Quantification of Dorsal Column Fiber Responses in a Model of Kilohertz-Frequency Spinal Cord Stimulation
Abstract
Introduction Kilohertz-frequency spinal cord stimulation (KHF-SCS) was recently proposed as a paresthesia-free treatment for persons with chronic pain that is potentially more effective than conventional (̃50 Hz) SCS. In SCS, the applied electrical stimulation is intended to activate the dorsal column (DC) axons. However, it is unclear how DC axons respond to kilohertz frequency signals. We developed a model of a DC fi- ber to quantify the responses of DC axons to the KHF-SCS signal. Methods We implemented a double-cable model of a DC fiber using published morphological data and ion channel dynamics. We also recorded the strength-duration relationship and the recovery cycle of single DC axons in anesthetized rats for model validation. We coupled the axon model to a patient-specific volume conductor model of SCS and applied the KHF-SCS signal to quantify thresholds for activation and con- duction block for different fiber diameters at different locations in the DCs. For cases exhibiting persistent activation, we quantified the de- gree of synchronization of the firing activity to the stimulation signal using the vector strength and quantified the similarity between the activities of pairs of fibers using the normalized spike time distance. Results Activation thresholds using the KHF-SCS signal increased sharply as the axons were placed deeper in the DCs. For the most superficial axons (textless 500 $mu$m from the surface of the spinal cord), the activation thresholds for one patient averaged 57.2 ± 10.1 mA, 19.1 ± 6.1 mA and 8.3 ± 3.2 mA for fiber diameters of 2, 6, and 10 $mu$m, respectively. Conduction block thresholds in the same DC region averaged 164.8 ± 20.4 mA, 61.2 ± 10.1 mA, and 34.7 ± 9.0 mA, for fiber diameters of 2, 6, and 10 $mu$m, respectively. The vector strength over the 10–50 mA amplitude range averaged 0.16 ± 0.09 and 0.11 ± 0.08 for 6 and 10 $mu$m diameter fibers, respectively, indicating a low degree of synchro- nization to the KHFSCS signal. For any given signal amplitude, the spike time distance decreased as the axons were placed at closer dis- tances, but it was always greater than 0.5. Conclusion Our model results showed thresholds for activation and block of DC axons well above the amplitudes used clinically (1–5 mA). If the KHF- SCS signal activates large superficial axons, then the axons would fire asynchronously to the stimulation signal and to other axons.
Leo Medina
Principal Investigator
Leo teaches computer engineering courses at Usach, and his research interests are in the neural engineering and computational neuroscience fields. His work has contributed to understand how nerve fibers respond to electrical stimulation.