isolate the impact of QSA.